[3,4]Shenda Hong 1]School of Biomedical Engineering, Sun Yat-sen University,
Shenzhen 518107, Guangdong, China. 2]Tianjin Key Laboratory of lonic-Molecular
Function of Cardiovascular Disease,Department of Cardiology, Tianjin Institute
of Cardiology, Second Hospital of Tianjin Medical University, Tianjin 300211,
China [3]National Institute of Health Data Science, Peking University, Beijing
100871, China

[4]Institute of Medical Technology, Health Science Center of Peking
University, Beijing 100191, China

# Multi-Channel Masked Autoencoder and Comprehensive Evaluations for
Reconstructing 12-Lead ECG from Arbitrary Single-Lead ECG

Jiarong Chen<EMAIL_ADDRESS>Wanqing Wu<EMAIL_ADDRESS>Tong
Liu<EMAIL_ADDRESS><EMAIL_ADDRESS>[  [  *  *

###### Abstract

In the context of cardiovascular diseases (CVD) that exhibit an elevated
prevalence and mortality, the electrocardiogram (ECG) is a popular and
standard diagnostic tool for doctors, commonly utilizing a 12-lead
configuration in clinical practice. However, the 10 electrodes placed on the
surface would cause a lot of inconvenience and discomfort, while the rapidly
advancing wearable devices adopt the reduced-lead or single-lead ECG to reduce
discomfort as a solution in long-term monitoring. Since the single-lead ECG is
a subset of 12-lead ECG, it provides insufficient cardiac health information
and plays a substandard role in real-world healthcare applications. Hence, it
is necessary to utilize signal generation technologies to reduce their
clinical importance gap by reconstructing 12-lead ECG from the real single-
lead ECG. Specifically, this study proposes a multi-channel masked autoencoder
(MCMA) for this goal. In the experimental results, the visualized results
between the generated and real signals can demonstrate the effectiveness of
the proposed framework. At the same time, this study introduces a
comprehensive evaluation benchmark named ECGGenEval, encompassing the signal-
level, feature-level, and diagnostic-level evaluations, providing a holistic
assessment of 12-lead ECG signals and generative model. Further, the
quantitative experimental results are as follows, the mean square errors of
0.0178 and 0.0658, correlation coefficients of 0.7698 and 0.7237 in the
signal-level evaluation, the average F1-score with two generated 12-lead ECG
is 0.8319 and 0.7824 in the diagnostic-level evaluation, achieving the state-
of-the-art performance. The open-source code is publicly available at
https://github.com/CHENJIAR3/MCMA.

###### keywords:

12-lead ECG signals, Signal Reconstruction, Generated Models, Autoencoder,
Evaluation Benchmark

##  1 Introduction

The cardiovascular disease (CVD)[1, 2] contributes the leading mortality all
around the world. Moreover, the prevalence rate continues to show an upward
trend in the developing areas in the past decades[3], posing a great challenge
for researchers and cardiologists to address. In clinical practice, clinicians
need to adopt some characterization tools[4] to diagnose cardiovascular
disease, and one of the most popular tools is the standard 12-lead
electrocardiogram (ECG). With the great development in deep learning, some
researchers have trained a cardiologist-level model with the 12-lead ECG, like
Ribeiro et al[5]. In conclusion, the 12-lead ECG could provide comprehensive
cardiac information from various views for doctors and classification models,
playing an essential role in cardiac healthcare.

However, the 12-lead ECG signal collection process will put at least 10
electrodes on the user’s surface, which would cause a lot of inconvenience and
discomfort for users, and make long-term cardiac health monitoring difficult.
Up to now, the standard 12-lead ECG is traditionally used in the hospital for
short-term diagnosis, lasting about 1 minute, while the cardiac abnormality
will need long-term monitoring[6] to capture the paroxysmal event. As a
consequence, researchers and markets are trying their best to explore some
user-friendly devices for ECG signals collecting in the real-world
application, including patch[7, 8, 6], smartwatch[9, 10, 11], and armband[12,
13, 14]. These wearable devices can be used to obtain single-lead ECG from the
surface, effectively improving the users’ usage comfort. However, in
comparison with the standard 12-lead ECG, the ambulatory signals could not
provide sufficient cardiac health-related information, since it only observes
the heart’s electrical activity from some limited angles. Although the single-
lead ECG can be used for cardiac abnormality classification, like the lead I
for the Atrial Fibrillation[15], the lead V1 for the Brugada Syndrome[16], and
the lead aVR for the Sinus Bradycardia[17], the full 12-lead ECG is necessary
to provide comprehensive information, matching the knowledge and needs of
clinical physicians, a limited or reduced number of leads ECG from wearable
devices will not work effectively for doctors.

Figure 1: The 12-lead ECG generation process with single-lead ECG, the input
single-lead ECG could be arbitrary, including I, II, III, aVR, aVL, avF, V1,
V2, V3, V4, V5, V6, and this case takes lead I as an example

Based on the mentioned above, it is of great importance to strike a harmonious
balance between clinical effectiveness and application feasibility. On the one
hand, the clinical standard 12-lead electrocardiogram to comprehensively
measure heart health[5]. However, it is challenging to collect the standard
12-lead ECG to complete various health-related tasks, since it will cause
somewhat inconvenience and discomfort with these surface electrodes. On the
other hand, wearable devices have been a popular choice for users, but they
can only collect reduced-lead or single-lead ECG, largely limiting their
clinical importance. Then, many researchers try to reduce the gap between the
reduced-lead and 12-lead ECG, like the challenge proposed by Reyna et al[18].
The challenge asks to access the diagnostic potential of the reduced-lead ECG,
including 6-lead, 4-lead, 3-lead, and 2-lead ECG, which would be compared with
the 12-lead ECG. Nejedly et al[19] adopt the ensemble learning, residual
network, and attention mechanism to finish this task, and they successfully
achieve state-of-the-art performance in this challenge. To this end, some
similar researches[20, 21, 22, 23] propose various deep learning technologies
into the varied-lead ECG signals. It is effective from the arrhythmia
classification task, but these mentioned studies only focus on the
classification performance, only providing an indirect approach to reduce the
gap between the reduced-lead and 12-lead ECG.

Consequently, to overcome these limitations, it is necessary to provide a
direct approach to reduce the gap between the reduce-lead (Specifically,
single-lead) and 12-lead ECG, that is, reconstructing 12-lead ECG with the
reduced-lead ECG[24, 25, 26, 27, 28, 29, 30, 31, 32, 33], as seen in Fig.1.
Although these methods can approximately reconstruct 12-lead ECG with the
limited-lead ECG, there is a research gap to fill for this 12-lead ECG
reconstruction task. Firstly, the traditional generative models usually focus
on the fixed single-lead, and it is difficult to reconstruct 12-lead ECG with
arbitrary single-lead ECG. Secondly, the related works[27, 28, 29, 32, 31, 33,
30] mainly focus on signal-level evaluation, instead of comprehensive
evaluation for this task, and it is known the signal-level evaluation result
will be influenced by various noises. Therefore, the contributions in this
study are as follows:

  * •

A novel 12-lead ECG reconstruction framework, MCMA, is proposed in this study,
and it can convert arbitrary single-lead ECG into a 12-lead ECG.

  * •

A benchmark for 12-lead ECG reconstruction tasks is proposed, ECGGenEval,
including signal-level, feature-level, and diagnostic-level.

  * •

The proposed framework can achieve state-of-the-art reconstruction performance
in the internal and external test sets, with a mean square error of 0.0178 and
a Pearson correlation coefficient of 0.7698.

The following contents will clearly present the study subjects, the proposed
methods and the comprehensive evaluation benchmark for validation, the
experimental results and discussion, and the drawn conclusions.

##  2 Study Subjects

The standard 12-lead ECG is one of the most popular schemes in clinical
practice, which could provide enough cardiac health information. As mentioned,
it is difficult to collect the long-term 12-lead ECG, since it causes a lot of
inconvenience. This section will present the definition of 12-lead ECG,
including time-domain and space-domain definitions. Firstly, a normal ECG
should include P-wave, QRS-complex, and T-wave, representing the corresponding
cardiac activity. For example, the P-wave means the atrial depolarization, if
the abnormal atrial depolarization process exists, there is a change in
P-wave-based ECG. Secondly, the 12-lead ECG needs 10 electrodes on the
surface, and each electrode position in the 12-lead ECG is seen in Table
LABEL:Table:12_lead.

Table 1: The electrode positions in 12-lead ECG Lead | Electrode position
---|---
I | Left Arm, Right Arm
II | Left Foot, Right Arm
III | Left Foot, Left Arm
aVR | Right Arm
aVL | Left Arm
aVF | Left Foot
V1 | 4th intercostal space at the right sternal border
V2 | 4th intercostal space at the left sternal border
V3 | Midpoint between V2 and V4
V4 | 5th intercostal space at the midclavicular line
V5 | Lateral to V4, at the left midaxillary line
V6 | Lateral to V5, at the left midaxillary line

According to Table LABEL:Table:12_lead, three limb leads belong to the bipolar
lead, which requires two electrodes to collect the single-lead ECG. The nine
remaining leads belong to the unipolar lead, and take the Wilson central
terminal as the common reference.

##  3 Data Source

To reconstruct the 12-lead ECG with single-lead ECG in the clinical practice,
this study conducts a large-scale 12-lead ECG datasets, consisting of 28,833
recordings from three public 12-lead ECG datasets, i.e., PTB-XL[45, 46],
CPSC2018[35], and CODE-test[5]. The proposed framework will be trained and
validated with PTB-XL initially, and using two external datasets to further
prove its feasibility.

###  3.1 PTB-XL

In this study, PTB-XL[45, 46] will be used for model training, validating, and
testing. As a large dataset, PTB-XL involves 21,799 clinical 10-second 12-lead
ECG signals, and the sampling frequency is 500Hz. Based on the clinical
standard, this dataset includes 71 kinds of ECG statements. As recommended,
this study will adopt the cross-validation folds, in which the folds from the
1st fold to the 8th fold will be the training set, the 9th fold and the 10th
fold act as the validation set and testing set, respectively. The ratio for
training:validation: and testing is about 8:1:1.

