# Crucial Feature Capture and Discrimination for Limited Training Data SAR ATR

Chenwei Wang, Siyi Luo, Jifang Pei,
Yulin Huang, Yin Zhang, and Jianyu Yang This work was supported by the
National Natural Science Foundation of China under Grants 61901091 and
61901090._Corresponding author: Jifang Pei._ The authors are with the
Department of Electrical Engineering, University of Electronic Science and
Technology of China, Chengdu 611731, China (e-mail<EMAIL_ADDRESS>dbw181101@163.com).

###### Abstract

Although deep learning-based methods have achieved excellent performance on
SAR ATR, the fact that it is difficult to acquire and label a lot of SAR
images makes these methods, which originally performed well, perform weakly.
This may be because most of them consider the whole target images as input,
but the researches find that, under limited training data, the deep learning
model can’t capture discriminative image regions in the whole images, rather
focus on more useless even harmful image regions for recognition. Therefore,
the results are not satisfactory. In this paper, we design a SAR ATR framework
under limited training samples, which mainly consists of two branches and two
modules, global assisted branch and local enhanced branch, feature capture
module and feature discrimination module. In every training process, the
global assisted branch first finishes the initial recognition based on the
whole image. Based on the initial recognition results, the feature capture
module automatically searches and locks the crucial image regions for correct
recognition, which we named as the golden key of image. Then the local extract
the local features from the captured crucial image regions. The feature
discrimination module provide a hybrid loss to enhance the intra-class
compactness and inter-class separability of the overall features and local
features and solve the poor performance of the global assisted branch after
the initialization. Finally, the overall features and local features are input
into the classifier and dynamically weighted using the learnable voting
parameters to collaboratively complete the final recognition under limited
training samples. The model soundness experiments demonstrate the
effectiveness of our method through the improvement of feature distribution
and recognition probability. The experimental results and comparisons on MSTAR
and OPENSAR show that our method has achieved superior recognition
performance. We will release our code and more experimental results at
https://github.com/cwwangSARATR/SARATR_FeaCapture_Discrimination.

###### Index Terms:

synthetic aperture radar (SAR), automatic target recognition (ATR), limited
data, crucial feature capture, local features discrimination

##  I Introduction

Synthetic aperture radar (SAR) is an active remote sensor, which can provide
high-resolution, day-and-night, and weather-independent images for a multitude
of civilian and military applications [1]. Automatic target recognition (ATR)
applies computer processing capabilities to predict the class of an unknown
target, which has become a very challenging problem in SAR application field
[2]. A standard architecture for efficient SAR ATR consists of three stages:
detection, discrimination, and classification. Each stage is inclined to
perform more complicated and elaborate processing than the prior stage and to
select candidate objects for the next stage of processing. There have been
many outstanding methods for SAR ATR, which can be divided into template-based
and model-based approaches [3, 4, 5, 6].

Due to deep learning as the fast-growing of the big data era trend, it is
proving to be a remarkably successful tool, sometimes even surpassing humans
in solving highly computational tasks [7], [8]. In recent years, researchers
all around the world have made increasing progress in solving the bottleneck
problem of SAR ATR with the help of deep learning-based algorithms [9, 10, 11,
12, 13, 14, 15]. For example, Chen and Wang [16] introduced CNNs into SAR ATR
and tested them on the standard ATR moving and stationary target acquisition
and recognition (MSTAR) data set. Wagner [17] suggested using a CNN to first
extract feature vectors and then feed them to an SVM for classification. Chen
et al. [18] proposed an all-convolutional network consisting of sparsely
connected layers without using fully connected layers to avoid overfitting.

However, deep learning networks require large amounts of labeled training
data. Therefore, an intrinsic problem of recognition performance degradation
emerges when the number of available labeled SAR target images is limited.
This will lead to serious overfitting and, consequently, significantly limit
or destroy the performance of the deep learning models. Meanwhile, the problem
of insufficient SAR images is basic and crucial in SAR application. For
example, for earthquake rescue or debris flow observation, SAR can provide
special imaging capability to help the rescue. However, there are various
buildings or vehicles in the scene, while different shapes or sizes of these
things will finally lead to the problem of insufficient SAR images, let alone
the various platforms and imaging conditions.

Figure 1: Framework of SCDR. Left part is the whole framework of SCDR. Upper
branch of left part perceive the whole SAR image and the bottom branch of left
part finishes the recognition only based on the crucial features extracted by
the feature capture module. Right part is the function of the discrimination
for the features. Yellow pentagons and circles are from the upper branch,
lavender pentagons and circles are from the bottom branch. Pentagons and
circles are features from different class types.

Currently, Most methods focus on improving recognition performance by training
the network, provided that available data is sufficient or even adequate.
While for the condition with severe lack of data, which is called the limited
training sample condition, the existing methods usually input the whole target
image as a whole to train a recognition network [19, 20, 21]. Generally, a
recognition network consists of a feature extractor and a classifier. The
features corresponding to the whole image are extracted first, and then
imported as a whole into the classifier to finish recognition[22, 23, 24, 25,
26, 27, 28, 29].

