# Channel Attention Networks for Robust MR Fingerprinting Matching

Refik Soyak, Ebru Navruz, Eda Ozgu Ersoy, Gastao Cruz, Claudia Prieto, Andrew
P. King, Devrim Unay, Ilkay Oksuz Copyright (c) 2020 IEEE. Personal use of
this material is permitted. However, permission to use this material for any
other purposes must be obtained from the IEEE by sending a request to pubs-
<EMAIL_ADDRESS>This work was funded by the Scientific and Technological
Research Council of Turkey (TUBITAK) grant number 118C353. This work was
supported by an EPSRC programme Grant (EP/P001009/1) and the Wellcome EPSRC
Centre for Medical Engineering at the School of Biomedical Engineering and
Imaging Sciences, King’s College London (WT 203148/Z/16/Z). The GPU used in
this research was generously donated by the NVIDIA Corporation. Correspondence
to I. Oksuz.R.Soyak, E.Navruz and E.O.Ersoy are with Electrical and
Electronics Engineering Department, Izmir University of Economics, Izmir,
Turkey.D.Unay is with Faculty of Engineering, Izmir Democracy University,
Izmir, Turkey.I. Oksuz, Gastao Cruz, Claudia Prieto and Andrew P. King are
with School of Biomedical Engineering and Imaging Sciences, King’s College
London, London, UK.I. Oksuz is with Computer Engineering Department, Istanbul
Technical University, Istanbul, Turkey. E-mail<EMAIL_ADDRESS>
###### Abstract

Magnetic Resonance Fingerprinting (MRF) enables simultaneous mapping of
multiple tissue parameters such as T1 and T2 relaxation times. The working
principle of MRF relies on varying acquisition parameters pseudo-randomly, so
that each tissue generates its unique signal evolution during scanning. Even
though MRF provides faster scanning, it has disadvantages such as erroneous
and slow generation of the corresponding parametric maps, which needs to be
improved. Moreover, there is a need for explainable architectures for
understanding the guiding signals to generate accurate parametric maps. In
this paper, we addressed both of these shortcomings by proposing a novel
neural network architecture consisting of a channel-wise attention module and
a fully convolutional network. The proposed approach, evaluated over 3
simulated MRF signals, reduces error in the reconstruction of tissue
parameters by 8.88% for T1 and 75.44% for T2 with respect to state-of-the-art
methods. Another contribution of this study is a new channel selection method:
attention-based channel selection. Furthermore, the effect of patch size and
temporal frames of MRF signal on channel reduction are analyzed by employing a
channel-wise attention.

###### Keywords:

Channel Attention, Deep Learning, MR Fingerprinting, Reconstruction

##  I Introduction

Magnetic Resonance Imaging (MRI) is an essential technique to visualize organs
and structures inside the body with applications in basic and clinical
sciences. However, although MRI is an adaptable and powerful tool for imaging,
it is limited to qualitative imaging that hinders its use in objective
evaluation. To overcome this limitation problem, Ma et al. [1] introduced
Magnetic Resonance Fingerprinting (MRF) as a quantitative MRI solution in
2013.

The key benefit of MRF is that it provides the opportunity to acquire and
quantify different tissue parameters such as the longitudinal relaxation time
(T1) and the transverse relaxation time (T2) within a single acquisition, and
thus eliminating the need for multiple acquisitions. In MRF, acquisition
parameters are varied pseudo-randomly so that each tissue generates a unique
signal evolution or fingerprint. Mapping generation is conventionally carried
out by applying a dictionary (template) matching algorithm where the acquired
signal is matched with the dictionary signal. However, this technique has some
shortcomings that need to be addressed such as the computational time required
for the dictionary matching algorithm. In dictionary matching algorithm, each
acquired signal needs to be compared with the simulated signals resulting in
high computational complexity. As the number of combinations in the dictionary
increases, reconstruction becomes more expensive with regard to time and
storage [2]. In addition and perhaps more importantly, MRF needs to make a
trade-off between accuracy and scanning time, and therefore relies on high
under-sampling in k-space. As consequence, dictionary matching may lead to
erroneous quantification in the generated maps [3].

##  II Related Works

In this section we provide an overview of the previous studies on dictionary
matching in MRF, and the neural network techniques that aim to accelerate this
process.

###  II-A Dictionary Matching

In the original proposal of MRF [1], a dictionary matching algorithm is used
to reconstruct the corresponding tissue parameters. Pattern recognition was
employed to map the T1 and T2 tissue parameters by matching the fingerprints
with a pre-defined dictionary of predicted signal evolutions. Later, different
dictionary matching algorithms were proposed to obtain faster and more
accurate results. McGivney et al.[4] compressed the dictionary by using
singular value decomposition (SVD), enabling faster computation due to the
smaller dictionary size. Gomez et al.[5] analyzed the spatiotemporal
dictionary and compared it with the temporal MRF dictionary. Besides, some
studies suggested to use iterative techniques. For instance, Cline et al.[6]
proposed a technique called AIR MRF that combines dictionary compression and
regularization for accelerated matching. Additionally, Zhao et al.[7] proposed
a statistical approach that uses maximum likelihood estimation to predict T1
and T2 tissue parameters accurately.

Figure 1: Channel Attention Module Architecture [8] where weighted input data
is produced with attention scores. $P_{max}^{c}$ denotes max-pooled features,
$P_{avg}^{c}$ denotes average-pooled features and $M^{c}$ denotes weighted
input data.

###  II-B Neural Network based Techniques

Successful applications of neural networks for computer vision motivated
medical imaging community to use them for accelerating image reconstruction
and mapping. Architectures such as Fully Connected Neural Networks (FCN),
Convolutional Neural Networks (CNN), and Long Short-Term Memory (LSTM) have
been recently investigated for these tasks. Cohen et al. [9] proposed a
4-layer fully connected neural network model with two hidden layers by using
magnitude images as input. Golbabaee et al. [10] presented a fully connected
model with 4 layers that performs dimension reduction with Principal Component
Analysis (PCA) at its first layer. Oksuz et al. [11] used Recurrent Neural
Network (RNN) to extract temporal information for the prediction of T1 and T2
values relying on the time series nature of the MRF fingerprint. Likewise,
Hoppe et al. [12] compared CNN and RNN architectures with magnitude and
complex-valued inputs, and suggested to use the RNN model with complex-valued
MRF signal without using spatial information.

Balsiger et al. [13] analyzed both spatial and temporal information to
reconstruct tissue parameters using a CNN architecture. Cao et al. [14]
applied a multi-layer perceptron with 4 hidden layers and optimized it to
prevent over-fitting. To further increase the speed of training and testing,
architectures with pre-processing and pre-training for feature extraction and
dimension reduction have been proposed. Since the high dimensionality of the
MRF signal requires more computational power to process and creates more
redundancy, one of the main focuses of the literature is to reduce signal
dimensionality. Thus, a dense network based feature extraction (prior to
U-Net) is proposed by Fang et al. [15] to extract important information while
reducing the number of channels. PCA followed by a Fully Connected
Convolutional architecture is used by Chen et al. [16]. In order to learn the
non-linear relationship between the spatiotemporal MRF image data and multiple
quantitative maps, Pirkl et al. [17] proposed to use a CNN architecture
combined with relaxation and diffusion-sensitized MRF sequence.

In this study, we propose a channel attention-based CNN architecture to weight
important channels before feeding into the CNN architecture. As our proposed
method is attention-based, it uses all channels in a weighted fashion instead
of reducing the channels, and therefore eliminates loss of temporal
information due to the channel reduction. Furthermore, the use of the channel
attention mechanism as proposed allows us in order to examine the relative
importance of the channels.

Accordingly, there are two major contributions of this work:

  * •

To the authors’ knowledge, this is the first paper that provides a thorough
analysis of attention based methods for magnetic resonance fingerprinting.

  * •

A wide analysis of attention-based channel selections for understanding the
significance of each signal in parametric map analysis synthetic.

##  III Method

In this section, we will provide the details of our proposed architecture to
estimate the MRF parameters.