###  3.2 CPSC2018

To demonstrate the advantages and feasibility, CPSC2018[35] is used as an
external testing set since the data distribution and information do not appear
in model training and choosing. CPSC2018 contains 6,877 12-lead ECG, and these
lengths varied from 6 seconds to 60 seconds with 500 Hz in sampling frequency.
This dataset mainly includes a 9-type ECG, which aims to find out the cardiac
arrhythmia detection tool.

###  3.3 CODE-test

The above datasets just focus on similarity evaluation for the generated
signals. This study will establish a benchmark for 12-lead ECG reconstruction.
Therefore, this process requires representative research for 12-lead ECG
classification, like Ribeiro et al[5]. This testing set is named CODE-test,
including 827 12-lead ECG collected from different patients.

###  3.4 Data Distribution

Since the generative model requires the 1024 point as input length, then the
data distribution for two large-scale datasets could be listed as Table
LABEL:Table:ptbxl_cpsc2018.

Table 2: The data description of PTB-XL and CPSC2018 Dataset | Role | Number
---|---|---
| Training Set | 87200
PTB-XL | Validation Set | 10965
| Internal testing set | 11015
CPSC2018 | External testing set | 55999

Table LABEL:Table:ptbxl_cpsc2018 presents the data distribution in PTB-XL and
CPSC2018, including the internal and external testing set, which will be used
for the signal-level and feature-level evaluation. Since CODE-test will be
used in the diagnostic-level evaluation, it is necessary to introduce the ECG
abnormality, as shown in Table LABEL:Table:code_test

Table 3: The data description of CODE-test Abbreviation | Description | Quantity | %
---|---|---|---
1dAVb | 1st degree AV block | 28 | 3.4%
RBBB | right bundle branch block | 34 | 4.1%
LBBB | left bundle branch block | 30 | 3.6%
SB | sinus bradycardia | 16 | 1.9%
AF | atrial fibrillation | 13 | 1.6%
ST | sinus tachycardia | 36 | 4.4%

Based on TableLABEL:Table:code_test, there are six arrhythmia types in this
dataset. It is important for the model to keep or generate pathological
information. Therefore, the classification performance with the real 12-lead
ECG will be adopted as the supremum, and the real single-lead ECG with padding
strategy will be used as the baseline.

##  4 Method

This section will introduce the details of the proposed framework, model
architecture, ECG dataset, and evaluation metric.

###  4.1 MCMA Input & Output

The proposed framework will be named as Multi-Channel Masked Autoencoder
(MCMA), which could mask different 11 leads and remain only a single-lead ECG
to generate the entire 12-lead ECG. The input of MCMA is single-lead ECG,
while the output of MCMA is 12-lead ECG. The signal length is 1024 for MCMA.
In this study, no preprocessing step is used to avoid influencing ECG signals,
like filtering or scaling.

###  4.2 Multi-Channel Configuration

In this study, MCMA, the proposed framework, needs to convert arbitrary
single-lead ECG into the standard 12-lead ECG, and the multi-channel
configuration will be used to reduce training and inference costs. On the one
hand, with the multi-channel configuration, only one model is necessary to
reconstruct 12-lead ECG from arbitrary single-lead ECG, distinguished from
related works, like garg et al[30] focus on utilizing lead II to reconstruct
12-lead ECG, making it difficult for their model to work with other single-
lead ECG as input. On the other hand, unlike Electrocardio panorama[39], the
input ECG is one of the standard 12-lead ECG, and the output is the standard
12-lead ECG. Therefore, the input shape for MCMA is ($1024\times 12$), which
could adapt different single-lead ECG as input.

###  4.3 Model Architecture

For this framework, it is necessary to design a proper model for 12-lead
reconstruction, aiming to learn the effective representation. Firstly, it is
necessary to take into account the locality and uncertainty of features within
the ECG signals and there is no feature alignment in signal preprocessing.
Therefore, the convolutional neural network can largely extract the local
feature, which can play a key module in this 12-lead ECG reconstruction task.
The designed model in MCMA is shown in Fig.2.

Figure 2: The detailed model architecture, a) the proposed model mainly
includes b) MCBlock and c) MCTBlock.

The designed model is mainly motivated by ResNet[40] and UNet[41]. The whole
model can be subdivided into two modules, namely, the downsampling and
upsampling modules, which are composed of the multi-convolution block
(MCBlock) and multi-convolution-transpose block (MCTBlock), respectively. The
kernel size is 13 and the window size is 2. The activation function is GELU.
To improve the gradient stability, layer normalization (LN) and instance
normalization (IN) are used in each block. The skip connections could speed up
the convergence rate of the model and improve the representation ability. At
the same time, the basic training recipe is provided in Table
LABEL:Table:hyperparamter, including some hyperparamaters settings, like batch
size and learning rate.

Table 4: The hyperparameters configuration  hyperparameters |  configuration
---|---
Batch size |  256
Epochs |  100
Signal Length |  1024
Optimizer |  Adam
Learning rate |  1e-3

Table LABEL:Table:hyperparamter will be mainly used in model training process,
further for reconstructing 12-lead ECG with single-lead ECG.

###  4.4 Training MCMA

####  4.4.1 Padding Strategy

Since the proposed framework will be used to reconstruct 12-lead ECG with
arbitrary single-lead ECG, and it is necessary to adopt a channel padding
strategy in this study. To retain the space information for each single-lead
ECG, the zero-padding strategy is proposed in this study. When the single-
channel ECG will be processed into the 12-channel format, while the other
channels will be set as zeros, as seen in Eq.1.

${P(ecg_{12},i)=I_{z}\times ecg_{12}[i]}$ (1)

In Eq.1, the shape of index matrix for zero-padding is $12\times 1$,
$I_{z}(i)=1$ with other elements being zeros. Specifically, the output shape
equals the input shape, and the shape of $ecg_{12}$ is $12\times N$, then the
shape of $ecg_{12}[i]$ is $1\times N$, so the output shape also is $12\times
N$. With zero-padding, MCMA could adaptively solve different inputs. To
highlight its advantages, the 12 copies for the single-lead ECG will be as a
comparison, named as the copy-padding strategy. The index matrix for copy-
padding strategy, $I_{c}$, all elements are 1. At the same time, the arbitrary
input lead and the fixed lead (lead I) will be compared. In addition, the
12-lead ECG is provided in model training, and the padding strategy aims to
mask the original 11-lead ECG with zeros or the remaining single-lead ECG in
the standard 12-lead ECG. Meanwhile, only the single-lead ECG exists in the
real-world application process, it should be with the padding strategy for the
proposed framework.

####  4.4.2 Loss Function

The generative models mainly involve autoencoder(AE)[42], generative
adversarial network(GAN)[38], diffusion model[43]. Although the diffusion
model has shown its great potential and ability in various tasks, the sampling
speed[44] is challenging. GAN[33, 32] and AE[30] have been studied by the
previous research works. In this study, the autoencoder will be considered as
a feasible solution for this 12-lead ECG reconstruction task, due to the
training stability. Further, the proposed framework will compare with the GAN-
based[33, 32] and AE-based[30] methods.

The autoencoder could extract the latent representation with the raw data and
convert the latent representation into the target output. The common loss
function for autoencoder, $L$, can be shown in Eq.2.

$L=||ecg_{12}-AE(ecg_{1})||=||ecg_{12}-AE(P(ecg_{12},i))||$ (2)

In Eq.2, $AE$ denotes the autoencoder, and the 12-lead and single-lead ECG
signals are represented by $ecg_{12}$ and $ecg_{1}$. $P$ means the padding
strategy, including zero-padding and copy-padding. Additionally, $i$ means the
index, varying from 1 to 12.

###  4.5 Inferencing MCMA

After the training process, MCMA would be used in real-world applications,
i.e., the inferencing (testing) process. Firstly, the single-lead ECG should
be provided as the input of MCMA. Secondly, the zeros-padding strategy will be
used in this process, like Eq.1, but only the single-lead ECG inputs. Thirdly,
the trained autoencoder could generate the reconstucted 12-lead ECG, which
could be used to evaluation or downstream tasks. Then, the application process
for MCMA could be seen in Eq.3.

$g_{ecg}=AE(I_{z}\times ecg_{1})$ (3)

In Eq.3, $g_{ecg}$ is the generated 12-lead ECG with MCMA, $ecg_{1}$ is the
single-lead ECG collected by wearable devices, $I_{z}$ could convert $ecg_{1}$
into the input of $AE$.

###  4.6 Comprehensive Evaluations

As mentioned, to fill the evaluation gap in this research field, this study
will introduce a comprehensive evaluation benchmark, named as ECGGenEval.
Specifically, this benchmark will contain 3 kinds of evaluation metrics, that
is, signal-level, feature-level and diagnostic-level. The following contents
will introduce the detailed evaluation metrics respectively.

####  4.6.1 Signal-Level

This study adopt the Pearson correlation coefficient ($PCC$) and mean square
error ($MSE$) in the signal-level evaluation. It is necessary to define the
real and generated ECG signal as $r_{ecg}$ and $g_{ecg}$. Then, the
definitions for PCC and MSE are shown in Eq.4 and Eq.5.

$PCC({r_{ecg}},{g_{ecg}})=\frac{\mu({r_{ecg}}\times{g_{ecg}})-\mu({r_{ecg}})\mu({g_{ecg}})}{\sigma({r_{ecg}})\sigma({g_{ecg}})}$
(4) $MSE({r_{ecg}},g_{ecg})=\mu(({{r_{ecg}}-{g_{ecg}}})^{2})$ (5)

In these equations, as Eq.4 and Eq.5, $\mu(*)$ and $\sigma(*)$ denotes the
mean value and standard deviation, respectively. The $PCC$ varies from -1 to
1, and the $MSE$ is at least bigger than 0. The relationship between $MSE$ and
generation performance is positively related, while the relationship between
$MSE$ and generation performance is negatively related. Therefore, based on
the signal-level evaluation, a better generative model should be with a higher
$PCC$ and lower $MSE$ from two different aspects.