However, it has been found that, under limited training data, the deep
learning model can’t capture the crucial image part in the whole image, rather
focus on the useless or even harmful image part for recognition [30, 31, 32,
33, 34, 35, 36, 37, 38]. The label information is limited so that the model
can’t obtain enough information to decide where to look at in the whole SAR
images and extract the discriminative feature, fail to achieve precise
recognition performance. Thus, under the limited training SAR samples, the
target recognition method based on the whole image is not ideal since the
extracted overall features contain a large number of useless or even harmful
local-image-region features rather than the discriminative feature from the
crucial image region.

Since only a part of the image region is relatively discriminative and
contributes mainly to the recognition performance, but under limited training
data, the model can’t capture this image part. Thus, we may assume that it is
possible to construct a network structure that can automatically search and
capture the discriminative image region from the whole image, focus on
extracting features from this region, and discard other local image regions
automatically. In this way, the model can capture the crucial image part for
recognition and improve the effectiveness and discrimination of the overall
feature of the whole image to achieve accurate recognition performance under
limited training data. We names such discriminative image region as the golden
key of image under limited training data SAR ATR. So as we can obtain a
network that is more suitable for recognition under limited training SAR
sample conditions, improve generalization ability and better enhance
recognition performance.

Therefore, we propose a SAR ATR method to search and capture discriminative
image region (SCDR), the method we designed can be illustrated as follows, as
shown in Fig. 1.

1) First, it inputs the whole image to the global assisted branch, extracts
the overall features and inputs them into the classifier to complete the
recognition, as shown in the yellow branch in Fig. 1.

2) The proposed feature capture module is then used to obtain the weights
assigned to different spatial location features when the global assisted
branch correctly recognizes, and normalize them to the range of 0-1. The
spatial location features with high weight is the crucial image region for
correct recognition, which is the so-called golden key of image. With the mean
value of all weights being the threshold, the golden key is binarized to form
a mask, which is then element-wise multiplied by the whole image to cut out
the golden key as shown in the orange square in Fig. 1.

3) For the segmented golden key, the depth features are extracted individually
in the local enhanced branch, as shown in the purple branch in Fig. 1.

4) As shown in the blue squares in Fig. 1, the intra-class compactness and
inter-class separateness of the overall and local features of the yellow and
purple branches are enhanced in feature discrimination module. Furthermore,
the feature discrimination module can help the model capture the crucial image
part when the model performs poorly at the start of training.

Finally, the yellow and purple branches extract the features of the whole
image and the golden key respectively. The features are then input into the
classifier to get the probability distribution of recognition respectively.
The learnable parameters are used to voting weight the two probability
distributions dynamically to get the final recognition probability
distribution. Therefore, the yellow and purple branches can collaborate to
complete the final recognition.

In this way, our SCDR can automatically search and capture the discriminative
local image region in the whole image, discard other useless or even harmful
image regions in the whole image, and focus on extracting features for this
discriminative image region to complete the final recognition in cooperation
with the overall features, which improves the recognition performance of the
overall method and solves the difficulty of target recognition under limited
training SAR samples in a targeted manner.

The working mechanism of the SCDR is similar to the mechanism of the human
brain to recognize objects in the real world. The SCDR first identifies the
class type of SAR image by observing the whole SAR image and finds the crucial
structures or features of the target in the image. Then the SCDR further
focuses on and discriminates the found crucial features, and finally
comprehensively considers the whole images and crucial features of the target
to achieve the recognition of the target classes.

The main contributions of this paper are summarized as follows:

(1) A novel framework for limited training data which comprehensively
considers the whole image and crucial features to recognize the target classes
is proposed. It not only perceives the whole target images, but also capture
the crucial features and enhances the effectiveness of these crucial features
for recognition.

(2) A feature capture module is proposed to locate the crucial features, and a
feature discrimination module is proposed to make the overall and local
features with more compactness and inter-class separability and solve the bad
initialization.

(3) The SCDR achieves the state-of-the-art performance of recognition on MSTAR
and OpenSARship data sets with limited training data. The method soudness
verification also validate the effectiveness of our methods.

The remainder of this paper is organized as follows. The related works are
introduced in Section II. The details of the SCDR is presented in Section III.
The effectiveness of the proposed method are validated by experiments in
Section IV, and Section V gives a conclusion.

##  II Related Works

Many researches of the insufficient SAR images in SAR ATR have been carried
out in recent years. These researches can be divided into two types based on
the numbers of the limited training samples and problem formulation, the
problem of the limited training data and the problem of FSL. In this section,
the researches of the limited training data and FSL in SAR ATR are introduced
as follows. Besides, the training and testing settings of the limited training
data and FSL are as shown in Fig. 2.