To empower MRF reconstruction capability, we employed channel-wise attention.
Through channel attention, time points are weighted based on attention scores
so that the model can understand which time points of the MRF signal are more
informative to generate the parametric maps. Channel-wise attention works by
aggregating the spatial information of the feature map by using pooling layers
to extract inter-channel relationships [8]. Our suggested channel attention
module consists of two pooling layers in parallel, shared dense layers, and a
sigmoid activation function. Assume, $P_{max}^{c}$ and $P_{avg}^{c}$ denote
max-pooled and avg-pooled features per channel $C$, respectively. These two
pooled layers are fed into shared dense layers as shown in Figure 1, so that
input ($I$) becomes $\mathbb{R}^{1\times 1\times C}$. In the first dense
layer, channel size is reduced to $\mathbb{R}^{1\times
1\times\nicefrac{{C}}{{ratio}}}$. The ratio, empirically fixed at 4, is a
hyper-parameter that controls the reduction. In the next dense layer, filter
size is up-scaled to the original size $\mathbb{R}^{1\times 1\times C}$. The
outputs of the shared dense layers are summed up and fed into a sigmoid
activation function. After the channel attention scores - also known as
attention maps - are produced, element-wise multiplication is performed to
weight the input $I$. The formulation of the channel attention is as follows:

$\alpha=\sigma(Dense(P_{max}^{c}(I))+Dense(P_{avg}^{c}(I)))$ (1)

where $\alpha$ denotes attention scores and $\sigma$ refers to the sigmoid
activation function. The dense layers are followed by a Rectified Linear Unit
(ReLu) activation function.

$M^{c}=I\otimes\alpha$ (2)

where $M^{c}$ is the output of attention weighted input $I$. The input
channels are weighted by element-wise multiplication ($\otimes$) of input $I$
and attention scores $\alpha$.

###  III-A Proposed Model: $CONV-ICA$

Figure 2: Our proposed CONV-ICA model. The algorithm operates on extracted
$4\times 4$ patches. Filters of convolution layers that follows the channel
attention module are determined as $32$, $64$, $138$, $64$ and Dense layer
with filter size is $2$ which is the number of tissue parameters is followed
by ReLu activation function.

In order to calculate the T1 and T2 maps we propose to use a Convolutional
network model on Input Channel Attention (CONV-ICA). The current literature
for reconstruction of medical images in MRF relies on reducing the number of
channels right after the input layer by using a dense layer or convolution
layers. However, this reduction causes loss of temporal information. To
overcome this problem, this study suggests that use of a channel attention
module before reducing channel size (also known as filter) as channel
attention helps to extract important temporal information by weighting the
channels and prevents the loss of that information. As illustrated in Fig. 2,
our proposed model consists of a channel attention module and four convolution
layers with filter sizes of 32, 64, 128, and 64, respectively. The output
layer is a dense layer with the filter size of 2 as it predicts tissue
parameters T1 and T2. All layers are followed by the ReLu activation function.
The proposed model predicts overlapped patches as shown in Fig. 2.

###  III-B Channel Analysis & Attention-based Channel Selection

In MRF, the data consists of many time points (or channels), which is 2000 in
this study, where some of them might be redundant and therefore may compromise
predictions and map reconstructions. Accordingly, analysis of these channels
is required to investigate which channels are most informative and important
for map reconstruction and to eliminate the redundant ones. For this purpose,
Balsiger et al. [13] zero-filled the channels one-by-one and compared the
results to understand the importance of the zero-filled channel. However, such
analysis may not be the best way to find the importance of channels as the
zero-filled channel could be learned by the network as informative for
reconstruction. To eliminate this issue, we propose to use an attention
mechanism that will attempt to intrinsically assign attention and score the
features of a given feature map by importance. In order to investigate the
importance of each channel by benefiting from the advantage of the attention
mechanism as explained, we used the channel attention module of Woo et al. [8]
as shown in Fig. 1.

Attention scores are produced after the sigmoid activation function as shown
in Fig. 3, and discussed in Section II-A. When attention scores were obtained
for each patch, scores of all patches are averaged within each individual
channel in order to obtain their distribution over the whole $2000$ channels
independently. For attention-based channel selection, n channels with the
highest attention scores are selected.

Figure 3: Architecture to produce the attention scores for each channel.
Pooling sizes for Max Pooling and Average Pooling are determined as $4\times
4$ which is input patch size. Units of dense layers are determined as $500$ by
dividing our signal length to the reduction ratio which is decided as $4$ and
is up-warded in the next dense layer to input channel length.

The essential channels for tissue parameter estimation could be selected
through the channel analysis proposed here, in contrast to the conventional
approach where PCA is applied as in [16]. We hypothesize that selection of the
most important n channels by analyzing the distribution of attention scores
over all channels (Fig. 4) is a better way for channel reduction and
elimination of redundant channels.

Figure 4: The first plot shows the change of flip angle, where Echo Time (TE)
and Repetition Time(TR) were fixed during acquisition, over the 2000 channels.
The second plot is the distribution of corresponding attention scores over the
2000 channels obtained from Channel Attention Module, which allows to observe
the importance of channels respectively.

##  IV Experimental Results

We provide details of our experimental setup and results of our proposed model
in comparison to state-of-the-art methods in this section. Methods of
comparisons - Balsiger et al. [13], Chen et al. [16], Hoppe et al. [18, 12],
and Fang et al. [15] \- are trained and tested by using 3-fold cross
validation. As all methods are evaluated over 3 subjects, cross-validation is
applied by selecting 1 subject for testing, and the other 2 for training, and
continued that process until each subject is selected for testing. Mean
absolute error in percentage (Eq. 3) is used as an evaluation metric.

The proposed model is fed by patch-wise input with size of $4\times 4$ and
only the magnitude of the signal was used in this study. ADAM [19]
optimization with a learning rate of 15$\times 10^{-4}$ was used while
training by minimizing the mean squared error. Batch size was experimentally
selected as $512$ and the model was trained for $100$ epochs. Early stopping
with patience parameter of 15 was used to prevent over-fitting. The Keras [20]
deep learning library with TensorFlow [21] back-end was used in the Google
Colaboratory environment with $25$ GB RAM of GPU.

Equation 3 below defines the mean absolute error in percentage metric, in
which $N$ represents the total number of pixels, $\hat{P}_{i}$ refers to the
estimated value and $P_{i}$ represents the actual value.

$\text{Error}=\frac{1}{N}\sum\limits_{i=1}^{N}\frac{\left|{P_{i}}-{\hat{P}_{i}}\right|}{max(P_{i})}\times
100$ (3)

###  IV-A Data

The model is trained and tested on a synthetically generated complex-valued
MRF signal. Extended Phase Graph (EPG) [22] is used to generate the MRF
dictionary for a range of T1 = [0: 2: 500] [500: 5: 1000] [1000: 10: 2000]
[2000: 50 : 4000] ms, and T2 = [0: 1: 100] [100: 2: 500] ms. Repetition Time
(TR) is fixed at 4.3ms for utilization of a gradient echo readout.

###  IV-B Model Comparison

Table I shows that proposed approach achieves the best performance for both T1
and T2 parameters as compared to the state-of-the-art models. The results
suggest that, using a channel attention mechanism to produce weighted channels
leads to a decrease in the reconstruction error for our data set as weighted
channels help to avoid losing the important temporal information while
reducing the number of channels. Because of under-sampling in k-space during
MRF acquisition, the dictionary matching algorithm produces erroneous
reconstructions.

Figure 5: Proposed model to state-of-the-art methods compared qualitatively by
testing on a test subject. T1 and T2 errors are the mean absolute differences
as shown in Eq.(3) between reconstructed parameters and true parameters in ms.
Backgrounds of reconstructed images are masked to highlight interested region
and errors in Table I are calculated accordingly. *SVD was used for channel
reduction from 2000 to 5 in pre-processing for Dictionary Matching. TABLE I:
Comparisons of proposed model with a variety of available techniques where
errors are calculated between ground truth images and background-masked
reconstructed images as shown in Figure 5 by using Mean Absolute Error (MAE)
in percentage. *SVD is used for channel reduction from 2000 to 5 in pre-
processing for Dictionary Matching.

Models | T1 - MAE(%) | T2 - MAE(%)
---|---|---
Dictionary Matching | 4 | 1.01
Dictionary Matching* | 4.7 | 1.96
Hoppe et al.[12] (RNN) | 5.61 | 1.79
Chen et al.[16] | 3.38 | 1.3
Hoppe et al.[18] (CNN) | 2.07 | 1.03
Balsiger et al.[13] | 1.82 | 1
Fang et al.[15] | 1.72 | 1.14
Proposed | 1.58 | 0.57

###  IV-C Segmentation Comparison

Table II expresses comparison of the proposed model and state-of-the-art
models for different brain regions, for instance, Skull Stripped, Gray Matter
(GM), White Matter (WM), and Cerebrospinal Fluid (CSF) that are extracted by
automated segmentation. For segmentation, the Statistical Parametric Mapping
(SPM12) [23] is used and errors due to automated segmentation were ignored.
Results demonstrate that the proposed method achieved the best reconstruction
performance for both parametric maps in all the brain sub-regions.