####  4.6.2 Feature-Level

Although the signal-level evaluation is established, since the original ECG
signals may be subject to varying degrees of influence from ambient noise,
some metrics in other levels are needed for objectively evaluating the
reconstruction performance. This section will introduce the heart rate for the
feature-level evaluation. It is known that R-waves in real 12-lead ECG signals
will theoretically occur simultaneously, and the generated signals should meet
this requirement. Firstly, the mean heart rate ($MHR$) at the $j$th lead could
be calculated, as shown in Eq.6.

$MHR(j)=\frac{60\times(n-1)}{\sum_{i=1}^{n-1}{(R(i+1,j)-R(i,j))}}$ (6)

In Eq.6, the $i$th detected R-wave in $j$th lead will be denoted as $R(i,j)$,
and it is expressed in seconds. Therefore, $MHR$ could represent the heartbeat
per minute. Since the 12 heart rates are obtained, it is time to measure the
heart rate consistency. In addition, some ECG signals collected in real-world
applications will be difficult for R-wave detection of their enormous noise,
so it is unnecessary to choose any lead as a reference. Based on the 12 $MHR$
from different 12-lead ECG, the average value $MMHR$ could be computed with
Eq.7. Further, the feature-level evaluation in this 12-lead ECG reconstruction
task will involve standard deviation ($SD$), Range (the difference between
maximum and minimum), and coefficient of variation ($CV$), and they are
expressed as $MHR_{SD}$, $MHR_{Range}$ and $MHR_{CV}$ respectively. The
calculation processes could be seen in Eq.8, Eq.9 and Eq.10, respectively.

${MMHR}=\frac{1}{12}\sum_{j=1}^{12}(MHR(j)$ (7)
$MHR_{SD}=\sqrt{\frac{1}{12}\sum_{j=1}^{12}(MHR(j)-MMHR)^{2}}$ (8)
$MHR_{Range}=\max(MHR)-\min(MHR)$ (9) $MHR_{CV}=\frac{MHR_{SD}}{MMHR}$ (10)

The reference values are from the original 12-lead ECG, which might be a bit
noisy. These feature-level values should be small if the inter-lead heart
rates are consistent. Additionally, the generated signals could provide a
smaller result, for the generative models can reduce the noise.

####  4.6.3 Diagnostic-Level

Further, this study also adopts the diagnostic-level evaluation for this
12-lead ECG reconstruction task. In the real-world application, there are some
trained classifiers with 12-lead ECG as input, which are difficult to address
some limited-lead ECG. The proposed framework could convert the limit-lead
(even single-lead) ECG into 12-lead ECG, which bridges the limited-lead ECG to
the trained classifiers. Therefore, it is necessary to evaluate the
classification performance with the generated 12-lead ECG. The representative
classification metric will be used in this study, mainly including the
precision ($Pre$), recall ($Rec$), specificity ($Spe$) and F1 score, as shown
in literature[5]. The classification metric will be related to the True
Positive (TP), True Negative (TN), False Positive (FP) and False Negative (FN)
for a special class, as seen in Eq.11, Eq.12, Eq.13 and Eq.14.

${Pre}=\frac{TP}{TP+FP}$ (11) ${Rec}=\frac{TP}{TP+FN}$ (12)
${Spe}=\frac{TN}{TN+FP}$ (13) ${F1}=\frac{2\times TP}{2\times TP+FN+FP}$ (14)

At the same time, the original classification performance with the real
12-lead ECG will be set as the standard reference, and the generated 12-lead
ECG with other methods will be used in the result comparison.

##  5 Results and Discussion

This study adopts a novel generative model to reconstruct 12-lead ECG with the
single-lead ECG, using an autoencoder for 12-lead ECG reconstruction. Firstly,
the training process details can be illustrated as seen in Fig.3.

Figure 3: The mean square error and Pearson correlation coefficient in the
training process. The red circle means training loss, the blue star is
validation loss, the black circle means training Pearson correlation
coefficient(PCC), and the black star means validation Pearson correlation
coefficient(PCC).

As seen in Fig.3, with the training epochs increasing, the mean square error
will be smaller and smaller, while the Pearson correlation coefficient will be
bigger and bigger. The training set will be used to weight updating, and the
validation set will be used for model selection. Based on the training
process, the saved model can be with 0.038 in mean square error and 0.7709 in
Pearson correlation coefficient.

###  5.1 Case Study

Further, to show the advantages of the proposed framework, the generated and
real 12-lead ECG should be clearly shown, in Fig.4, in which the generated and
the real signals are colored blue and red.

Figure 4: The 12-lead ECG reconstruction performance in the internal testing
set PTB-XL, the red lines are the real signals while the blue lines represent
the generated signals.

Fig.4 demonstrates the great generation ability of the proposed framework. For
example, the average $MSE$ and $PCC$ between the generated and real 12-lead
ECG is 0.0032 and 0.9560, and it is concluded that the generator can generate
12-lead ECG with single-lead ECG. Besides the internal testing dataset (i.e.,
PTB-XL), the external testing dataset’s (i.e., CPSC2018) reconstruction
performance will demonstrate the proposed framework’s advantages from another
aspect, as seen in Fig.5.

Figure 5: The 12-lead ECG reconstruction performance in the external testing
set CPSC2018, the red lines are the real signals while the blue lines
represent the generated signals. Figure 6: The generated and real 10-second
12-lead ECG, demonstrating its advantages for variable-duration ECG
reconstruction, the red lines are the real signals while the blue lines
represent the generated signals.

Based on the experimental result provided in Fig.4 and Fig.5, it is shown that
the multi-channel masked autoencoder (MCMA) could be used to reconstruct the
12-lead ECG with single-lead ECG. In the clinical practice, the ECG collected
by wearable devices could be with different signal length, instead of the
fixed length. It is necessary to demonstrate the proposed framework cloud also
works with the variable-duration ECG signals, and the signal reconstruction
result with 10-second ECG is seen in Fig.6. In this case, the 5000 points
should be filled with the extra 120 points, and it could be as the 5
individual samples for MCMA to reconstruct 12-lead ECG with single-lead ECG as
input.