Limited training sample problem: In the problem of limited SAR images, there
are one training dataset and one testing dataset. The sample number of every
target class type in the training dataset is limited. For example, if there
are 10 SAR images for all 10 class types, the training dataset has $10\times
10=100$ SAR images in total. The models just employ 100 SAR images to train
and test. Sometimes, some methods also construct a semi-supervised structure
to employ the resting images as unlabeled samples besides the $K$ labeled
images in training. Under this condition, the input information to model is
more than the $K$ labeled images.

For example, Wang et al. [39] designed a semi-supervised learning framework
mainly containing a self-consistent augmentation rule to utilize unlabeled
data during training for the limited SAR images. Zhang et al. [40] adopted the
feature augmentation and ensemble learning strategies to concatenate cascaded
features from optimally selected convolutional layers to obtain more
comprehensive representation information from limited data. Sun et al. [41]
introduced an attribute-guided transfer learning method employing an angular
rotation generative network, where the shared attribute between the source and
target domains is the target aspect angle, to address the problem of the lack
of training data at different aspect angles. Zhang et al. [42] designed a
semi-supervised transfer learning method for limited SAR training data, which
adopts learned parameters from a pre-trained GAN, achieving up to 23.58%
accuracy improvement compared with other random-initialized models. Besides,
they also proposed another transfer learning method for limited SAR training
data, where the pre-trained layers are reused to transfer the generic
knowledge [43].

Figure 2: Limited SAR images and FSL. One example of 3 images for each class
for limited SAR images and FSL, the circles of the different colors denote the
images of the different labeled target classes.

FSL problem: In the problem of FSL, there is one support dataset with a
limited number of samples for each class type, which plays the same role as
the training dataset in limited SAR images. There is also one training dataset
with a sufficient number of samples for other class types. The class types are
disjoint between the training dataset and support dataset. Take the MSTAR
dataset as an example, total of 10 class types, for 5-way 10-shot of FSL,
5-way means 5 class types in the support dataset, 10-shot means 10 SAR images
for each type of 5 class types, there are $5\times 10=50$ SAR images in the
support dataset. Meanwhile, there is a training dataset that has sufficient
SAR images of the remaining 5 class types disjoint from the support dataset.

Fu et al. [22] adopted three transfer learning methods and meta-learning in
the few-shot SAR target classification to mitigate the difficulties with few
training data. Wang et al. [28] proposed a hybrid inference network (HIN)
containing an embedding network as the first stage and a hybrid inference
strategy as the second stage, which obtained good results in the case of
three-target classification for FSL. They also proposed a convolutional
bidirectional long short-term memory prototypical network that was trained to
map SAR images into a new feature space and utilized Euclidean distance to
obtain the recognition results, achieving over 90% recognition accuracy in the
5-shot scenario [44]. [29] then proposed an FSL approach that uses a
convolutional bidirectional long short-term memory network to extract azimuth-
insensitive features and further improved the performance. Yang et al. [45]
proposed a mixed loss graph attention network (MGA-NET) containing a data
augmentation module, embedding network, and multilayer graph attention
network, which increased the classification accuracy in 3-way 1-shot and 3-way
5-shot scenarios. Rostami et al. [46] introduced a deep transfer learning
method for FSL by transferring knowledge from the optical domain through
learning a shared invariant cross-domain embedding space for discrimination.
Wang et al. [47] proposed an attribute-guided multi-scale prototypical network
(AG-MsPN) combined with sub-band decomposition, obtaining superior performance
in few-shot case.

Although these related researches have improved the recognition performance of
SAR ATR under limited training data and FSL, some of them regard the whole SAR
images as the input, the useless or even harmful image region inevitably
limited their performance. In this paper, our method focuses on the problem of
the limited training data, it searches and captures the crucial image region
in the whole image, which is named as the golden key of image under limited
training data. Then our method focuses on extracting features from the golden
key of image to complete the final recognition in cooperation with the overall
features. In this way, it can tackle with the core problem of limited training
samples in SAR ATR in a targeted manner.

##  III Proposed Method

In this section, the proposed framework of the SCDR is described in detail and
the feature capture module and the feature discrimination module are also
presented.

###  III-A Framework of SCDR

To help the network search and capture crucial features and improve the
discrimination of these features, first, we should know which local regions of
the image are important for the recognition of the network. So as these image
region can be regarded as the golden key of image. Then, the discrimination or
effectiveness of these features should be improved by enhancing the
compactness of the features in the same class and the separability of the
features among different classes. Finally, the core problem of limited
training samples in SAR ATR can be solved.

As shown in Fig. 1, the whole framework of SCDR is constructed by two branches
and one core module: the upper yellow branch with feature capture module, the
bottom lavender branch to recognize from the local features, the blue
discrimination module to enhance the feature effectiveness. The upper yellow
branch with feature capture module is designed for searching the crucial
features of the images and capturing these features which are important for
the recognition. The bottom lavender branch is to judge whether the right
recognition can be obtained only by these features to measure the
effectiveness of these features and the capability of the upper branch. The
blue discrimination module can calculate the cosine similarity between the
feature maps of the two branches and enhance the inner-class compactness and
inter-class separability of the features maps of the two branches, which can
finally improve the discrimination of these features.