TABLE II: Proposed model and state-of-the-art methods compared quantitatively
for segmented brain tissues, such as Skull Stripped, Gray Matter (GM), White
Matter (WM), and Cerebrospinal Fluid (CSF). Mean Absolute Errors in percentage
3 are calculated between segmentation of ground truth and reconstructed image
for both T1 and T2 tissue parameters.

| SKULL STRIPPED | GM | WM | CSF
---|---|---|---|---
Models | T1 - MAE(%) | T2 - MAE(%) | T1 - MAE(%) | T2 - MAE(%) | T1 - MAE(%) | T2 - MAE(%) | T1 - MAE(%) | T2 - MAE(%)
Dictionary Matching | 2.80 | 0.68 | 0.99 | 0.06 | 0.34 | 0.03 | 2.20 | 0.57
Dictionary Matching* | 2.77 | 1.38 | 0.97 | 0.21 | 0.40 | 0.11 | 2.14 | 1.04
Hoppe et al.[12] (RNN) | 3.89 | 1.51 | 2.03 | 0.34 | 1.17 | 0.18 | 2.96 | 1.16
Chen et al.[16] | 1.57 | 0.94 | 0.62 | 0.18 | 0.33 | 0.08 | 1.19 | 0.75
Hoppe et al.[18] (CNN) | 0.98 | 0.74 | 0.38 | 0.08 | 0.22 | 0.04 | 0.77 | 0.59
Balsiger et al.[13] | 0.83 | 0.73 | 0.40 | 0.21 | 0.21 | 0.15 | 0.66 | 0.54
Fang et al.[15] | 0.76 | 0.84 | 0.35 | 0.38 | 0.19 | 0.23 | 0.59 | 0.62
Proposed | 0.68 | 0.37 | 0.31 | 0.04 | 0.15 | 0.01 | 0.54 | 0.29

Figure 6: Example results for ground truth (true) image, reconstructions of
proposed, Fang et al.[15] and Hoppe et al.[18] architectures. Four blocks show
the reconstruction capabilities for Gray Matter region, White Matter,
Cerebrospinal Fluid (CSF) and Skull Stripped respectively. Both T1 and T2
tissue parameters and error maps are visualized for each architecture.  TABLE
III: Comparison of number of trainable parameters in million, training time in
minutes and prediction time in seconds between the proposed model and various
available techniques as well as the dictionary matching method. All methods
except Hoppe et al. [18], used patch-wise input. Chen et al. [16] used PCA and
reduced channels to 10 components. *SVD is used for channel reduction from
2000 to 5 in pre-processing for Dictionary Matching.

Model | # of Trainable Params (mn) | Training Time (min) | Prediction Time (sec)
---|---|---|---
Dictionary Matching | - | - | 16392
Dictionary Matching* | - | - | 13032
Hoppe et al.[12] (RNN) | 16.17 | 15 | 43.61
Chen et al.[16] | 0.41 | 1.95 | 7.44
Hoppe et al.[18] (CNN) | 0.22 | 4 | 1.45
Balsiger et al.[13] | 9.74 | 61.66 | 145.32
Fang et al.[15] | 1.97 | 58.33 | 18.58
Proposed | 2.74 | 30 | 21.81

The qualitative results presented in Fig. 5 visually demonstrate the
reconstruction performances of the proposed model and the models in comparison
for the T1 and T2 parameters. The rows marked as T1 and T2 (1st and 3rd rows,
respectively), show the reconstructed tissue parameters by the models. T1
error and T2 error images (2nd and 4th rows, respectively) show the
differences between the reconstructed and the true tissue parameters. These
qualitative results further support that the proposed model achieves the best
performance visually for the reconstruction of T1 and T2 tissue parameters.

###  IV-D Effect of Channel Selection

The channels are analyzed to investigate the important channels for
reconstruction and to eliminate redundant ones. Through the determination of
the most important channels, $n$ channels are selected to enhance tissue
parameter reconstruction. We proposed a new channel selection method:
$attention-based~{}selection$. To evaluate the performance of the proposed
channel selection method empirically, we experimented with two more channel
selection schemes, PCA-based and random, and carried out a performance
comparison with our proposed method. Table IV shows MAE errors in percentage
(Equation 3), between the ground truth and reconstructed image for $n$ number
of channels selected by the methods: Attention-based, PCA, and Random.
Following the channel selection, the proposed model CONV-ICA is used for
training. For performance evaluation, 3-fold cross validation is carried out
by using the mean absolute error in percentage as a metric. Quantitative
results presented in Table IV show that attention-based channel reduction
results in a decrease in the reconstruction error while PCA-based and random
selection schemes cause to increase the reconstruction error. The important
advantage of attention-based channel selection is reducing the need of
resources and run time for algorithms.

TABLE IV: Comparison of cross validated mean absolute error (MAE) errors in
percentage for each channel selection method, attention-based selection,
reduction by PCA and random channel selection when $n$ number of channels are
selected for both T1 and T2 values.

Method / $n$ | T1 - MAE(%) | T2 - MAE(%)
---|---|---
Attention / 100 | 2.07 | 0.79
PCA / 100 | 6.22 | 1.48
Random / 100 | 2.26 | 0.84
Attention / 200 | 1.88 | 0.68
PCA / 200 | 4.49 | 1.71
Random / 200 | 2.08 | 0.69
Attention / 300 | 1.93 | 0.77
PCA / 300 | 4.85 | 1.65
Random / 300 | 2.08 | 0.78

Figure 7: Channel selection methods are compared with true tissue parameters,
T1 and T2 respectively, when channel size is reduced from 2000 to 40. The rows
marked as T1 and T2 (1st and 3rd rows, respectively), show the reconstructed
tissue parameters by the models. T1 error and T2 error images (2nd and 4th
rows, respectively) show the differences between the reconstructed and true
tissue parameters.

###  IV-E Effect of Patch Size

In this study, we are utilizing patches to calculate the tissue parameter maps
using our architecture. Patch-wise input helps spatial information to be
learned by the models. In this section, various patch sizes are tested in
order to examine the effect of patch size for reconstruction capability. Table
V shows that the use of 8$\times$8 as the patch size achieves the lowest
reconstruction error values for both T1 and T2 tissue parameters. Patch size
12$\times$12 performs the second-best reconstruction for both T1 and T2 value.
As a result, it is observed that patch size 8$\times$8 is optimal for the
lowest reconstruction error. However, because of insufficient computational
resources, patch size was selected as 4$\times$4 in this study. For
investigation of the effect of patch size, attention-based channel selection
is applied to reduce channel size from 2000 to 40 and patch size is increased
accordingly.

TABLE V: Comparison of various patch sizes and reconstruction mean absolute
errors (Eq.3) in percentage respectively. Because of lack of resources, time
points were decreased to increase patch size. After attention-based channel
selection is performed where channel size is reduced from 2000 to 40, patch
sizes are increased and reconstruction errors are observed.

Patch Size | T1 - MAE (%) | T2 - MAE (%)
---|---|---
4$\times$4 | 2.67 | 1.05
8$\times$8. | 2.46 | 0.99
12$\times$12 | 2.63 | 1.05
16$\times$16 | 2.88 | 1.12
24$\times$24 | 3.02 | 1.19

##  V Discussion

We proposed a new deep learning architecture to address the drawbacks of the
dictionary matching algorithm whilst accelerating and improving reconstruction
of T1 and T2 values. The proposed method takes advantage of the channel
attention mechanism which focuses on important time frames in temporal domain.
Therefore, channel attention mechanism at the beginning of the model helps to
eliminate the loss of temporal information, while fully convolutional network
extracts the spatial information from patch-wise input to reconstruct from MRF
signal more accurately than the previously proposed methods. Qualitative and
quantitative results demonstrate that the use of the channel attention
mechanism at the beginning of the model, where temporal information is mostly
lost due to direct channel reduction (e.g. from 2000 to 32), increases
reconstruction capability by 8.88% for T1 value and 75.44% for T2 value.