Table 5: The signal-level evaluation of mean square error (MSE) and Pearson correlation coefficient (PCC) between the generated and real 12-lead ECG in the internal testing set, PTB-XL Input Output | I | II | III | aVR | aVL | aVF | V1 | V2 | V3 | V4 | V5 | V6 | Mean
---|---|---|---|---|---|---|---|---|---|---|---|---|---
| MSE
I | 0.0035 | 0.0099 | 0.0124 | 0.0035 | 0.0058 | 0.0104 | 0.0151 | 0.0465 | 0.0449 | 0.0306 | 0.0200 | 0.0142 | 0.0181
II | 0.0076 | 0.0036 | 0.0113 | 0.0031 | 0.0087 | 0.0056 | 0.0167 | 0.0492 | 0.0480 | 0.0296 | 0.0183 | 0.0132 | 0.0179
III | 0.0071 | 0.0079 | 0.0068 | 0.0059 | 0.0053 | 0.0053 | 0.0173 | 0.0505 | 0.0543 | 0.0393 | 0.0249 | 0.0171 | 0.0201
aVR | 0.0055 | 0.0057 | 0.0166 | 0.0019 | 0.0091 | 0.0093 | 0.0151 | 0.0471 | 0.0443 | 0.0271 | 0.0157 | 0.0115 | 0.0174
aVL | 0.0049 | 0.0098 | 0.0081 | 0.0053 | 0.0042 | 0.0076 | 0.0165 | 0.0485 | 0.0499 | 0.0368 | 0.0238 | 0.0164 | 0.0193
aVF | 0.0080 | 0.0050 | 0.0082 | 0.0048 | 0.0071 | 0.0044 | 0.0174 | 0.0502 | 0.0523 | 0.0354 | 0.0225 | 0.0156 | 0.0192
V1 | 0.0071 | 0.0099 | 0.0175 | 0.0047 | 0.0093 | 0.0114 | 0.0094 | 0.0366 | 0.045 | 0.0361 | 0.0228 | 0.0153 | 0.0187
V2 | 0.0088 | 0.0108 | 0.0171 | 0.0059 | 0.0101 | 0.0114 | 0.0134 | 0.0215 | 0.0301 | 0.0351 | 0.0268 | 0.0179 | 0.0174
V3 | 0.0082 | 0.0106 | 0.0179 | 0.0054 | 0.0098 | 0.0116 | 0.0156 | 0.0315 | 0.0171 | 0.0229 | 0.0225 | 0.0169 | 0.0158
V4 | 0.0073 | 0.0089 | 0.0162 | 0.0044 | 0.0095 | 0.0103 | 0.0165 | 0.0427 | 0.0299 | 0.0128 | 0.0149 | 0.0137 | 0.0156
V5 | 0.0067 | 0.0075 | 0.0161 | 0.0036 | 0.0093 | 0.0096 | 0.0164 | 0.047 | 0.0413 | 0.0198 | 0.0096 | 0.0104 | 0.0164
V6 | 0.0065 | 0.0070 | 0.0161 | 0.0033 | 0.0093 | 0.0094 | 0.0159 | 0.0479 | 0.0459 | 0.0252 | 0.0125 | 0.0084 | 0.0173
Mean | 0.0068 | 0.0081 | 0.0137 | 0.0043 | 0.0081 | 0.0089 | 0.0154 | 0.0433 | 0.0419 | 0.0292 | 0.0195 | 0.0142 | 0.0178
| PCC
I | 0.9759 | 0.7604 | 0.5216 | 0.9116 | 0.813 | 0.5204 | 0.832 | 0.741 | 0.7358 | 0.8096 | 0.854 | 0.8676 | 0.7786
II | 0.8349 | 0.9809 | 0.6089 | 0.9264 | 0.6254 | 0.8544 | 0.8045 | 0.7165 | 0.7111 | 0.8212 | 0.8761 | 0.8917 | 0.8043
III | 0.8345 | 0.8017 | 0.9618 | 0.8097 | 0.8559 | 0.8715 | 0.7884 | 0.7012 | 0.6503 | 0.7276 | 0.7919 | 0.8111 | 0.8005
aVR | 0.9048 | 0.8996 | 0.3094 | 0.9811 | 0.6043 | 0.6031 | 0.8346 | 0.7358 | 0.7444 | 0.8440 | 0.9035 | 0.9195 | 0.7737
aVL | 0.9125 | 0.7406 | 0.8367 | 0.8327 | 0.9615 | 0.6851 | 0.8069 | 0.7233 | 0.6877 | 0.7505 | 0.8048 | 0.8219 | 0.797
aVF | 0.8105 | 0.9148 | 0.8306 | 0.8516 | 0.7156 | 0.9672 | 0.7871 | 0.7045 | 0.6667 | 0.7599 | 0.8177 | 0.84 | 0.8055
V1 | 0.8396 | 0.7501 | 0.2350 | 0.8570 | 0.5780 | 0.4618 | 0.9733 | 0.8154 | 0.7181 | 0.7524 | 0.8117 | 0.8396 | 0.7193
V2 | 0.7905 | 0.7131 | 0.2801 | 0.8070 | 0.5498 | 0.4605 | 0.867 | 0.9732 | 0.8532 | 0.7654 | 0.7691 | 0.7911 | 0.7183
V3 | 0.8100 | 0.7256 | 0.2358 | 0.8265 | 0.5509 | 0.4640 | 0.8231 | 0.875 | 0.9867 | 0.8831 | 0.8244 | 0.8157 | 0.7351
V4 | 0.8405 | 0.7895 | 0.3260 | 0.8697 | 0.5692 | 0.5464 | 0.8066 | 0.7765 | 0.8657 | 0.9856 | 0.9164 | 0.8805 | 0.7644
V5 | 0.8649 | 0.8346 | 0.327 | 0.9063 | 0.5857 | 0.5831 | 0.8107 | 0.7396 | 0.7713 | 0.9163 | 0.9833 | 0.9463 | 0.7724
V6 | 0.8683 | 0.8515 | 0.3227 | 0.9174 | 0.5872 | 0.5981 | 0.8199 | 0.7273 | 0.7299 | 0.8667 | 0.9474 | 0.9804 | 0.7681
Mean | 0.8572 | 0.8135 | 0.4830 | 0.8748 | 0.6664 | 0.6346 | 0.8295 | 0.7691 | 0.7601 | 0.8235 | 0.8584 | 0.8671 | 0.7698
|  |  |  |  |  |  |  |  |  |  |  |  |
Table 6: The signal-level evaluation of mean square error (MSE) and Pearson correlation coefficient (PCC) between the generated and real 12-lead ECG in the external testing set, CPSC2018 Input Output | I | II | III | aVR | aVL | aVF | V1 | V2 | V3 | V4 | V5 | V6 | Mean
---|---|---|---|---|---|---|---|---|---|---|---|---|---
| MSE
I | 0.0256 | 0.0334 | 0.0345 | 0.0274 | 0.0269 | 0.0326 | 0.0567 | 0.0914 | 0.1022 | 0.1032 | 0.1179 | 0.1384 | 0.0659
II | 0.0302 | 0.0268 | 0.0320 | 0.0263 | 0.0303 | 0.0272 | 0.0605 | 0.0971 | 0.1051 | 0.1034 | 0.1178 | 0.1379 | 0.0662
III | 0.0307 | 0.0310 | 0.0275 | 0.0293 | 0.0267 | 0.0272 | 0.0609 | 0.0989 | 0.1133 | 0.1151 | 0.1274 | 0.1439 | 0.0693
aVR | 0.0289 | 0.0299 | 0.0383 | 0.0241 | 0.0314 | 0.0313 | 0.0566 | 0.0937 | 0.1016 | 0.101 | 0.1155 | 0.1367 | 0.0657
aVL | 0.0284 | 0.0345 | 0.0298 | 0.0296 | 0.0247 | 0.0305 | 0.0592 | 0.0943 | 0.1106 | 0.1154 | 0.1284 | 0.1449 | 0.0692
aVF | 0.0315 | 0.0282 | 0.0287 | 0.0283 | 0.0286 | 0.0262 | 0.0626 | 0.0996 | 0.1111 | 0.1110 | 0.1249 | 0.1423 | 0.0686
V1 | 0.0309 | 0.0346 | 0.0386 | 0.0281 | 0.0314 | 0.0337 | 0.0455 | 0.0802 | 0.1035 | 0.1133 | 0.1277 | 0.1438 | 0.0676
V2 | 0.0315 | 0.0354 | 0.0387 | 0.0299 | 0.0313 | 0.0341 | 0.0544 | 0.0558 | 0.0811 | 0.1065 | 0.1295 | 0.1463 | 0.0645
V3 | 0.0309 | 0.0342 | 0.0406 | 0.0291 | 0.0316 | 0.0335 | 0.0579 | 0.0684 | 0.0638 | 0.0907 | 0.1213 | 0.1426 | 0.0620
V4 | 0.0303 | 0.0327 | 0.0406 | 0.0279 | 0.0319 | 0.0333 | 0.0596 | 0.0833 | 0.0787 | 0.0772 | 0.1120 | 0.1380 | 0.0621
V5 | 0.0296 | 0.0323 | 0.0400 | 0.0269 | 0.0317 | 0.0332 | 0.059 | 0.0913 | 0.0943 | 0.0895 | 0.1000 | 0.1339 | 0.0635
V6 | 0.0296 | 0.0322 | 0.0396 | 0.0266 | 0.0318 | 0.0331 | 0.0589 | 0.0955 | 0.1029 | 0.0977 | 0.1104 | 0.1247 | 0.0652
Mean | 0.0298 | 0.0321 | 0.0357 | 0.0278 | 0.0299 | 0.0313 | 0.0577 | 0.0875 | 0.0974 | 0.1020 | 0.1194 | 0.1395 | 0.0658
| PCC
I | 0.9671 | 0.7713 | 0.4671 | 0.8942 | 0.7086 | 0.5503 | 0.7277 | 0.6537 | 0.6914 | 0.8072 | 0.8586 | 0.8681 | 0.7471
II | 0.7900 | 0.979 | 0.5957 | 0.9285 | 0.4784 | 0.8804 | 0.6703 | 0.6045 | 0.6693 | 0.8075 | 0.8614 | 0.8741 | 0.7616
III | 0.7669 | 0.8115 | 0.9573 | 0.7981 | 0.8078 | 0.8752 | 0.6609 | 0.5923 | 0.5994 | 0.7108 | 0.7646 | 0.7821 | 0.7606
aVR | 0.8715 | 0.9110 | 0.2685 | 0.9767 | 0.4172 | 0.6680 | 0.7228 | 0.6434 | 0.7084 | 0.8395 | 0.8985 | 0.9147 | 0.7367
aVL | 0.8412 | 0.7250 | 0.8048 | 0.7829 | 0.9460 | 0.6755 | 0.6875 | 0.6341 | 0.6238 | 0.7113 | 0.7594 | 0.7756 | 0.7473
aVF | 0.7409 | 0.9168 | 0.841 | 0.8418 | 0.6257 | 0.968 | 0.6339 | 0.5812 | 0.6184 | 0.7431 | 0.7870 | 0.8031 | 0.7584
V1 | 0.7742 | 0.7329 | 0.2269 | 0.8151 | 0.3979 | 0.4976 | 0.9559 | 0.7495 | 0.6783 | 0.7281 | 0.7662 | 0.7907 | 0.6761
V2 | 0.7301 | 0.6853 | 0.2112 | 0.7685 | 0.3921 | 0.4459 | 0.7724 | 0.9631 | 0.8494 | 0.7754 | 0.7501 | 0.7500 | 0.6745
V3 | 0.7541 | 0.7376 | 0.1042 | 0.8111 | 0.3556 | 0.5020 | 0.7073 | 0.8577 | 0.9825 | 0.9000 | 0.8303 | 0.8107 | 0.6961
V4 | 0.7838 | 0.7939 | 0.1143 | 0.8595 | 0.3475 | 0.5326 | 0.678 | 0.7320 | 0.8797 | 0.9833 | 0.9141 | 0.8781 | 0.7081
V5 | 0.8218 | 0.8115 | 0.1602 | 0.8938 | 0.3788 | 0.5447 | 0.689 | 0.6655 | 0.7591 | 0.914 | 0.9787 | 0.9374 | 0.7129
V6 | 0.8299 | 0.8147 | 0.1884 | 0.9052 | 0.3801 | 0.5535 | 0.691 | 0.6276 | 0.6944 | 0.8567 | 0.9353 | 0.9757 | 0.7044
Mean | 0.8060 | 0.8075 | 0.4116 | 0.8563 | 0.5196 | 0.6411 | 0.7164 | 0.6921 | 0.7295 | 0.8147 | 0.8420 | 0.8467 | 0.7237
|  |  |  |  |  |  |  |  |  |  |  |  |

To evaluate the 12-lead ECG reconstruction performance for the proposed
framework, a comprehensive evaluation benchmark is built in the mentioned
content, named ECGGenEval. Therefore, the experimental results for MCMA are
calculated in this section with the proposed benchmark, ECGGenEval, including
the signal-level, feature-level, and diagnostic-level evaluation.

###  5.2 Signal-Level

First of all, the signal-level evaluation is the primary evaluation metric,
such as MSE and PCC. Unlike the traditional methods, this scheme has the
advantage that arbitary single-lead ECG can be output to 12-lead ECG without
training multiple generative models, effectively reducing the model training
cost. The experimental results of MSE and PCC are shown in Table 5, where the
horizontal direction represents the output and the vertical direction
represents the input. Besides, the reconstruction performance in the external
dataset, CPSC2018, is seen in Table 6.