By inputting the whole SAR image into the upper branch with feature capture
module, the recognition results on whole images are obtained to calculate one
loss of recognition ${{L}_{whole}}$, and the corresponding crucial features of
the input images are output as the input of the bottom branch. Then the bottom
branch also outputs the recognition results on these crucial features to
calculate another loss of recognition ${{L}_{local}}$, and the feature maps of
the two branches are input into the discrimination module to calculate the
loss of the feature discrimination ${{L}_{disc}}$. The final loss can be
calculated as follows:

$\displaystyle{L={{\lambda}_{1}}{{L}_{whole}}+{{\lambda}_{2}}{{L}_{local}}+{{\lambda}_{3}}{{L}_{disc}}}$
(1)

where ${\lambda_{1}}$, ${\lambda_{2}}$ and ${\lambda_{3}}$ are the weighting
coefficients.

As shown in Fig. LABEL:fig3, the process of the SCDR is also described in
detail. Given a SAR image ${\mathbf{x}}_{i}$ of $y_{i}$ class type, by
inputting ${\mathbf{x}}_{i}$ into the upper branch, the output feature maps of
the feature embedding in the upper branch is
$\mathbf{M}_{i}^{whole}\left({\mathbf{x}}_{i}\right)\in{{\mathbb{R}}^{h\times
w\times c}}$, and the classifier gives the class predictions
${{p}_{whole}}\left({{y}_{j}}|{{\mathbf{x}}_{i}}\right)$, the probability of
the sample ${\mathbf{x}}_{i}$ classified to $j\text{th}$ class. The loss of
recognition ${{L}_{whole}}$ can be obtained as

$\displaystyle{{{L}_{whole}}\left({{\mathbf{x}}_{i}}\right)=-\sum\limits_{j=1}^{K}{{{y}_{j}}}\text{log}\left({{p}_{whole}}\left({{y}_{j}}|{{\mathbf{x}}_{i}}\right)\right)}$
(2)

where $K$ is the class number.

Then, the feature capture module employs the predictions
${{{p}_{whole}}\left({{y}_{j}}|{{\mathbf{x}}_{i}}\right)}$ and the feature
maps ${{\bf{M}}_{i}^{whole}\left({{\mathbf{x}}_{i}}\right)}$ to capture the
crucial features in the input SAR images, ${{\mathbf{x}}_{i}^{local}}$, which
is important for the recognition of the upper branch.

These features ${{\mathbf{x}}_{i}}^{local}$ in the input SAR images are
severed as the input of the bottom branch. Then the feature maps
$\mathbf{M}_{i}^{local}\left({{\mathbf{x}}_{i}}\right)\in{{\mathbb{R}}^{h\times
w\times c}}$ and the class predictions
${{p}_{local}}\left({{y}_{j}}|{{\mathbf{x}}_{i}}\right)$ are also output by
the feature embedding and the classifier in the bottom branch. The loss of
recognition ${{L}_{local}}$ can be obtained as follows:

$\displaystyle{{{L}_{local}}\left({{\mathbf{x}}_{i}}\right)=-\sum\limits_{j=1}^{K}{{{y}_{j}}}\text{log}\left({{p}_{local}}\left({{y}_{j}}|{{\mathbf{x}}_{i}}\right)\right)}$
(3)

Through the process and two losses above, the upper and bottom branches can
recognize the target classes on the whole images and crucial features. The
performance of the bottom branch can be treated as the distinguishing level of
these crucial features. The upper branch is optimized by the recognition
errors by the whole images in the upper branch and the crucial features in the
bottom branch. Through the optimization in the training, our method can
enhance the effectiveness of these crucial features and improve the
recognition performance.

###  III-B Feature Capture Module

The feature capture module aims to search and capture crucial features in
images for the final recognition. When inputting a whole SAR image to the deep
learning models, the deep learning models classify the images into a specific
target class based on the extracted feature maps. These feature maps are from
different spatial local regions of the images and play different roles in the
recognition. The feature capture module relies on the final recognition
results to find crucial image regions for the correct prediction and the
corresponding weights for crucial features. This is the reasons that we named
these image regions as the golden key of image under limited training data.
Motivated by [48], the process of the feature capture module is designed as
two stages as follows.

The first stage is to search crucial features for the final recognition in the
upper branch. Through the final class prediction, the feature maps can be
weighted integrated together to find crucial features. The process of the
weighted integration is described as follow. Given an input SAR image
${{\mathbf{x}}_{i}}$ of $y_{i}$ class type and the feature maps before the
classifier,
$\mathbf{M}\left({{\mathbf{x}}_{i}}\right)\in{{\mathbb{R}}^{h\times w\times
c}}$, the feature maps ${\bf{M}}\left({{\mathbf{x}}_{i}}\right)$ firstly go
through the global average pooling to integrate global features into
$\mathbf{F}\left({{\mathbf{x}}_{i}}\right)\in{{\mathbb{R}}^{1\times 1\times
c}}$, and the output of the classifier go through one SoftMax to get the final
prediction $\mathbf{pred}\in{{\mathbb{R}}^{1\times K}}$ on the class of
${{\mathbf{x}}_{i}}$. Then the prediction
$\mathbf{pred}\in{{\mathbb{R}}^{1\times K}}$ is employed to choose the
corresponding weights ${{\mathbf{W}}_{FC}}$ of the full connection layer as