In addition to input channel attention, we suggest a new channel selection
method: attention-based selection. As MRF data consists of many channels and
thus requires high computational resources to process, selection of the most
informative channels is needed to decrease the demand of resources such as
RAM. Throughout the experiments, it has been observed that approximately 200
channels are sufficient to significantly reduce the need for resources, while
maintaining the reconstruction capability. Besides, it helps to accelerate
runtime and computational time as data becomes smaller. Additionally and more
importantly, during the acquisition of the MRF signal, the parameters are
continuously varied to get unique signal evaluations, which may create
redundant temporal information [11]. Therefore, channel selection in MRF data
is crucial to keep the most informative and the least redundant temporal
frames. Results shows that attention-based selection helps for the best
reconstruction among other channel selection methods such as PCA and Random
selection for the T1 and T2 tissue parameters. As attention-based channel
selection method is deep learning-based, increasing the amount of data will
lead to better generalization of channel selection in a more reliable manner,
and could outperform random selection significantly in bigger data sets.

In the future, the proposed input channel attention mechanism could be adapted
to the U-Net architecture [24] which has shown promising reconstruction
capabilities recently [25] and other powerful architectures for MRF tissue
reconstruction. MRF signal is originally a complex-valued data comprising real
and imaginary parts. While the magnitude of the MRF signal is exploited solely
in this study (similar to most of the state-of-the-art), in the future it is
worth exploring the combined use of real and imaginary parts of the signal as
some studies suggest [12, 26, 27]. Finally, as a future study, we aim to
validate our method on larger data sets and other anatomical regions.

In conclusion, this study shows that employing channel reduction at the
beginning of the model causes loss of temporal information which is important
for the reconstruction of T1 and T2 parameters. To overcome this problem, we
proposed deep learning-based input channel attention that can be easily
applied to each model. Additionally, we analyzed effect of patch size on
reconstruction performance, and furthermore demonstrated quantitatively and
qualitatively that the proposed attention-based channel selection achieves the
best reconstruction performance.

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# STOPGAP - a Time-of-Flight Extension for the Belle II TOP Barrel PID System
as a Demonstrator for CMOS Fast Timing Sensors

Oskar Hartbrich∗, Umberto Tamponi+, Gary S. Varner∗
∗University of Hawaii at Manoa,+INFN Torino

(2021)

###### Abstract

The Belle II barrel region is instrumented with the Time of Propagation (TOP)
particle identification system based on sixteen fused-silica bars arranged
around the interaction point acting as Cherenkov radiator. Due to the
mechanical design of the TOP system these quartz bars do not overlap, but
leave a gap of around $2\text{\,}\mathrm{cm}$ between them. This leads to
around $6\text{\,}\mathrm{\char 37\relax}$ of all tracks in the nominal TOP
acceptance region to escape without traversing any of the quartz bars and thus
not giving any usable particle identification information from the TOP system
and an additional $3\text{\,}\mathrm{\char 37\relax}$ of tracks being degraded
due to edge effects. We propose a possible solution to remedy these gaps in
the TOP acceptance in the form of a Supplemental TOP GAP instrumentation
(STOPGAP) that covers the dead area between adjacent quartz bars with fast
silicon detectors to directly measure the time-of-flight of traversing
particles for particle identification purposes. Modern, fast timing silicon
sensors and readouts can offer sufficient time resolution for the task at
hand, so that STOPGAP modules could be built compact enough to fit into the
limited space available in the area of interest between the Belle II central
drift chamber (CDC) and the TOP system.

In this article, we present a simulation study demonstrating the feasibility
of a silicon time-of-flight system based on its reconstruction performance in
$\Upsilon(4S)\rightarrow B\bar{B}$ events simulated using the Belle II
simulation and reconstruction software. We discuss the performance
requirements for possible sensor technologies and demonstrate that such a
project could be realised with novel, fast monolithic CMOS sensors that are
expected to reach MIP timing resolutions of down to $50\text{\,}\mathrm{ps}$.
Additionally, we discuss the use of fast timing layers at lower radii for
track triggering as well as particle identification at low momenta
$<1\text{\,}\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}\mathrm{c}$.

##  1 Introduction

The physics program of super B-factories requires the best possible
reconstruction of all final state particles in a given event. The
differentiation between charged particles species (electrons, muons, pions,
kaons, protons) is accomplished by dedicated particle identification (PID)
subdetectors and further assisted by their ionization energy loss ($dE/dx$) as
measured in the tracking system as well as their energy deposition in the
electromagnetic calorimeter and the muon system. The Belle II barrel region is
instrumented with the Time of Propagation (TOP) particle identification
system, which measures the detection time of Cherenkov photons generated
sixteen $2625\text{\times}450\text{\times}20\text{\,}\mathrm{mm}$ quartz
radiator bars arranged around the interaction point (IP). The photons are
trapped inside the bars by total internal reflection and transmitted to an
array of pixelated photo-sensors (MCP-PMTs). The measured time difference
between the particle collision and the photon arrival time is the sum of two
contributions: first, the particle’s time of flight from the IP to the quartz
bar, which is inversely proportional to the particle velocity. Second, the
photon propagation time inside the quartz bar, which is a function of the
Cherenkov angle [1, 2] and thus the particle velocity. The particle crossing
the bar is identified comparing the time distribution of the photons detected
in each photo-sensors pixel with the expected ones for different mass
hypotheses. The TOP is responsible for most of the for hadron identification
capability in the barrel region, which corresponds to $\approx 80\%$ of the
total Belle II acceptance. The mechanical design of the TOP modules leaves
gaps in the azimuthal direction ($\phi$) of about $2\text{\,}\mathrm{cm}$
width in between the individual quartz bars, accounting for about
$6\text{\,}\mathrm{\char 37\relax}$ of missing geometric coverage in the
nominal TOP acceptance. Tracks passing through the outermost edges of a TOP
bar also have reduced particle identification performance, effectively
widening this gap to around $16\text{\,}\mathrm{\char 37\relax}$ of tracks
with no or degraded TOP PID. Many physics analyses foreseen in the Belle II
physics program require the positive identification of several final state
particles, multiplying the impact of the TOP quartz gap. A particularly
important case is represented by the analyses based on the full event
reconstruction (FEI) with the tagging of the opposite B meson, like the
semileptonic B decays with undetected neutrinos. Such decays are of particular
interest for searches of phenomena beyond the standard model and, in some
cases, can be uniquely explored at Belle II. Flavor tagging, used for CP
violation measurements, also depends on the efficiency and quality of lepton
and hadron identification.

The TOP does not only contributes to the particle identification, but plays a
central role in the global Belle II reconstruction. A most critical component
for both particle identification and tracking in the silicon vertex detector
is the event time $T_{0}$. The TOP detector is the most precise timing
instrument in the Belle II apparatus and thus plays an important role in its
determination. However, the TOP contribution to the $T_{0}$ measurement
strongly depends on the number of tracks in the TOP acceptance. Especially
with the expected increase in background rates, the impact of a precise
$T_{0}$ determination will continue to grow in importance. Thus, not only the
particle identification, but the overall quality of the Belle II event
reconstruction would be improved by extending the TOP coverage.

A possible solution to remedy the gaps in the TOP acceptance is to install a
supplemental time-of-flight detector that covers the non-instrumented areas
between adjacent quartz bars. Since the available space around the installed
TOP modules is quite limited, one or multiple layers of fast-timing silicon
detectors would serve this scope. The Supplemental TOP Gap Instrumentation
(STOPGAP) has become feasible with the advent of modern silicon sensor types
with very short signal collection times and excellent time resolutions in the
range of a few tens of picoseconds, which we will show to be sufficient to
provide particle identification in the momentum range
$0.05\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{c}5.0\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{c}$
and path lengths of $1\text{\,}\mathrm{m}2\text{\,}\mathrm{m}$ at super
B-factory experiments such as Belle II.

There is around $45\text{\,}\mathrm{mm}$ of free space between the the outer
shell of the Belle II Central Drift Chamber (CDC) and the inner wall of the
TOP module enclosures. This is sufficient to fit two layers of silicon sensors
$40\text{\,}\mathrm{mm}$ wide, and the additional required services, to cover
the gap between the TOP quartz bars along their whole length. Fig.1 shows a
sketch of the geometry around the gap between two TOP module enclosures and a
possible STOPGAP module geometry.