Based on the mentioned experimental results, it is known that the proposed
framework could reconstruct high-fidelity 12-lead ECG with single-lead ECG.
The average MSE and PCC in PTB-XL are 0.0178 and 0.7698, while the average MSE
and PCC in CPSC2018 are 0.0658 and 0.7237, respectively. The reconstruction
performance in the internal and external testing dataset could demonstrate its
advantages, and MCMA could reconstruct the standard 12-lead ECG with arbitrary
single-lead ECG as input. Therefore, the proposed method can provide a
feasible solution when collecting the standard 12-lead ECG is inconvenient and
difficult, like remote cardiac healthcare.

###  5.3 Feature-Level

To avoid the noise influence, and meet the clinical requirement, this study
proposes the feature-level evaluation metric, including the standard deviation
$MHR_{SD}$, Range $MHR_{Range}$ and coefficient of variation $MHR_{CV}$. The
feature-level evaluation results in the internal testing set PTB-XL and
external testing set CPSC2018 are shown in Table 7 and Table 8, respectively.
Since the proposed method can convert arbitary single-lead ECG into 12-lead
ECG, these tables will involve 13 groups of experimental results, the first
group will be the reference value as the original 12-lead ECG input.

Table 7: The feature-level evaluation for the generated and real 12-lead ECG in PTBXL Input Metric | $MHR_{SD}$ | $MHR_{CV}$ | $MHR_{Range}$
---|---|---|---
Original | 2.2137 | 3.21% | 7.2195
I | 1.6276 | 2.41% | 5.0632
II | 1.3492 | 2.00% | 4.0276
III | 1.6850 | 2.43% | 5.1826
aVR | 1.3884 | 2.09% | 4.1997
aVL | 1.5817 | 2.31% | 4.8872
aVF | 1.4986 | 2.19% | 4.5079
V1 | 1.3668 | 2.01% | 4.1093
V2 | 1.4561 | 2.12% | 4.3951
V3 | 1.4063 | 2.06% | 4.2434
V4 | 1.3385 | 1.98% | 4.0322
V5 | 1.3796 | 2.04% | 4.1673
V6 | 1.3571 | 2.02% | 4.1031
Mean | 1.4529 | 2.14% | 4.4099
|  |  |

Table 7 demonstrates that the heart rate estimation in different leads is
similar in the generated 12-lead ECG and better than the original 12-lead ECG.
Normally, the estimated heart rate from the real 12-lead ECG might be
different, for the channel-special noise existing, while the estimated value
should be the same theoretically. At the same time, the optimal result is from
the generated 12-lead ECG by lead V4 ECG. In this experiment, the R-peak
recognition algorithm[47] might influence the experimental result.

Table 8: The feature-level evaluation for the generated and real 12-lead ECG in CPSC2018 Input Metric | $MHR_{SD}$ | $MHR_{CV}$ | $MHR_{Range}$
---|---|---|---
Original | 2.1313 | 2.65% | 7.1267
Lead I | 1.3633 | 1.81% | 4.3808
Lead II | 0.9823 | 1.33% | 3.0902
Lead III | 1.3029 | 1.73% | 4.1343
aVR | 1.0209 | 1.39% | 3.2029
aVL | 1.3417 | 1.77% | 4.312
aVF | 1.1825 | 1.58% | 3.7303
V1 | 1.1336 | 1.52% | 3.5885
V2 | 1.1692 | 1.57% | 3.6568
V3 | 1.1199 | 1.51% | 3.5077
V4 | 1.0807 | 1.49% | 3.3710
V5 | 1.0963 | 1.50% | 3.4172
V6 | 1.0997 | 1.51% | 3.4346
Mean | 1.1578 | 1.56% | 3.6522
|  |  |

Based on the experimental result on Table 7 and Table 8, the conclusion can be
drawn as following. For CPSC2018, the optimal result is from the generated
12-lead ECG by lead II ECG. The generated 12-lead ECG from arbitary single-
lead ECG could produce a good heart rate consistency in different leads, and
it can even be better than the original 12-lead ECG in some cases, due to the
ECG signal denoising function in the proposed framework. Therefore, the
feature-level evaluation can demonstrate the advantages of the MCMA.
Additionally, the ECG morphological features in the single-lead would like to
be calculated, demonstrating the similarity and consistency in the generated
and real ECG signals.

Taking lead I as example, Table 9 shows the difference between the generated
signals from 12 different inputs and the real ECG, including the Heart rate
(HR, unit: bpm), P_amplitude (P_amp, unit: mv), P_duration (P_dur, unit: ms),
PR_interval (PR, unit: ms), QRS_amplitude (QRS_amp, unit: unit: mv),
QRS_duration (QRS_dur, unit: ms), T_amplitude (T_amp, unit: mv), ST (unit:
ms), QT_interval (QT, unit: ms), QTc (unit: ms), and Heart rate variation
(unit: ms). In this table, amp and dur represent the amplitude and duration,
bpm means beat per minute, while ms and mv are millisecond and millivolt. As a
reference, the calculated morphological feature values for the original lead I
ECG are 74.2593bpm, 0.1159mv, 118.9081ms, 173.9268ms, 0.8535mv, 92.2338ms,
0.2123mv, 124.9686ms, 410.7288ms, 452.4418ms, 68.8162ms. Since the proposed
framework could convert arbitary single-lead ECG into 12-lead ECG, Table 9
involves 12 groups of experimental result, including lead I ECG.

Table 9: The feature-level evaluation of absolute and relative morphological feature difference between the generated and original lead I ECG  Input Metric | HR | P_amp | P_dur | PR | QRS_amp | QRS_dur | T_amp | ST | QT | QTc | HRV
---|---|---|---|---|---|---|---|---|---|---|---
I | 0.5718 | 0.0369 | 7.1689 | 6.9264 | 0.2594 | 3.6948 | 0.0686 | 10.1397 | 10.6262 | 12.53 | 12.945
% | 0.83% | 40.59% | 6.67% | 4.02% | 34.89% | 3.99% | 38.58% | 9.29% | 2.72% | 2.87% | 29.23%
II | 0.6144 | 0.0402 | 10.3392 | 11.0876 | 0.2876 | 8.495 | 0.0777 | 21.1166 | 18.8347 | 21.7852 | 15.5677
% | 0.89% | 42.14% | 9.79% | 6.51% | 43.83% | 9.00% | 45.76% | 16.47% | 4.57% | 4.72% | 33.01%
III | 0.6612 | 0.0377 | 9.8265 | 10.2947 | 0.2861 | 7.8738 | 0.0744 | 18.8939 | 17.3506 | 19.8629 | 16.1653
% | 0.98% | 37.87% | 9.23% | 6.02% | 43.01% | 8.32% | 42.44% | 15.48% | 4.25% | 4.34% | 35.83%
aVR | 0.7057 | 0.0393 | 9.5391 | 10.0386 | 0.2857 | 7.6208 | 0.074 | 17.9166 | 17.3683 | 20.2003 | 16.4932
% | 1.05% | 39.81% | 9.07% | 5.93% | 42.57% | 8.11% | 41.73% | 14.48% | 4.24% | 4.41% | 42.87%
aVL | 0.7025 | 0.0412 | 10.0827 | 10.3801 | 0.2852 | 8.5999 | 0.0801 | 22.6017 | 19.9419 | 22.7184 | 16.0154
% | 1.02% | 43.13% | 9.55% | 6.01% | 42.94% | 9.29% | 48.01% | 16.92% | 4.86% | 4.93% | 43.83%
aVF | 0.8456 | 0.0412 | 10.584 | 11.6172 | 0.2782 | 8.0677 | 0.087 | 24.6724 | 22.678 | 25.9355 | 20.782
% | 1.23% | 42.18% | 10.00% | 6.58% | 41.67% | 8.61% | 54.04% | 19.48% | 5.52% | 5.62% | 84.92%
V1 | 0.6776 | 0.0406 | 8.4764 | 8.8283 | 0.2817 | 7.148 | 0.0719 | 15.8229 | 14.2657 | 16.4709 | 14.8274
% | 0.99% | 43.68% | 7.89% | 5.15% | 41.23% | 7.66% | 42.11% | 12.52% | 3.49% | 3.61% | 31.62%
V2 | 0.8388 | 0.0377 | 9.4705 | 10.4393 | 0.2694 | 6.6889 | 0.0697 | 17.5462 | 16.8356 | 19.6939 | 18.2729
% | 1.23% | 42.29% | 8.84% | 5.99% | 38.14% | 7.09% | 41.84% | 15.76% | 4.18% | 4.35% | 61.52%
V3 | 0.8084 | 0.0425 | 11.2461 | 11.3603 | 0.2804 | 8.8347 | 0.0921 | 25.7338 | 22.9555 | 26.3674 | 20.4351
% | 1.19% | 42.60% | 10.94% | 6.56% | 42.56% | 9.59% | 57.04% | 19.09% | 5.60% | 5.75% | 63.80%
V4 | 0.6599 | 0.0404 | 10.7843 | 10.4909 | 0.294 | 8.0254 | 0.079 | 23.2426 | 21.0381 | 24.2838 | 16.5114
% | 0.98% | 41.75% | 10.17% | 6.08% | 45.63% | 8.59% | 46.96% | 18.18% | 5.13% | 5.25% | 36.52%
V5 | 0.663 | 0.0416 | 11.7688 | 11.911 | 0.2909 | 9.1403 | 0.0827 | 24.2244 | 21.3619 | 24.411 | 16.0495
% | 0.99% | 43.73% | 11.33% | 6.90% | 45.50% | 9.68% | 51.35% | 18.46% | 5.18% | 5.27% | 31.43%
V6 | 0.6571 | 0.0421 | 11.4455 | 11.8411 | 0.2885 | 8.8592 | 0.0827 | 23.5203 | 21.4196 | 24.5041 | 15.9346
% | 0.95% | 45.04% | 11.04% | 6.94% | 44.48% | 9.43% | 50.78% | 18.10% | 5.24% | 5.33% | 30.94%
|  |  |  |  |  |  |  |  |  |  |

Based on Table 9, the ECG morphological features of the generated ECG are
extremely close to that of the original real ECG. The duration similarity is
better than amplitude similarity. Like the heart rate, the maximum difference
is 0.8456 and 1.23% in lead aVF, which largely presents the feasibility of the
proposed framework. Besides, it is necessary to study other leads with some
cutting-edge technologies, and lead I is one of the mostly used cases in the
standard 12-lead ECG. Besides the R-peak, it is difficult to find the
morphological features with other lead ECG, especially the subtle feature.
Therefore, ECGGenEval focuses on the mean heart rate in different leads ECG
for feature-level evaluation, like Table 8 and Table 7.