$\displaystyle{\mathbf{W}_{FC}^{p}={{\mathbf{W}}_{FC}}\left[\text{argmax}\left(\mathbf{pred}\right)\right]=\left\\{{{w}_{1}},{{w}_{2}},\ldots{{w}_{c}}\right\\}}$
(4)

where $\left[{{\rm{argmax}}\left({{\cdot}}\right)}\right]$ means the
corresponding index of maximum value, $K$ means the class number of the
targets, ${{w}_{1}},{{w}_{2}},\ldots{{w}_{c}}$ means the parameters from the
full connected layers.

The second stage is to capture the corresponding local parts in the input
image based on the crucial features from the first stage, and cut out the
local parts from the input image to input into the bottom branch. Then crucial
features to be captured,
${{\mathbf{M}}_{fea_{c}apture}}\in{{\mathbb{R}}^{h\times w}}$, can be
calculated by

$\displaystyle{{{\mathbf{M}}_{fea_{c}apture}}=\operatorname{reshape}\left(\sum\limits_{j=1}^{c}{{{w}_{j}}{{\mathbf{M}}_{j}}\left({{\mathbf{x}}_{i}}\right)}\right)}$
(5)

where ${\mathop{\rm reshape}\nolimits}\left(\cdot\right)$ means reshaping
these local features into the size of the input image ${\mathbf{x}}_{i}$. The
local parts to be captured, ${\mathbf{I}_{local}}$, are computed by

$\displaystyle{{\mathbf{I}_{local}}=\mu
B\left({{\mathbf{M}}_{fea_{c}apture}},\varphi\right)\odot{\mathbf{x}}_{i}}$
(6)

where ${\mathbf{I}_{local}}$ means the input for the bottom branch,
$B\left({{\cdot}}\right)$ means binarization with threshold $\varphi$, and
$\mu$ means the weight for the feature capture module, $\odot$ means Hadamard
product.

Through the feature capture module, the bottom branches can force the upper
branch to locate the golden keys of image. For further enhancement of crucial
features, the discrimination module is proposed and described in detail as
follows.

###  III-C Feature Discrimination Module

For the further enhancement of the crucial features in inner-class compactness
and inter-class separability, feature discrimination module is necessary for
the limited training sample in SAR ATR.

As shown in Fig. 1, the feature discrimination module aims to force the
direction of the feature vectors of the same class closer and the direction of
the feature vectors of the different classes more distant. To achieve this
goal, the discrimination module calculates the cosine similarities of the
features and organizes a novel loss with a margin of the feature directions
between the different classes and the same class.

The discrimination module has two stages as shown in Fig. LABEL:fig3: find the
hardest negative image and the hardest positive image, calculate the
discrimination loss. In the first stage, for an input SAR image
${\mathbf{x}}_{i}$ of $y_{i}$ class type and the feature maps of the branches,
$\mathbf{M}_{i}^{whole}\left({\mathbf{x}}_{i}\right)$ and
$\mathbf{M}_{i}^{local}\left({\mathbf{x}}_{i}\right)$, in all inputted images
$\left\\{{{\mathbf{x}}_{1}^{1},{\mathbf{x}}_{1}^{2},\ldots,{\mathbf{x}}_{K}^{N}}\right\\}\in{\mathbb{R}^{K\times
N}}$, $K$ classes and ${N}$ samples each class, the discrimination module
firstly calculates the cosine similarity of all the features. The cosine
similarity is computed as

$\displaystyle\begin{split}{sim_{\cos}}\left({{{\mathbf{x}}_{{i}}}{{,}}{{\mathbf{x}}_{{j}}}}\right){{=}}\frac{{f\left({{\mathbf{M}}_{i}^{whole}\left({{{\mathbf{x}}_{{i}}}}\right)}\right)}}{{{{\left\|{f\left({{\mathbf{M}}_{i}^{whole}\left({{{\mathbf{x}}_{{i}}}}\right)}\right)}\right\|}_{2}}}}\cdot\frac{{f\left({{\mathbf{M}}_{j}^{local}\left({{{\mathbf{x}}_{{j}}}}\right)}\right)}}{{{{\left\|{f\left({{\mathbf{M}}_{j}^{local}\left({{{\mathbf{x}}_{{j}}}}\right)}\right)}\right\|}_{2}}}}\end{split}$
(7)

where ${\left\|\cdot\right\|_{2}}$ means the $\rm{L}_{2}$-norm and
$f\left({\cdot}\right)$ means flattening feature maps.