Figure 1: Conceptual sketch of supplemental TOP gap instrumentation module in
the cross section of two adjacent TOP modules as seen from the backward side.
The solid light blue lines show the outlines of the readout side of the TOP
quartz bar box. The dashed light blue lines show the outline of the rest of
the TOP quartz bar box. The TOP quartz cross section is shown in dark blue.
The dashed black lines roughly show the dimensions of a possible STOPGAP
module, with the two dashed circles indicating possible cooling lines or
cabling channels and a layer of silicon sensors shown in pink.

##  2 MC Performance Study

We performed Monte Carlo (MC) study of the STOPGAP performance using simulated
$\Upsilon(4S)\to B\bar{B}$. The existing structures of Belle II detectors are
simulated using Geant4, and the charged particles’ trajectories are
reconstructed using the publicly available Belle II analysis software
framework [3, 4]. The STOPGAP response is calculated using a parametric MC
approach using the extrapolated impact point of the track of the inner TOP
surface, which approximately corresponds to the planned radial position of the
STOPGAP modules. To simulate the STOPGAP response several contributions to the
total time resolution have been considered, both reducible and irreducible:
sensor readout resolutions from
$20\text{\,}\mathrm{ps}100\text{\,}\mathrm{ps}$, global clock distribution
jitter ($10\text{\,}\mathrm{ps}$), the SuperKEKB bunch overlap time
($15\text{\,}\mathrm{ps}$), and track length uncertainty, parameterized
assuming a $5\text{\,}\mathrm{mm}$ resolution on the impact point of the track
in the Z direction. The particle identification is then performed by
evaluating a likelihood constructed from the these time resolution components,
all assumed to be Gaussian. The resulting selection and mis-identification
fractions for charged pions and kaons are shown for a sensor resolution of
$50\text{\,}\mathrm{p}\mathrm{s}$ in Fig.2. Detailed plots for both pion an
kaon (mis-) identifications are attached Figs.9,10 in the appendix. A STOPGAP
system with a combined time resolution for sensor and readout of
$50\text{\,}\mathrm{ps}$ would perform significantly better than the TOP
system in the momentum range $p<$2\text{\,}\mathrm{GeV}$$. A
$30\text{\,}\mathrm{ps}$ system would outperform TOP in the whole momentum
range.

Figure 2: Selection and mis-identification probabilities at $LL_{K}-LL{\pi}>0$
of a simulated STOPGAP PID system for charged kaons as a function of particle
momentum, shown for a simulated sensor with $50\text{\,}\mathrm{p}\mathrm{s}$
MIP timing resolution with additional timing contributions as explained in the
text. Solid curves are the kaon selection efficiencies, while the dashed
curves show the mis-identification probability for $\pi\rightarrow K$. Shaded
areas indicate the statistical uncertainties of the data points.

Fig.3 shows the reconstructed invariant mass of $\phi\rightarrow K^{+}K^{-}$
decays selected from the simulated dataset. A $50\text{\,}\mathrm{ps}$ STOPGAP
system achieves more than twice better signal-to-noise ratio near the $\phi$
mass peak. The improved efficiency is entirely defined by the difference in
kaon efficiency, which is only $90\text{\,}\mathrm{\char 37\relax}$ for TOP,
but driven by the MIP efficiency in STOPGAP.

Figure 3: Invariant mass distribution from charged kaons selected at
$LL_{K}t>LL{\pi}$ for both tracks, with both tracks in the TOP acceptance. The
black line shows the unselected spectrum. The shaded areas indicates the
fraction corresponding to true $\phi$ decays. The TOP system achieves a S/N of
0.37 ($\mu\pm 2\sigma$), while the STOPGAP reconstruction achieves a S/N of
0.79 in the same invariant mass window.

The next step will be the implementation of a realistic STOPGAP geometry into
the Belle II simulation, which will allow us to study the combined performance
of TOP+STOPGAP as well as its impact on specific physics channels of interest.
This would also allow realistic studies of the resilience of a time of flight
system vs. beam backgrounds. The expected improvement in the combined particle
identification has to be understood to optimize the number of sensor layers
and their ideal dimensions and arrangement.

###  2.1 Backgrounds

We identified two main sources of background affecting STOPGAP: backsplash
from showers in the electromagnetic calorimeter located few centimeters behind
the TOP, and beam-induced backgrounds. We expect the former to be easily
identifiable in the majority of cases, since backsplash hits are necessarily
later in time that the initial particle hit and in addition should deposit
significant energy in the corresponding ECL crystal. The beam background are
discussed in subsection 4.1, where in lieu of a true GEANT4-based simulation
study, we use the occupancy in the vertex detector as a proxy for the
background level and perform some extrapolations for a few conservative sensor
parameters to show that the expected impact is minimal.

##  3 Timing Layers at Lower Radii

Several of the currently proposed and discussed upgrades of the Belle II
vertexing system plan to increase the inner radius of the current drift
chamber replacing its inner layers with silicon sensors. The thin silicon
sensors proposed for the vertexing upgrade are unlikely to provide enough
$dE/dx$ discrimination for low momentum particle as the CDC does currently.
Additionally, the CDC currently provides track triggering for transverse
particle momenta $p_{T}$ down to around $100\text{\,}\mathrm{MeV}$, which a
full silicon inner tracking system might not be able to provide. We thus
explore here the potential of recovering the PID and track triggering
capabilities for low $p_{T}$ particles by analytical modelling of dedicated
timing layers at $250\text{\,}\mathrm{mm}$ and/or $450\text{\,}\mathrm{mm}$
radius.

For pion/kaon separation purposes, the region of
$p_{T}<$500\text{\,}\mathrm{MeV}$$ is most relevant, as higher $p_{T}$ will
reach the dedicated PID subdetectors TOP, ARICH and also generally provide a
$dE/dx$ measurement from the remaining part of the CDC or a potential TPC
replacement. We calculate the time of flight from the IP until the first
crossing of the timing layer radius as a function of particle momentum and
mass, including the path length of the circular segment that describes its
trajectory. In order to keep the calculation simple and conservative, we
assume $\left|p\right|=p_{T}$ here.

The resulting time of flight differences between charged kaons and pions are
then divided by the assumed time resolution of a timing layer, resulting in a
measure or particle identification in standard deviations of separation. These
numbers are then compared to an estimate of the $dE/dx$ particle separation of
the CDC as shown in Fig.4. This study indicates that a
$50\text{\,}\mathrm{ps}$ MIP timing resolution layer at
$250\text{\,}\mathrm{mm}$ radius yields consistently better pion/kaon
separation than the CDC, while a $450\text{\,}\mathrm{mm}$ radius timing layer
leads to at least double the separation power between pions and kaons over the
CDC in the momentum region inspected here.

Figure 4: Pion/kaon separation performance of a MIP timing layer compared to
an estimated $dE/dx$ PID at different radii. The arrows indicate the lower
$p_{T}$ cutoff for each system due to its radius.

To estimate the general feasibility of timing layers to provide track triggers
for Belle II, simplified trigger model is combined with extrapolations from
the beam background estimates described in Table 1 below. The individual layer
geometry is assumed as a cylinder length of three times its radius, leading to
a covered area of $1.2\text{\,}{\mathrm{m}}^{2}$ at
$250\text{\,}\mathrm{m}\mathrm{m}$ radius or $3.8\text{\,}{\mathrm{m}}^{2}$ at
$450\text{\,}\mathrm{mm}$ radius.

For each examined timing layer radius, the expected background hit rates at
full luminosity are extrapolated from all given radii and their ensemble mean
and min-max envelope used for further calculations. An additional simplifying
assumption made here is that background hits are spatially uncorrelated.

A timing system at the trigger level would likely not work at the full
granularity of the used sensor technology, but instead operate on larger areas
for coincidence. We thus conservatively assume here that the effective
”trigger region” of coincidence of such a system is
$10\text{\,}{\mathrm{cm}}^{2}$. Such regions would be formed by OR’ing the
outputs of all individual sensor channels in that region. For the purposes of
this study a ”track” consists of $N$ stacked (or geometrically associated)
trigger regions firing coincident in time within a conservative window of
$1\text{\,}\mathrm{ns}$ (corresponding to a $\pm 5\text{\,}\sigma$ range of an
assumed $100\text{\,}\mathrm{ps}$ MIP timing resolution at the trigger level).
Individual tracks are considered coincident when $M$ track occur within a time
window of $5\text{\,}\mathrm{ns}$, which roughly covers the time of flight
differences between electrons and protons at the relevant radii and momenta
here.