###  5.4 Diagnostic-Level

The downstream task can demonstrate the clinical importance of the generated
12-lead ECG, and the classifier is trained and validated by Ribeiro et al[5].
The proposed framework could generate 12-lead ECG with single-lead ECG, and
the single-lead ECG could not be processed by a classifier trained with
12-lead ECG. For example, the classification performance of the generated
12-lead ECG with lead I completed by the pretrained model[5] is expressed in
Table 10.

Table 10: The diagnostic-level evaluation of classification performance with the generated 12-lead ECG from lead I ECG Class Metric | $Pre$ | $Rec$ | $Spe$ | $F1$
---|---|---|---|---
1dAVb | 0.8696 | 0.7143 | 0.9962 | 0.7843
RBBB | 0.8788 | 0.8529 | 0.9950 | 0.8657
LBBB | 1.0000 | 0.9000 | 1.0000 | 0.9474
SB | 0.6957 | 1.0000 | 0.9914 | 0.8205
AF | 0.6667 | 0.6154 | 0.9951 | 0.6400
ST | 0.9211 | 0.9459 | 0.9962 | 0.9333
Mean | 0.8386 | 0.8381 | 0.9956 | 0.8319
|  |  |  |

As Table 10, the classifier could adopt the generated 12-lead ECG for
arrhythmia classification. The average F1-score over 6 classes is 0.8319.
Then, it is proven that MCMA could convert the single-lead ECG into the
12-lead ECG, and the generated 12-lead ECG can retain the pathological
information, and it is different to the signal-level and feature-level
evaluation. Therefore, with the multi-channel masked autoencoder, it is
possible to complete arrhythmia classification with single-lead ECG, like lead
I ECG in Table 10. Additionally, the proposed framework can reconstruct
12-lead ECG with arbitary single-lead ECG. Further, the detailed diagnostic-
level evaluations are shown in Table 11, including the original 12-lead ECG
(as the reference), the single-lead ECG (i.e., MCMA input) and the generated
12-lead ECG (i.e., MCMA output), which shows the gain from the proposed
framework.

Table 11: The diagnostic-level evaluation of classification performance gain with the generated 12-lead ECG by MCMA Input Metric | $Pre$ | $Rec$ | $Spe$ | $F1$
---|---|---|---|---
Original 12-lead ECG[5] | 0.8747 | 0.9100 | 0.9958 | 0.8872
I | 0.3971 | 0.1309 | 0.991 | 0.1824
I+MCMA | 0.8386 | 0.8381 | 0.9956 | 0.8319
MCMA Gain | 0.4415 | 0.7072 | 0.0046 | 0.6495
II | 0.0682 | 0.0339 | 0.9778 | 0.0333
II+MCMA | 0.8099 | 0.7976 | 0.9935 | 0.7824
MCMA Gain | 0.7417 | 0.7637 | 0.0157 | 0.7491
III | 0.1667 | 0.0056 | 0.9998 | 0.0108
III+MCMA | 0.6983 | 0.6509 | 0.9915 | 0.6524
MCMA Gain | 0.5316 | 0.6453 | -0.0083 | 0.6416
aVR | 0 | 0 | 0.9985 | 0
aVR+MCMA | 0.5005 | 0.4675 | 0.9770 | 0.4690
MCMA Gain | 0.5005 | 0.4675 | -0.0215 | 0.4690
aVL | 0 | 0 | 0.9998 | 0
aVL+MCMA | 0.6265 | 0.637 | 0.9862 | 0.6136
MCMA Gain | 0.6265 | 0.637 | -0.0136 | 0.6136
aVF | 0 | 0 | 1 | 0
aVF+MCMA | 0.5411 | 0.6057 | 0.9794 | 0.5167
MCMA Gain | 0.5411 | 0.6057 | -0.0206 | 0.5167
V1 | 0.2641 | 0.251 | 0.9973 | 0.2573
V1+MCMA | 0.7579 | 0.8707 | 0.9921 | 0.8073
MCMA Gain | 0.4938 | 0.6197 | -0.0052 | 0.5500
V2 | 0.1667 | 0.0611 | 1 | 0.0894
V2+MCMA | 0.7094 | 0.7983 | 0.9900 | 0.7410
MCMA Gain | 0.5427 | 0.7372 | -0.01 | 0.6516
V3 | 0.2428 | 0.1267 | 0.9909 | 0.1469
V3+MCMA | 0.7654 | 0.8422 | 0.9927 | 0.7972
MCMA Gain | 0.5226 | 0.7155 | -0.0063 | 0.6503
V4 | 0.1667 | 0.009 | 1 | 0.0171
V4+MCMA | 0.7900 | 0.8130 | 0.9929 | 0.786
MCMA Gain | 0.6233 | 0.804 | -0.0071 | 0.7689
V5 | 0 | 0 | 1 | 0
V5+MCMA | 0.7918 | 0.8053 | 0.9931 | 0.7895
MCMA Gain | 0.7918 | 0.8053 | -0.0069 | 0.7895
V6 | 0.0833 | 0.0049 | 0.9996 | 0.0093
V6+MCMA | 0.7514 | 0.7896 | 0.9921 | 0.7580
MCMA Gain | 0.7918 | 0.8053 | -0.0069 | 0.7895
|  |  |  |

According to Table 11, the classification performance of the generated 12-lead
ECG is better than that of single-lead ECG and similar to the real 12-lead
ECG, which can demonstrate the classification performance gain brought by
MCMA. The generated 12-lead from lead I could provide the closest
classification performance, the average $F1$ score is 0.8319, which exceeds
other cases. From the view of classification task, the classification
performance in the above tables demonstrates the generated 12-lead ECG can be
used for cardiac abnormality detection, which can prove its advantage in
bridging the single-lead ECG and 12-lead ECG, and it is effective to generate
the pathological information with single-lead ECG as input.

###  5.5 Comparison

MCMA will be compared with other research works, including Grag et al[30], Seo
et al[32], and Joo et al[33]. As known, Grag et al [30] adopts the lead II,
while Seo et al[32] and Joo et al[33] utilizes the lead I. Moreover, MCMA
could convert arbitary single-lead ECG into the standard 12-lead ECG. The
comparisons in signal-level, feature-level, and diagnostic-level are shown in
Table 12, Table 13 and Table 14.

Based on the comparison results, it is known that the proposed framework can
achieve state-of-the-art performance on the ECGGenEval, including the signal-
level, feature-level, and diagnostic-level evaluation. For example, the MSE
for generating 12-lead ECG with lead II is 0.0179, better than Grag et.al[30].
The internal and external testing set could prove its advance over other
researchers. Therefore, MCMA can be used for 12-lead ECG reconstruction tasks
while the single-lead ECG is collected, providing a novel solution in real-
world cardiac healthcare applications. It is possible to improve the clinical
importance of the wearable devices, playing an important role in ECG
monitoring.