Then the rank list of the cosine similarity is obtained as $\mathbf{Score}$,
the discrimination module tries to find the most similar features among all
the local features of different classes named hardest negative
${{\mathbf{M}}_{neg\\_hard}^{local}\left({{{\mathbf{x}}_{i}}}\right)}$, and
the least similar features of the same class named hardest positive
${{\mathbf{M}}_{pos\\_hard}^{local}\left({{{\mathbf{x}}_{i}}}\right)}$.

$\displaystyle{{{\mathbf{M}}_{neg\\_hard}^{local}\left({{{\mathbf{x}}_{{i}}}}\right)}\leftarrow
sort\left(\mathbf{Score},descending\right)[0]}$ (8)
$\displaystyle{{{\mathbf{M}}_{pos\\_hard}^{local}\left({{{\mathbf{x}}_{{i}}}}\right)}\leftarrow
sort\left(\mathbf{Score},ascending\right)[0]}$ (9)

where $sort\left(\cdot\right)$ means sort by descending or ascending. The
hardest negative is the first features after sorting by descending and the
hardest positive is the first features after sorting by ascending.

The second stage is to calculate the discrimination loss as follows:

$\displaystyle{{{L}_{disc}}=\max\left({{l}_{neg}}+\psi-{{l}_{pos}},0\right)}$
(10)

where ${{l_{neg}}}$ means the similarity between ${{{\mathbf{x}}_{i}}}$ and
the most similar samples of different classes
$\mathbf{M}_{neg\\_hard}^{local}$, ${{l_{pos}}}$ means the similarity between
${{{\mathbf{x}}_{{i}}}}$ and the least similar samples of different classes
$\mathbf{M}_{pos\\_hard}^{local}$, the constant $\psi$ means the margin of the
similarity between ${{l_{neg}}}$ and ${{l_{pos}}}$. In this way, the
discrimination loss can achieve that the similarity of the features from the
same classes are larger $\psi$ than the similarity of the features from the
different classes.

${{l_{neg}}}$ and ${{l_{pos}}}$ are calculated as

$\displaystyle{l_{neg}}{\text{ =
}}\sum{\frac{{f\left({{\mathbf{M}}_{i}^{whole}\left({{x_{i}}}\right)}\right)}}{{{{\left\|{f\left({{\mathbf{M}}_{i}^{whole}\left({{x_{i}}}\right)}\right)}\right\|}_{2}}}}\odot\frac{{f\left({{\mathbf{M}}_{neg\\_hard}^{local}}\right)}}{{{{\left\|{f\left({{\mathbf{M}}_{neg\\_hard}^{local}}\right)}\right\|}_{2}}}}}$
(11) $\displaystyle{l_{pos}}{\text{ =
}}\sum{\frac{{f\left({{\mathbf{M}}_{i}^{whole}\left({{x_{i}}}\right)}\right)}}{{{{\left\|{f\left({{\mathbf{M}}_{i}^{whole}\left({{x_{i}}}\right)}\right)}\right\|}_{2}}}}\odot\frac{{f\left({{\mathbf{M}}_{pos\\_hard}^{local}}\right)}}{{{{\left\|{f\left({{\mathbf{M}}_{pos\\_hard}^{local}}\right)}\right\|}_{2}}}}}$
(12)

where $\sum\cdot$ means one function that sums all vector elements.

The role of the discrimination loss can be treated as finding the most
discriminable local parts among the different classes and the most compact or
common local features in the same class.

The proposed SCDR firstly utilized the two branches to recognize the target
classes on the whole images and the local parts of images separately. The
feature capture module is proposed to find the crucial local parts. Then the
discrimination module is proposed to enhance the inner-class compactness and
inter-class separability of the local features. Through the above innovations,
our method can achieve superior recognition performance under the condition of
limited training SAR data.

##  IV Experiments and Results

In this section, we validate the effectiveness and robustness of the proposed
method on the MSTAR and OpenSARShip datasets. First, the two datasets are
employed to evaluate the method and the corresponding preprocess are
introduced in detail. Then, the testing sample heatmaps of the network
without/with our method are shown to validate the method soundness. The
heatmaps represent the weight of each spatial location on the testing image
for the correct recognition. In our method, the local image regions are
generated by binarizing the heatmaps. At the same time, the experimental
results under the standard operating condition (SOC) and extended operating
conditions (EOCs) are demonstrated. The recognition results on the OpenSARShip
dataset are also given. Finally, the comparisons with other SAR ATR methods
are presented.

###  IV-A Dataset and Network Configuration

Figure 3: SAR images and corresponding optical images of targets. Figure 4:
SAR images and corresponding optical images of three-class targets in the
OpenSARShip dataset.

In the experiment, we choose two benchmark datasets for SAR ATR, the moving
and stationary target acquisition and recognition (MSTAR) and the OpenSARShip,
to evaluate our proposed SCDR.