Based on these assumptions, the trigger rates from pure beam backgrounds can
be calculated. The event $T_{0}$ reconstruction at the trigger level is not
expected to reach the resolution of the timing layers discussed here, so a
single timing layer can only form a coincidence with itself. This is
prohibitive in expected noise rates, so we only investigate cases of different
radial configurations of two timing layers forming a coincidence.

Fig.5 shows the results of the model described above for the beam backgrounds
expected at full design luminosity of SuperKEKB. Depending on the radius, each
additional track required for a trigger decreases the background trigger rate
by 2-4 orders of magnitude. Increasing the dual timing layer radius from
$250\text{\,}\mathrm{mm}$ to $450\text{\,}\mathrm{mm}$ decreases the
background trigger rates by at least one to two orders of magnitude.

Notably, a configuration with two single timing layers at
$250\text{\,}\mathrm{mm}$ and $450\text{\,}\mathrm{r}$adius, respectively, is
estimated to yield background trigger rates right in between the double-layer
options. However, the base assumption of spatially uncorrelated background
hits is much more likely to be accurate in this configuration. Additionally a
distanced two-layer setup would enable a coarse estimation of the Z-origin of
a triggered track, enabling a selection of tracks from the IP, as well as a
coarse estimation of the track momentum (or at least its charge) on the
trigger level at the cost of increased complexity in the required trigger
reconstruction logic.

The uncertainties from the beam background extrapolations generally span at
least an order of magnitude, and the systematic uncertainties from the
assumptions described above are not included in the figure at all. The given
numbers nevertheless show the fundamental feasibility of a timing track
trigger system, at least for triggering events with two or more tracks in its
acceptance.

Figure 5: Estimated background rate of double layers of fast timing
coincidence track trigger at $250\text{\,}\mathrm{mm}$ and
$450\text{\,}\mathrm{mm}$ radii as well as for two single track trigger timing
layers at $250\text{\,}\mathrm{mm}$ and $450\text{\,}\mathrm{mm}$ radius.

##  4 Requirements

We now review the requirements for a STOPGAP upgrade to the Belle II TOP
detector system or even its full replacement. The technological requirements
for timing layers could be extracted in the same general way, but are not
discussed in further detail here.

Depending on the details of the chosen STOPGAP geometry,
$1\text{\,}{\mathrm{m}}^{2}3\text{\,}{\mathrm{m}}^{2}$ of active area will be
needed to fill the gaps in the TOP acceptance with a single sensor layer. In
case a double-layer design is necessary, that area would double accordingly.
For reference, a full replacement of the TOP system would require around
$18\text{\,}{\mathrm{m}}^{2}$ of timing sensitive sensor.

As was described earlier, the particle identification performance of a time-
of-flight system is fundamentally limited by the single MIP detection
efficiency of the used sensor technology. A MIP efficiency as close as
possible to $100\text{\,}\mathrm{\char 37\relax}$ is thus a strong requirement
for such a system.

The allowable material budget for a STOPGAP module should generally not exceed
the material budget of a full TOP module consisting of several $\mathrm{mm}$
of aluminium and around $2\text{\,}\mathrm{cm}$ of quartz (about
$0.2\text{\,}\mathrm{X}_{\mathrm{0}}$). Since there will be some effective
overlap between the two structures, minimising the STOPGAP material budget
will be helpful in reducing potential impacts on the photon reconstruction
from conversions in the material in front of the ECL crystals.

In the following, the expected background hit rates and radiation dosages are
discussed. This discussion is based on extrapolations of the expected beam
background rates and radiation dosages - without additional safety factors -
at full SuperKEKB luminosities at the radii of the currently installed Belle
II vertex detector [5]. The given numbers are extrapolated to the radius of
the TOP system and potential radii of timing trigger layers. The original
values as well as our radial extrapolations are given in Table 1.

Table 1: Estimated hit rates and radiation dosages at full SuperKEKB luminosity of $8\text{\times}{10}^{35}\text{\,}{\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$ for the existing Belle II VXD layer radii [5]. The given numbers for a STOPGAP system or timing trigger layers at $250\text{\,}\mathrm{mm}450\text{\,}\mathrm{mm}$ are extrapolated from the given ensemble of VXD estimates. The given range for each radius is the minimum and maximum value obtained from the ensemble. Layer | Radius | Hit Rate | NIEL | Total Ionising Dose
---|---|---|---|---
| in $\mathrm{mm}$ | in $\mathrm{Hz}\text{\,}{\mathrm{cm}}^{-2}$ | in $\mathrm{n}_{eq}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}$ | in $\mathrm{R}\mathrm{a}\mathrm{d}$
1 (PXD) | $14$ | $22.6\text{\times}{10}^{6}$ | $10\text{\times}{10}^{12}$ | $2\text{\times}{10}^{6}$
2 (PXD) | $22$ | $11.3\text{\times}{10}^{6}$ | $5\text{\times}{10}^{12}$ | $600\text{\times}{10}^{3}$
3 (PXD) | $39$ | $1.41\text{\times}{10}^{6}$ | $0.2\text{\times}{10}^{12}$ | $100\text{\times}{10}^{3}$
4 (SVD) | $80$ | $290\text{\times}{10}^{3}$ | $0.1\text{\times}{10}^{12}$ | $20\text{\times}{10}^{3}$
5 (SVD) | $115$ | $220\text{\times}{10}^{3}$ | $0.1\text{\times}{10}^{12}$ | $10\text{\times}{10}^{3}$
6 (SVD) | $135$ | $150\text{\times}{10}^{3}$ | $0.1\text{\times}{10}^{12}$ | $10\text{\times}{10}^{3}$
STOPGAP | $1167$ |  2416 ($13624015$) |  $1.05\text{\times}{10}^{9}$ ($0.22\text{\times}{10}^{9}1.78\text{\times}{10}^{9}$) |  158 ($94288$)
Trigger 1 | $450$ |  $16.2\text{\times}{10}^{3}$ ($9.2\text{\times}{10}^{3}27\text{\times}{10}^{3}$) |  $7.08\text{\times}{10}^{9}$ ($1.50\text{\times}{10}^{9}12.0\text{\times}{10}^{9}$) |  1062 ($6321936$)
Trigger 2 | $250$ |  $52.6\text{\times}{10}^{3}$ ($29.7\text{\times}{10}^{3}87.5\text{\times}{10}^{3}$) |  $23.0\text{\times}{10}^{9}$ ($4.87\text{\times}{10}^{9}38.7\text{\times}{10}^{9}$) |  3442 ($20486272$)

###  4.1 Estimation of STOPGAP hit rates

Based on Table 1, we calculate a STOPGAP background rate of $2.4\pm
0.9\text{\,}\mathrm{kHz}\text{\,}{\mathrm{cm}}^{-2}$ at the SuperKEKB design
luminosity of
$8\text{\times}{10}^{35}\text{\,}{\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$.
In order to be conservative, we assume an additional safety factor of 5, and
an extra luminosity factor of 5 for an assumed maximum background hit rate of
$60\text{\,}\mathrm{kHz}\text{\,}{\mathrm{cm}}^{-2}$. Further assuming a
conservative readout open time window of $100\text{\,}\mathrm{ns}$ (to broadly
cover an assumed trigger time jitter of $10\text{\,}\mathrm{ns}$ and a maximum
time of flight of individual particles of $20\text{\,}\mathrm{ns}$), we arrive
at a background occupancy of $0.60\pm 0.23\text{\,}\mathrm{\char
37\relax}\text{\,}{\mathrm{cm}}^{-2}$. Finding the hit on the STOPGAP sensor
that corresponds to a given track needs to consider around
$1\text{\,}{\mathrm{cm}}^{2}$ of sensor area due to the limited Z-pointing
resolution of the CDC tracking. We thus arrive at a very conservatively
estimated chance of $0.6\text{\,}\mathrm{\char 37\relax}$ that there is a
background hit in the same spatial and temporal region of interest on the
STOPGAP surface for a given charged particle track.

###  4.2 Radiation Hardness of STOPGAP

As given in Table 1, the expected non-ionizing lattice displacement (NIEL) at
the STOPGAP radius is on the order of
$1\text{\times}{10}^{9}\text{\,}\mathrm{n}_{eq}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}$.
This value is compatible with the NIEL estimates obtained as part of the
original TOP irradiation expectation studies. Similarly, the total ionizing
radiation dose at the STOPGAP radius is estimated to be $0.16\pm
0.07\text{\,}\mathrm{K}\mathrm{R}\mathrm{a}\mathrm{d}$. These values are
several orders of magnitude lower than those expected and observed in the
(HL-)LHC environments. Radiation hardness is thus not expected to of
significant importance in the selection of a suitable technology option.