Table 12: The signal-level comparison of different methods in PTB-XL and CPSC2018  Dataset | Metric | Method | Input | I | II | III | aVR | aVL | aVF | V1 | V2 | V3 | V4 | V5 | V6 | Mean
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
PTB-XL | MSE |  Grag et al[30] | II | 0.0122 |  0.0001 | 0.0123 | 0.0031 | 0.0122 | 0.0031 | 0.0323 | 0.0690 | 0.0735 | 0.0477 | 0.0374 | 0.0474 | 0.0292
|  | MCMA | II | 0.0076 | 0.0036 | 0.0113 | 0.0031 | 0.0087 | 0.0056 | 0.0167 | 0.0492 | 0.048 | 0.0296 | 0.0183 | 0.0132 | 0.0179
|  |  Seo et al[32] | I | 0.0001 | 0.0148 | 0.0149 | 0.0037 | 0.0038 | 0.0148 | 0.0263 | 0.0579 | 0.0640 | 0.0477 | 0.0388 | 0.0482 | 0.0279
|  |  Joo et al[33] | I | 0.0002 | 0.0189 | 0.0187 | 0.0050 | 0.0059 | 0.0190 | 0.0317 | 0.0868 | 0.0920 | 0.0686 | 0.0517 | 0.0546 | 0.0378
|  | MCMA | I | 0.0035 | 0.0099 | 0.0124 | 0.0035 | 0.0058 | 0.0104 | 0.0151 | 0.0465 | 0.0449 | 0.0306 | 0.0200 | 0.0142 | 0.0181
| PCC |  Grag et al[30] | II | 0.8087 | 0.9986 | 0.6409 | 0.9330 | 0.6029 | 0.8873 | 0.7792 | 0.7344 | 0.7056 | 0.7959 | 0.8482 | 0.8427 | 0.7981
|  | MCMA | II | 0.8349 | 0.9809 | 0.6089 | 0.9264 | 0.6254 | 0.8544 | 0.8045 | 0.7165 | 0.7111 | 0.8212 | 0.8761 | 0.8917 | 0.8043
|  |  Seo et al[32] | I | 0.9983 | 0.7527 | 0.5849 | 0.9189 | 0.8576 | 0.5407 | 0.8237 | 0.7805 | 0.7472 | 0.7931 | 0.8346 | 0.8295 | 0.7885
|  |  Joo et al[33] | I | 0.9962 | 0.6807 | 0.4571 | 0.8905 | 0.8178 | 0.4021 | 0.7827 | 0.6928 | 0.6416 | 0.7112 | 0.7837 | 0.7827 | 0.7199
|  | MCMA | I | 0.9759 | 0.7604 | 0.5216 | 0.9116 | 0.813 | 0.5204 | 0.8320 | 0.7410 | 0.7358 | 0.8096 | 0.8540 | 0.8676 | 0.7786
CPSC2018 | MSE |  Grag et al[30] | II | 0.0215 | 0.0024 | 0.0289 | 0.0668 | 0.0306 | 0.0101 | 0.0958 | 0.1232 | 0.1532 | 0.1651 | 0.2047 | 0.2579 | 0.0967
|  | MCMA | II | 0.0302 | 0.0268 | 0.0320 | 0.0263 | 0.0303 | 0.0272 | 0.0605 | 0.0971 | 0.1051 | 0.1034 | 0.1178 | 0.1379 | 0.0662
|  |  Seo et al[32] | I | 0.0036 | 0.0315 | 0.0454 | 0.0408 | 0.0162 | 0.0339 | 0.0861 | 0.1171 | 0.1488 | 0.1694 | 0.2084 | 0.2655 | 0.0972
|  |  Joo et al[33] | I | 0.0108 | 0.0409 | 0.0455 | 0.0371 | 0.0228 | 0.0428 | 0.0993 | 0.1834 | 0.1827 | 0.1821 | 0.2185 | 0.2755 | 0.1118
|  | MCMA | I | 0.0256 | 0.0334 | 0.0345 | 0.0274 | 0.0269 | 0.0326 | 0.0567 | 0.0914 | 0.1022 | 0.1032 | 0.1179 | 0.1384 | 0.0659
| PCC |  Grag et al[30] | II | 0.7552 | 0.9981 | 0.5686 | 0.9264 | 0.4242 | 0.8901 | 0.6225 | 0.5803 | 0.6329 | 0.7861 | 0.8376 | 0.8369 | 0.7382
|  | MCMA | II | 0.7900 | 0.9790 | 0.5957 | 0.9285 | 0.4784 | 0.8804 | 0.6703 | 0.6045 | 0.6693 | 0.8075 | 0.8614 | 0.8741 | 0.7616
|  |  Seo et al[32] | I | 0.9978 | 0.7402 | 0.4153 | 0.8932 | 0.7442 | 0.4830 | 0.7129 | 0.6268 | 0.6619 | 0.7828 | 0.8378 | 0.8382 | 0.7278
|  |  Joo et al[33] | I | 0.995 | 0.7303 | 0.3517 | 0.8827 | 0.7181 | 0.4701 | 0.6453 | 0.5385 | 0.5238 | 0.7481 | 0.8104 | 0.8002 | 0.6845
|  | MCMA | I | 0.9671 | 0.7713 | 0.4671 | 0.8942 | 0.7086 | 0.5503 | 0.7277 | 0.6537 | 0.6914 | 0.8072 | 0.8586 | 0.8681 | 0.7471
|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Table 13: The feature-level comparison of different method in PTB-XL and CPSC2018  Dataset | Method | Input | $MHR_{SD}$ | $MHR_{CV}$ | $MHR_{Range}$
---|---|---|---|---|---
PTB-XL | Original | * | 2.2137 | 3.21% | 7.2195
| Grag et al[30] | Lead II | 1.1608 | 1.70% | 3.5872
| MCMA | Lead II | 1.3492 | 2.00% | 4.0276
| Seo et al[32] | Lead I | 1.8943 | 2.74% | 6.3984
| Joo et al[33] | Lead I | 2.6891 | 4.03% | 8.8273
| MCMA | Lead I | 1.6276 | 2.41% | 5.0632
CPSC2018 | Original | * | 2.1313 | 2.65% | 7.1267
| Grag et al[30] | Lead II | 0.9545 | 1.24% | 3.0523
| MCMA | Lead II | 0.9823 | 1.33% | 3.0902
| Seo et al[32] | Lead I | 2.1899 | 2.79% | 7.5269
| Joo et al[33] | Lead I | 2.4136 | 3.31% | 8.1059
| MCMA | Lead I | 1.3633 | 1.81% | 4.3808
|  |  |  |  |
Table 14: The diagnostic-level comparison of different methods in CODE-test  Method | Input | $Pre$ | $Rec$ | $Spe$ | $F1$
---|---|---|---|---|---
Reference | 12-lead ECG | 0.8747 | 0.9100 | 0.9958 | 0.8872
Grag et al[30] | Lead II | 0.7268 | 0.8542 | 0.9881 | 0.7808
Input for MCMA | Lead II | 0.0682 | 0.0339 | 0.9778 | 0.0333
MCMA | Lead II | 0.8099 | 0.7976 | 0.9935 | 0.7824
Seo et al[32] | Lead I | 0.8248 | 0.8480 | 0.9948 | 0.8299
Joo et al[33] | Lead I | 0.7817 | 0.7846 | 0.9938 | 0.7730
Input for MCMA | Lead I | 0.3971 | 0.1309 | 0.9910 | 0.1824
MCMA | Lead I | 0.8386 | 0.8381 | 0.9956 | 0.8319
|  |  |  |  |

###  5.6 Ablation Study

MCMA utilizes two key modules, one for arbitary single-lead ECG
reconstruction, and another for zero-padding strategy. Then, it is necessary
to compare with different settings, including fixed-channel(lead I as an
example) and copy-padding strategy. The signal-level evaluation metric, mean
square error (MSE) and Pearson correlation coefficient (PCC) will be used. The
experimental results comparison with different settings could be shown in
Table 15, including the lead I and the average value for 12 single-lead ECG.
In the most cases, MCMA has achieved excellent result in 12-lead ECG
reconstruction task.

Table 15: The module importance in MCMA Channel |  Padding Strategy |  Input |  Mean MSE |  Mean PCC
---|---|---|---|---
Fixed- |  Zeros |  Lead I |  0.0176 |  0.7885
Multi- |  Copy |  Lead I |  0.0191 |  0.7205
Multi- |  Zeros |  Lead I |  0.0181 |  0.7786
Fixed- |  Zeros |  12 Single-lead |  0.0505 |  0.1342
Multi- |  Copy |  12 Single-lead |  0.0195 |  0.7069
Multi- |  Zeros |  12 Single-lead |  0.0177 |  0.7697
|  |  |  |

As Table 15 showing, the proposed framework is effective. Firstly, the multi-
channel strategy could support arbitary single-lead to generate 12-lead ECG.
Although the reconstruction performance of lead I is slightly lower than the
fixed-channel. When the lead I ECG inputs, the fixed-channel could have a MSE
of 0.0176 and a PCC of 0.7885 better than MCMA, a MSE of 0.0181 and a PCC of
0.7786. However, for the fixed-channel, it is difficult to realize 12-lead ECG
reconstruction with other leads, and the training and inference cost is
largely different in training and storing 12 models with this setting.
Secondly, the zero-padding strategy is better than the copy-padding strategy,
while the two strategies both support the 12-lead reconstruction with
arbitrary single-lead ECG. The mean MSE and PCC in MCMA are 0.0177 and 0.7697,
while the mean MSE and PCC in copy-padding are 0.0195 and 0.7069. Therefore,
based on the experimental result, MCMA is feasible to reconstruct 12-lead ECG
with arbitrary single-lead ECG as input.

###  5.7 Discussion

Therefore, based on the experimental results, it is concluded that MCMA could
generate the standard 12-lead ECG with arbitary single-lead ECG as input. At
the same time, this study establishes a comprehensive evaluation benchmark,
ECGGenEval, including the signal-level evaluation, feature-level evaluation,
and diagnostic-level evaluation. The experimental results prove that MCMA can
work well in ECGGenEval, which could be a baseline for the future work. In the
internal testing set, MCMA could perform a MSE of 0.0178 and a PCC of 0.7698,
and the lowest MSE is 0.0156 in the lead V4 while the highest PCC is 0.8055 in
the lead aVF. In the external testing set, MCMA could perform a MSE of 0.0658
and a PCC of 0.7237, and the lowest MSE is 0.062 in the lead V3, while the
highest PCC is 0.7616 in the lead II.

At the same time, for the feature-level evaluation, MCMA could get a
$MHR_{SD}$ of 1.4529, a $MHR_{CV}$ of 2.10%, and a $MHR_{Range}$ of 4.4099 in
the internal testing set, while the results are 1.1578, 1.56%, and 3.6522 in
the external testing set. In the classification task, the highest ${F}_{1}$ is
0.8319, bridging the gap between the single-lead ECG and 12-lead ECG.

##  6 Conclusion

In conclusion, this study proposes a novel generative framework to reconstruct
12-lead ECG with single-lead ECG, as multi-channel masked autoencoder (MCMA),
and it involves two main contributions. Firstly, unlike other methods, the
proposed framework could convert arbitary single-lead ECG into the standard
12-lead ECG. The experimental results showed that the proposed framework had
excellent performance, achieving state-of-the-art performance on the proposed
benchmark, ECGGenEval, including the signal-level, feature-level, and
diagnostic-level evaluation. For example, the average Pearson correlation
coefficients in the internal and external testing set are 0.7698 and 0.7237,
and it is shown that the zero-padding strategy could play an important role in
the proposed framework. In the future, the proposed framework could be adopted
in clinical practice, which provides a novel feasible solution for long-term
cardiac health monitoring.

## Acknowledgements

This work was supported by National Natural Science Foundation of China (No.
62102008).

## Code Availability

The open-source code is publicly available at
https://github.com/CHENJIAR3/MCMA.

## Data Availability

All datasets used in this study are openly available. PTB-
XL:https://physionet.org/content/ptb-
xl/1.0.3/,CPSC-2018:http://2018.icbeb.org/Challenge.html, CODE-
test:https://zenodo.org/records/3765780.