MSTAR was released by the Defense Advanced Research Project Agency and the Air
Force Research Laboratory. The data was collected by the Sandia National
Laboratory STARLOS sensor platform. As a benchmark dataset evaluating SAT ATR
performance, the MSATR contains a large number of SAR images including ten
different types of ground targets, where tank, rocket launcher, armored
personnel carrier, air defense unit, and bulldozer, are acquired as 1-ft
resolution X-band SAR images in the range from $\text{0}{}^{\circ}$ to
$\text{360}{}^{\circ}$. These targets are captured with different aspect
angles, depression angles, and serial numbers. Ten different classes of ground
targets used in our experiments are of different serial numbers with different
depression angles. The SAR and corresponding optical images of ten types of
targets are shown in Fig. 3.

The OpenSARShip dataset aims to develop sophisticated ship detection and
classification algorithms under high interference. The data was collected from
41 Sentinel-1 images under various environmental conditions. There are 17
types of SAR ships, 11346 ship chips in total, being integrated with automatic
identification system (AIS) messages. The labels in this dataset are reliable
because these labels of ships are based on AIS information [49]. In our
experiment, we adopt the ground range detected (GRD) data which are under
Sentinel-1 IW mode with a resolution of $2.0m\times 1.5m$. For the size of
ships, the length ranges from 92m to 399m and the width ranges from 6m to 65m.
In the following experiments, both the VV and VH data are employed in the
training, validation, and testing procedures. Fig. 4 shows the sample SAR
images of a three-class target.

The configurations of the training process and the network are presented here.
The size of input SAR images is $224\times 224$ by applying bilinear
interpolation to the original data. The values of ${\lambda_{1}}$,
${\lambda_{2}}$ and ${\lambda_{3}}$ are set as 1, 0.5 and 0.5. The value of
${{\rm{margin}}}$ is set as 0.3. The values of ${v_{1}}$, ${v_{2}}$, ${v_{3}}$
and ${v_{4}}$ are set as 2, 2, 8 and 2 respectively. The proposed method is
tested and evaluated on a GPU cluster with Intel(R) Xeon(R) CPU E5-2698 v4 @
2.20GHz, eight Tesla V100 with eight 32GB memories. The proposed method is
implemented using the open-source PyTorch framework with only one Tesla V100.
The batch size is set as 128. The learning rate is initialized as 0.01 and
reduced with the 0.5 ratios for every 25 epochs. There are also 10 epochs to
warm up for training. Other hyperparameters are shown in Fig. LABEL:fig3. We
choose swin-transformer as the backbone, which is more suitable for SAR image
feature learning. Because SAR images are different from optical images, due to
its specific imaging process, each scattering point of SAR images is related
to the actual scene in a larger range. Therefore, the feature extraction
models for SAR images more needs construction of long-distance information.

###  IV-B Method Soundness Verification

In this section, the soundness verification experiments of our method are
evaluated. We run two experiments with 20 training samples each class under
different network configurations. The first network configuration is the
normal recognition network just without our proposed method, single upper
yellow branch in Fig. LABEL:fig3. The second network configuration is our
method shown in Fig. LABEL:fig3. The training and testing samples are from the
MSTAR dataset, the distribution of the whole MSTAR dataset is shown in Table
I. The training data were collected at a $\text{17}{}^{\circ}$ depression
angle and randomly sampled 20 each class, and the testing data were collected
at a $\text{15}{}^{\circ}$ depression angle, the whole testing data are
employed in the testing phase. We all trained the networks with two different
configurations with 120 epochs and employed the parameters of the last epochs
to shown the results.

First, the recognition ratios of the first configuration (without our method)
is 74.59%, the recognition ratios of our methods is 94.97%. Then, the heatmaps
of two different configurations is shown in Fig. 5. It is clear that the first
network configuration can’t focus on the discriminative local image region,
rather focus on the background which is useless for the recognition. Our
method can capture the discriminative local image region in the whole image,
discard other useless or even harmful image regions in the whole image.

From the comparison of two different network configurations in recognition
ratios and heatmaps, the recognition ratios of our method obviously outperform
the one of the network without our method. The heatmaps of two different
network configurations also shows the superiority of our method and the reason
of the higher recognition ratios. Therefore, the soundness of our method has
been validated.

Figure 5: Heatmaps of testing samples under two different network
configurations with 20 training samples each class in MSTAR. The first network
configuration is the normal recognition network just without our proposed
method, single upper yellow branch in Fig. LABEL:fig3. The second network
configuration is our method shown in Fig. LABEL:fig3. The recognition ratios
without our method is 74.59%, the recognition ratios of our methods is 94.97%.
Notion that in our method, the local image regions are generated by binarizing
the heatmaps.

###  IV-C Recognition Results

In this section, the recognition results of our method in MSTAR and
OpenSARShip dataset are shown. The experiment configuration are described at
first, then the results are presented and analysed.

####  IV-C1 Recognition Results under SOC in MSTAR

Under the MSTAR dataset including ten different targets, the recognition
performance of our proposed SCDR is evaluated in the experimental setup of
SOC. The training data were collected at a $\text{17}{}^{\circ}$ depression
angle, and the testing data were collected at a $\text{15}{}^{\circ}$
depression angle. The distribution of training and testing images in the
experimental setup are listed in Table I. Note that in Table I, the number of
each target indicates the number of raw SAR images in the MSTAR dataset. In
the following experiments, if given a 10-way X-shot experiment, the X here
represents the number of randomly chosen images from the raw SAR images.