###  4.3 Granularity

Based on the occupancy estimates and the tracking extrapolation resolution
presented above, a sensor granularity of around
$1\text{\,}\mathrm{c}\mathrm{m}^{2}$ would be sufficient. The time resolution
contribution from an uncertainty in the trajectory path length due to the
Z-pointing resolution term is generally small. With sufficient granularity in
Z-direction, the inclusion of STOPGAP hits into the track fit would further
eliminate that uncertainty. $1\text{\,}\mathrm{mm}$ of STOPGAP sensor
granularity in Z corresponds to around a $1\text{\,}\mathrm{ps}$ additional
time resolution contribution from track path length uncertainty.

###  4.4 Summary

Especially in comparison to the detector upgrades under discussion and
construction for the HL-LHC, the requirements on hit rates, radiation hardness
and granularity are entirely negligible for a STOPGAP application. The driving
factors of its performance are the single MIP timing resolution and a MIP
efficiency of $>99\text{\,}\mathrm{\char 37\relax}$. As discussed above,
STOPGAP modules are expected to yield useful particle identification
capabilities for time resolutions $<100\text{\,}\mathrm{p}\mathrm{s}$.

For timing layers at lower radii, the requirements on hit rate and radiation
hardness are stronger than for the STOPGAP case, but still tame compared to
HL-LHC developments. As part of the inner tracking detector, finer granularity
and a much reduced material budget would be required compared to STOPGAP.

##  5 Existing Sensor Options and Readout Technologies

There are several options for sensors and readout technologies. We briefly
review some of the existing technologies planned used for the HL-LHC upgrades
and under consideration for e.g. the EIC detector concepts.

#### Low Gain Avalanche Diodes

(LGAD) are planned for the end cap timing layers of the CMS and ATLAS high
luminosity upgrades [6, 8]. Due to their doping profiles, LGAD sensors are
fabricated in specialised non-standard processes and thus rather expensive.
They generally require hybridized readout chips bump bonded to them, further
increasing their cost and difficulty in assembly and handling. Current LGAD
designs have a large dead zone between neighbouring readout pads and hence
require double layers for greater than $99\text{\,}\mathrm{\char 37\relax}$
MIP efficiency. Recently first working prototypes of AC coupled LGADs have
shown to remediate the efficiency gaps between pixels. Integrated readouts for
LGAD sensors are under development e.g. for the ATLAS upgrade by OMEGA
(ALTIROC [9]) and for the CMS upgrade by FNAL (ETROC [8, 10]). The target time
resolution for LGAD layers is $30\text{\,}\mathrm{p}\mathrm{s}$ for a double
layer. Under ideal conditions, unirradiated single LGAD layers have
demonstrated down to around $20\text{\,}\mathrm{p}\mathrm{s}$ timing
resolution for single MIPs.

#### LYSO+SiPM

systems were originally considered for time-of-flight positron emission
tomography applications [7], but are now also used for in HEP detectors,
specifically the the CMS barrel timing layer (BTL) [8]. The CMS BTL uses small
staves of scintillating LYSO:Ce crystals around
$5\text{\times}5\text{\times}50\text{\,}\mathrm{mm}$ read out by one silicon
photomultiplier (SiPM) on each of the smaller faces. Timing resolutions of
down to $30\text{\,}\mathrm{p}\mathrm{s}$ for single MIPs have been
demonstrated. This approach is fundamentally limited in the possible
granularity by the minimum feasible size of the LYSO crystals to around
$1\text{\,}{\mathrm{cm}}^{2}$. The necessary material budget is limited by the
required thickness of the LYSO crystal of a few $\mathrm{m}\mathrm{m}$ to
yield enough scintillation photons for a timing measurement of the required
precision. Since SiPMs generally have large internal amplification, the noise
requirements on the readout electronics are less demanding, enabling high
readout channel densities per chip (see e.g. CMS TOFHiR [11]).

In summary, all existing fast timing sensor technologies are potentially
feasible for a STOPGAP system. As a matter of fact the LYSO+SiPM CMS BTL
modules would almost fit into the available space between TOP modules the way
they have been designed and constructed for the CMS upgrade. However, neither
the achievable granularity nor the material budget of (at the very least) a
few $\mathrm{mm}$ of LYSO crystals is suitable for an application at lower
radii. LGADs are a potential option for both STOPGAP and track timing layers,
with drawbacks in granularity, MIP efficiency and cost per area. AC-LGADs can
potentially solve the first two points, but they do not address the cost issue
and have also not been demonstrated in full-scale systems yet.

##  6 Timing with fast MAPS

As discussed in great details in ref.[12], the fundamental limitation in
improving the timing resolution of silicon sensors is the achievable signal-
to-noise ratio (SNR) of its output signal. LGADs address this via
amplification of the ionisation charge signal in a thin avalanche
amplification layer. A feasible alternative is to improve the SNR by means of
a lower noise and thus higher powered electronic amplification of the pixel
output signal. This has been demonstrated in principle by the NA62 Gigatracker
[13], which achieves $130\text{\,}\mathrm{p}\mathrm{s}$ time resolution on
single MIP hits per layer with a hybridized fast timing frontend bonded to
$200\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick silicon sensors without
internal avalanche amplification.

The next step towards monolithic fast timing sensors is to integrate high-
powered low noise preamplifiers and discriminators directly into the sensor.
This is ideally produced in a CMOS process, leveraging the cost benefits and
scalability of industrial CMOS fabrication. Such a chip would fully integrate
the readout electronics and sparsification logic into the sensor wafer to also
greatly simplify the required complexity of the electronics downstram of the
sensor layer: An intelligent readout logic ideally only requires power and a
reference clock as inputs, and delivers lists of hits and their timings via a
fast serial output line. This would be realised in a single, thin layer of
silicon with a minimum of material budget. Figure 6 shows a comparison of
existing fast timing technologies with the current state of MAPS and the
potential for fast MAPS.

Figure 6: Comparison of existing fast MIP timing technologies and the
potential for fast MAPS. The granularity of a LYSO+SiPM is limited in practice
and the material budget is relatively high compared to silicon sensors. LGADs
have shown good timing resolutions, but are expensive and somewhat limited in
granularity (AC-LGAD might solve the granularity issue in the near future).
Current MAPS are cost effective, highly granular and radiation hard, but their
time resolution falls short by orders of magnitude compared to LYSO+SiPM and
LGADs.

At least two groups are actively pursuing first steps towards MAPS with single
MIP time resolutions of $<100\text{\,}\mathrm{p}\mathrm{s}$. The University of
Geneva is working on small pixels produced in $130\text{\,}\mathrm{nm}$ IHP
SG13G2SiGe BiCMOS [14, 15]. They have shown to achieve single MIP time
resolutions down to $60\text{\,}\mathrm{p}\mathrm{s}$ in laboratory conditions
for small hexagonal pixels of $65\text{\,}\mathrm{\SIUnitSymbolMicro m}$ side
length. In the current prototype, the power consumption necessary to achieve
this time resolution is outright prohibitive at around
$50\text{\,}\mathrm{kW}\text{\,}{\mathrm{m}}^{-2}$.

The IRFU Saclay group has produced a prototype of their CACTUS concept in a
$150\text{\,}\mathrm{nm}$ LFoundry HVCMOS process [16]. The sensor is based on
their experience and layout of the ATLAS monopix family, modified for the best
possible time resolution. Their test structure includes
$1\text{\times}1\text{\,}\mathrm{mm}$ and
$1\text{\times}0.5\text{\,}\mathrm{mm}$ pads. Their achieved single MIP time
resolutions on the first available iteration are in the order of hundreds of
$\mathrm{p}\mathrm{s}$. The reason for this worse than expected performance
has been understood as mis-estimated parasitic capacitances of the metal layer
power rails running across the pixel. A future iteration of the same concept
is expected to perform better. Figure 7 shows a picture of the Geneva
prototype chip as well as a diagram of the CACTUS test structures.

(a) Die photograph of the University of Geneva fast monolithic pixel prototype
based on SiGe HBT amplifiers. The hexagonal structures are individual test
pixels of $130\text{\,}\mathrm{\SIUnitSymbolMicro m}$ side length (left) and
$65\text{\,}\mathrm{\SIUnitSymbolMicro m}$ side length (right). [14, 15]

(b) Schematic of the CACTUS HVCMOS prototype chip consisting of arrays of
$1\text{\times}1\text{\,}\mathrm{mm}$ and
$1\text{\times}0.5\text{\,}\mathrm{mm}$ test pixels with additional digital
logic and contact pads on the top and bottom. [16]

Figure 7: Early fast CMOS sensor prototypes.