## Author Contribution

Jiarong Chen: Formal Analysis, Methodology, Visualization, Writing-original
draft; Wanqing Wu: Supervision; Tong Liu: Supervision; Shenda Hong:
Investigation, Supervision, Funding acquisition, Resource.

## Competing Interests

The authors declare no competing interests.

## References

  *   * [1] Nabel, E. G.  Cardiovascular disease.  _New Engl. J. Med._ 349, 60–72 (2003).
  * [2] Roth, G. A. _et al._ Global, regional, and national age-sex-specific mortality for 282 causes of death in 195 countries and territories, 1980–2017: a systematic analysis for the global burden of disease study 2017\.  _Lancet_ 392, 1736–1788 (2018).
  * [3] Amini, M., Zayeri, F. & Salehi, M.  Trend analysis of cardiovascular disease mortality, incidence, and mortality-to-incidence ratio: results from global burden of disease study 2017.  _BMC Public Health_ 21, 1–12 (2021).
  * [4] Holter, N. J.  New method for heart studies: Continuous electrocardiography of active subjects over long periods is now practical.  _Science_ 134, 1214–1220 (1961).
  * [5] Ribeiro, A. H. _et al._ Automatic diagnosis of the 12-lead ecg using a deep neural network.  _Nat. Commun._ 11, 1760 (2020).
  * [6] Turakhia, M. P. _et al._ Diagnostic utility of a novel leadless arrhythmia monitoring device.  _Am. J. Cardiol._ 112, 520–524 (2013).
  * [7] Lai, D., Bu, Y., Su, Y., Zhang, X. & Ma, C.-S.  Non-standardized patch-based ecg lead together with deep learning based algorithm for automatic screening of atrial fibrillation.  _IEEE J. Biomed. Health Inform._ 24, 1569–1578 (2020).
  * [8] Liu, C.-M. _et al._ Enhanced detection of cardiac arrhythmias utilizing 14-day continuous ecg patch monitoring.  _Int. J. Cardiol._ 332, 78–84 (2021).
  * [9] Tison, G. H. _et al._ Passive detection of atrial fibrillation using a commercially available smartwatch.  _JAMA Cardiol._ 3, 409–416 (2018).
  * [10] Bumgarner, J. M. _et al._ Smartwatch algorithm for automated detection of atrial fibrillation.  _J. Am. Coll. Cardiol._ 71, 2381–2388 (2018).
  * [11] Perez, M. V. _et al._ Large-scale assessment of a smartwatch to identify atrial fibrillation.  _New Engl. J. Med._ 381, 1909–1917 (2019).
  * [12] Rachim, V. P. & Chung, W.-Y.  Wearable noncontact armband for mobile ecg monitoring system.  _IEEE Trans. Biomed. Circuits Syst._ 10, 1112–1118 (2016).
  * [13] Li, B. M. _et al._ Influence of armband form factors on wearable ecg monitoring performance.  _IEEE Sensors J._ 21, 11046–11060 (2021).
  * [14] Lázaro, J. _et al._ Wearable armband device for daily life electrocardiogram monitoring.  _IEEE Trans. Biomed. Eng._ 67, 3464–3473 (2020).
  * [15] Hong, S. _et al._ Encase: An ensemble classifier for ecg classification using expert features and deep neural networks (2017).  DOI:10.22489/CinC.2017.178-245.
  * [16] Zanchi, B. _et al._ Identification of brugada syndrome based on p-wave features: an artificial intelligence-based approach.  _Europace_ 25, euad334 (2023).
  * [17] Lu, L. _et al._ Decoding 2.3 million ecgs: Interpretable deep learning for advancing cardiovascular diagnosis and mortality risk stratification.  _Eur. Heart J.-Digit. Health_ ztae014 (2024).
  * [18] Reyna, M. A. _et al._ Will two do? varying dimensions in electrocardiography: The physionet/computing in cardiology challenge 2021 (2021).  DOI:10.23919/CinC53138.2021.9662687.
  * [19] Nejedly, P. _et al._ Classification of ecg using ensemble of residual cnns with attention mechanism (2021).  DOI:10.23919/CinC53138.2021.9662723.
  * [20] Srivastava, A. _et al._ Channel self-attention deep learning framework for multi-cardiac abnormality diagnosis from varied-lead ecg signals (2021).  DOI:10.23919/CinC53138.2021.9662886.
  * [21] Han, H. _et al._ Towards high generalization performance on electrocardiogram classification (2021).  DOI:10.23919/CinC53138.2021.9662737.
  * [22] Wickramasinghe, N. L. & Athif, M.  Multi-label cardiac abnormality classification from electrocardiogram using deep convolutional neural networks (2021).  DOI:10.23919/CinC53138.2021.9662787.
  * [23] Bruoth, E. _et al._ A two-phase multilabel ecg classification using one-dimensional convolutional neural network and modified labels (2021).  DOI:10.23919/CinC53138.2021.9662878.
  * [24] Edenbrandt, L. & Pahlm, O.  Vectorcardiogram synthesized from a 12-lead ecg: superiority of the inverse dower matrix.  _J. Electrocardiol._ 21, 361–367 (1988).
  * [25] Nelwan, S. P., Kors, J. A., Meij, S. H., van Bemmel, J. H. & Simoons, M. L.  Reconstruction of the 12-lead electrocardiogram from reduced lead sets.  _J. Electrocardiol._ 37, 11–18 (2004).
  * [26] Maheshwari, S., Acharyya, A., Rajalakshmi, P., Puddu, P. E. & Schiariti, M.  Accurate and reliable 3-lead to 12-lead ecg reconstruction methodology for remote health monitoring applications.  _IRBM_ 35, 341–350 (2014).
  * [27] Atoui, H., Fayn, J. & Rubel, P.  A novel neural-network model for deriving standard 12-lead ecgs from serial three-lead ecgs: application to self-care.  _IEEE T. Inf. Technol. Biomed._ 14, 883–890 (2010).
  * [28] Sohn, J., Yang, S., Lee, J., Ku, Y. & Kim, H. C.  Reconstruction of 12-lead electrocardiogram from a three-lead patch-type device using a lstm network.  _Sensors-basel._ 20, 3278 (2020).
  * [29] Gundlapalle, V. & Acharyya, A.  A novel single lead to 12-lead ecg reconstruction methodology using convolutional neural networks and lstm (2022).  DOI:10.1109/LASCAS53948.2022.9789045.
  * [30] Garg, A., Venkataramani, V. V. & Priyakumar, U. D.  Single-lead to multi-lead electrocardiogram reconstruction using a modified attention u-net framework (2023).  DOI:10.1109/IJCNN54540.2023.10191213.
  * [31] Lee, J., Oh, K., Kim, B. & Yoo, S. K.  Synthesis of electrocardiogram v-lead signals from limb-lead measurement using r-peak aligned generative adversarial network.  _IEEE J. Biomed. Health Inform._ 24, 1265–1275 (2020).
  * [32] Seo, H.-C., Yoon, G.-W., Joo, S. & Nam, G.-B.  Multiple electrocardiogram generator with single-lead electrocardiogram.  _Comput. Meth. Prog. Bio._ 221, 106858 (2022).
  * [33] Joo, J. _et al._ Twelve-lead ecg reconstruction from single-lead signals using generative adversarial networks (2023).  DOI:10.1007/978-3-031-43990-2_18.
  * [34] Chen, T.-M., Huang, C.-H., Shih, E. S., Hu, Y.-F. & Hwang, M.-J.  Detection and classification of cardiac arrhythmias by a challenge-best deep learning neural network model.  _iScience_ 23 (2020).
  * [35] Liu, F. _et al._ An open access database for evaluating the algorithms of electrocardiogram rhythm and morphology abnormality detection.  _J. Med. Imaging Health Inform._ 8, 1368–1373 (2018).
  * [36] Hannun, A. Y. _et al._ Cardiologist-level arrhythmia detection and classification in ambulatory electrocardiograms using a deep neural network.  _Nat. Med._ 25, 65–69 (2019).
  * [37] Drew, B. J., Pelter, M. M., Adams, M. G., Wung, S.-F. _et al._ 12-lead st-segment monitoring vs single-lead maximum st-segment monitoring for detecting ongoing ischemia in patients with unstable coronary syndromes.  _Am. J. Crit. Care_ 7, 355 (1998).
  * [38] Goodfellow, I. _et al._ Generative adversarial networks.  _Commun. ACM_ 63, 139–144 (2020).
  * [39] Chen, J., Zheng, X., Yu, H., Chen, D. Z. & Wu, J.  Electrocardio panorama: synthesizing new ecg views with self-supervision.  _arXiv preprint arXiv:2105.06293_ (2021).
  * [40] He, K., Zhang, X., Ren, S. & Sun, J.  Deep residual learning for image recognition (2016).  DOI:10.1109/CVPR.2016.90.
  * [41] Ronneberger, O., Fischer, P. & Brox, T.  U-net: Convolutional networks for biomedical image segmentation (2015).
  * [42] Hinton, G. E. & Salakhutdinov, R. R.  Reducing the dimensionality of data with neural networks.  _science_ 313, 504–507 (2006).
  * [43] Ho, J., Jain, A. & Abbeel, P.  Denoising diffusion probabilistic models.  _Advances in neural information processing systems_ 33, 6840–6851 (2020).
  * [44] Song, J., Meng, C. & Ermon, S.  Denoising diffusion implicit models.  _arXiv preprint arXiv:2010.02502_ (2020).
  * [45] Strodthoff, N., Wagner, P., Schaeffter, T. & Samek, W.  Deep learning for ecg analysis: Benchmarks and insights from ptb-xl.  _IEEE J. Biomed. Health Inform._ 25, 1519–1528 (2021).
  * [46] Wagner, P. _et al._ Ptb-xl, a large publicly available electrocardiography dataset.  _Sci. Data_ 7, 154 (2020).
  * [47] Makowski, D. _et al._ NeuroKit2: A python toolbox for neurophysiological signal processing.  _Behav. Res. Methods_ 53, 1689–1696 (2021).