These projects show that it is indeed possible to achieve
sub-$100\text{\,}\mathrm{p}\mathrm{s}$ timing with monolithic CMOS detectors,
even though none of the projects has produced a sensor prototype that is
currently feasible for practical use. The relatively tame requirements of a
STOPGAP sensor on hit rates, radiation hardness and (in principle) readout
granularity, at least compared to the requirements for HL-LHC applications,
opens up STOPGAP as an ideal test bed for emerging fast timing CMOS MAPS
technologies.

The primary goal of such a dedicated project would be to develop a prototype
pixel structure with an integrated preamplifier close to the thermodynamic
limit in noise per power consumption. Figure 8 shows the required effective
noise charge of an in-pixel amplifier for different target time resolutions
and silicon sensor thicknesses.

While it is unlikely for any realistic fast MAPS sensor to reach the timing
performance of (AC-)LGADs, it should be possible to get close to it within a
factor of two. While LGADs or other future sensors might remain the technology
choice for applications demanding the highest possible MIP timing resolution,
the prospect of achieving almost comparable resolutions with significantly
reduced cost is extremely appealing. Opening up the fast timing frontier for
MAPS also enables future MAPS tracker projects to include as much time
resolution into their designs as needed for the application. Establishing fast
MAPS is thus of prime importance not only for HEP detectors, but for
technologically related instrumentation as a whole.

Fast MAPS have the potential to fulfill all needed requirements for a STOPGAP
system or a timing layers in an upgraded inner tracking system. Since the
technical requirements, especially for STOPGAP, are fairly tame apart from the
MIP time resolution, it poses an ideal prototype project to establish fast
MAPS for HEP instrumentation.

Figure 8: Preamplifier requirements on effective noise charge (ENC) and
peaking time to achieve a given time resolution with a silicon sensor without
internal amplification. The shaded area indicates the signal collection time
for a sensor of the given thickness. Calculation based on [12].

##  7 Resource estimates and timeline

The resource estimate for the whole project is divided into two parts: the
development of the MAPS technology, and the actual construction of the
detector modules. The given numbers come with great uncertainties and should
be considered as rough guidelines.

###  7.1 R&D for fast MAPS

Making significant steps towards very fast CMOS sensors with timing resolution
around $50\text{\,}\mathrm{p}\mathrm{s}$ is the most important fundamental
building block of this proposal. In that regard the goal of building a STOPGAP
system is a vehicle to motivate the extensive R&D needed towards such fast
CMOS sensors. On the way, the current practical limitations of this technology
choice will be discovered and, eventually, overcome.

The current efforts towards achieving the best time resolution with CMOS
sensors use fabrication processes of $130\text{\,}\mathrm{nm}$ and
$150\text{\,}\mathrm{nm}$ structure size. Since the noise figure is correlated
to the process feature size, an immediate improvement in time resolution (or
alternatively the power draw at a fixed time resolution) can be achieved
moving the development to the next smaller node of $65\text{\,}\mathrm{nm}$.
To this end, a suitable $65\text{\,}\mathrm{nm}$ process with sufficiently
high surface resistivity to support high voltage biasing needs to be
identified and qualified first. An general drawback of
$65\text{\,}\mathrm{nm}$ processes respect to $130\text{\,}\mathrm{nm}$ or
$150\text{\,}\mathrm{nm}$ ones are the higher costs per submission and the
lower availability of multi project wafer shuttle projects, increasing the
costs of such developments. At least two engineering submissions and extensive
laboratory test bench and testbeam campaigns will be necessary to develop and
validate a sensor layout that achieves the necessary time resolutions at an
acceptable power budget.

The second step is to integrate TDC electronics and the readout logic onto the
same chip. Recent developments in $65\text{\,}\mathrm{nm}$ processes have
demonstrated TDCs with bin widths $<10\text{\,}\mathrm{p}\mathrm{s}$ [10, 17].
We thus do not expect fundamental issues in designing an on-chip TDC that
reaches the resolution range of
$20\text{\,}\mathrm{p}\mathrm{s}30\text{\,}\mathrm{p}\mathrm{s}$ needed to
read out our sensors.

The intermediate goal of this proposed R&D program is the construction of a
small sized prototype detector with active area of a few ${\mathrm{cm}}^{2}$
in order to validate the sensor technology in a realistic environment. This
prototype will be installed inside Belle II and operated synchronously with
the other detectors while recording physics collisions. The readout of the
prototype does not necessarily need to be constructed using a final chip with
fully integrated electronics, but could e.g. be read out using a picoTDC [17]
integrated into the prototype module. Demonstrating the time-of-flight
resolution for single MIPs in the environment of an active HEP experiment will
not only validate the sensor technology, but also uncover the practical issues
with operating a sensor in realistic conditions compared to test beam or bench
tests. The ultimate capstone of the program would be a working prototype of a
fully integrated monolithic detector module with integrated sparsified readout
that demonstrates the required timing and hit rate capabilities at least in a
test beam environment.

We believe that such a program is not feasible without significant funding for
at least three to five years. Out of that time, we coarsely estimate around
one to two years will be needed to finish the sensor design, at least one year
is needed for the integrated timing frontend and readout logic, and an
additional year will be needed for integration onto one common mixed signal
chip. Depending on available person power and expertise, parts of this design
and test effort can run in parallel. To acquire the necessary momentum, the
strong support of an existing local work group with extensive expertise in
CMOS sensor design and a profound interest in pushing the possibilities of
fast MAPS to its limits is required at the very least for the first one to two
years.

###  7.2 STOPGAP construction

Ultimately, 16 STOPGAP modules with around
$1\text{\,}{\mathrm{m}}^{2}2\text{\,}{\mathrm{m}}^{2}$ of total active sensor
area will have to be built and installed. Apart from the significant funding
requirements for the sensor production itself, this will need detailed
concepts for the mechanics, cooling, service routing and installation
procedure for these modules. None of these tasks have even been considered so
far. First steps towards a STOPGAP module design in the form of finite element
simulations to estimate the required stiffness and eventual mechanical mock-
ups could in principle start in parallel with the sensor R&D program outlined
above.

##  8 Summary and Outlook

Around $6\text{\,}\mathrm{\char 37\relax}$ of the charged tracks in the
nominal coverage of the TOP particle identification system in the Belle II
barrel region pass near or through the gaps between the TOP quartz radiator
bars and thus do not yield usable PID information. An additional
$10\text{\,}\mathrm{\char 37\relax}$ of tracks suffer from degraded PID
performance from passing too close to the quartz edges. The STOPGAP project
aims to fill these gaps in coverage with fast-timing silicon sensors to
measure the time of flight of such particles to improve the Belle II particle
identification coverage. Examining the possible high precision timing
technologies, CMOS timing detectors appear to be most promising for the
requirements of a Belle II upgrade. We propose to start a significant CMOS
timing sensor R&D program with a series of prototypes and beam tests. The
intermediate goal would be to integrate a small sensor protoype into Belle II
and to operate it in physics collisions.

##  Appendix A Appendix

Figure 9: Kaon selection and mis-identification probabilities at
$LL_{K}-LL{\pi}>0$ of a simulated STOPGAP PID system for charged kaons as a
function of particle momentum, shown for simulated sensor resolutions in the
range of $20\text{\,}\mathrm{p}\mathrm{s}100\text{\,}\mathrm{p}\mathrm{s}$ MIP
timing. Solid curves are the kaon selection efficiencies, while the dashed
curves show the mis-identification probability for $\pi\rightarrow K$. Shaded
areas indicate the statistical uncertainties of the data points. Figure 10:
Pion selection and mis-identification probabilities at $LL_{K}-LL{\pi}>0$ of a
simulated STOPGAP PID system for charged kaons as a function of particle
momentum, shown for simulated sensor resolutions in the range of
$20\text{\,}\mathrm{p}\mathrm{s}100\text{\,}\mathrm{p}\mathrm{s}$ MIP timing.
Solid curves are the kaon selection efficiencies, while the dashed curves show
the mis-identification probability for $\pi\rightarrow K$. Shaded areas
indicate the statistical uncertainties of the data points.

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