TABLE I: Original Image Number of Different Depressions for SOC Class | Training | Testing
---|---|---
Number | Depression | Number | Depression
BMP2-9563 | 233 | $\text{17}{}^{\circ}$ | 195 | $\text{15}{}^{\circ}$
BRDM2-E71 | 298 | 274
BTR60-7532 | 256 | 195
BTR70-c71 | 233 | 196
D7-92 | 299 | 274
2S1-b01 | 299 | 274
T62-A51 | 299 | 273
T72-132 | 232 | 196
ZIL131-E12 | 299 | 274
ZSU234-d08 | 299 |  | 274 |

In Table II, the recognition performance of the proposed SCDR is demonstrated
quantitatively. The first row lists the number of training images in each
target class. The type of targets in the first column is given as the class
and series linking with hyphens. It is noted that there is no additional
training dataset or support dataset except k-shot for each class. The $N$
training images are augmented by $10$ times through randomly sampling $10$
image chips of $224\times 224$ SAR images from a $384\times 384$ SAR image
after the bilinear interpolation, which ensures the central target is complete
[6]. All the recognition ratios of the ten targets in MSTAR and the average
recognition ratio listed in Table II are calculated after 20 experiments.

TABLE II: Recognition Performance (%) under SOC on MSTAR Class | Labeled Number in Each Class
---|---
1 | 2 | 5 | 10 | 20 | 25 | 40 | 80
BMP2-9563 | 21.03 | 32.41 | 63.36 | 80.86 | 87.14 | 98.88 | 89.23 | 92.30
BRDM2-E71 | 36.13 | 35.09 | 89.52 | 96.37 | 98.80 | 98.11 | 98.91 | 99.63
BTR60-7532 | 46.67 | 60.53 | 69.14 | 95.26 | 95.36 | 96.48 | 94.87 | 95.89
BTR70-c71 | 42.35 | 39.50 | 70.18 | 95.21 | 94.15 | 95.54 | 96.94 | 98.46
D7-92 | 59.12 | 82.24 | 81.43 | 94.09 | 93.88 | 100.00 | 97.81 | 100.00
2S1-b01 | 33.58 | 26.85 | 87.26 | 98.78 | 99.61 | 98.79 | 99.27 | 100.00
T62-A51 | 37.36 | 40.24 | 81.60 | 92.00 | 93.88 | 96.06 | 99.27 | 98.90
T72-132 | 37.24 | 57.24 | 60.40 | 84.07 | 94.00 | 95.79 | 99.49 | 99.48
ZIL131-E12 | 41.97 | 50.95 | 80.36 | 97.63 | 95.04 | 94.52 | 99.27 | 100.00
ZSU234-d08 | 74.09 | 65.59 | 70.28 | 67.08 | 97.78 | 94.44 | 100.00 | 100.00
Average | 43.75 | 48.74 | 74.64 | 88.58 | 94.97 | 96.74 | 97.81 | 98.72

It is clear that when the number of training samples is larger than 25 shots
for each class, the recognition ratios can achieve more than 97.80%. When the
number of training sample are 80 and 40, the recognition ratios are 98.72% and
97.81%, respectively. When there are 25, 20 and 10 training samples, the
average recognition ratios are 96.74%, 94.97% and 88.58%, respectively. When
the training samples are limited to 5-shot and 2-shot, there are a total of 50
or 20 SAR images for training before augmentation. In this case, our proposed
SCDR still obtains 74.64% and 48.74% recognition accuracy for ten-class
recognition. The recognition ratios of BMP2-9563, T72-132 and T62-A51 are more
largely influenced by the limited training samples than that of other class
types. From all the recognition ratios of the ten targets under 2-shot, part
of them are still recognized. As the training samples are decreasing, the
recognition performance of BMP2-9563, BTR60-7532, BRDM2-E7, T62-A51 and
ZIL131-E12 are influenced more obviously than that of the other five target
types. The proposed SCDR can obtain the uplifting average recognition ratios
of 48.74%, which is mainly decreased by the recognition of the six target
types above.

From the experimental results and analysis above, the proposed SCDR can
achieve outstanding recognition performance when the training samples are
ranging from 2 to 80 for each target type in ten classes under SOC in MSTAR.

####  IV-C2 Recognition Results under EOCs in MSTAR

The extended operating condition (EOC) consists of EOC- CV (configuration
variant), EOC-D (depression variant) and EOC-VV (version variant). The
experiments of EOCs are similar to the practical situation and hard to achieve
high performance because of the large variance between the training samples
and testing samples. When it comes to the limited training sample, the
performance of EOCs is extremely hard to be improved.

It is known that variance in depression angle can dramatically exacerbate
recognition performance. The testing dataset is captured at a
$\text{30}{}^{\circ}$ depression angle and the training dataset is the SAR
images of four corresponding classes at a $\text{17}{}^{\circ}$ depression
angle as listed in Table III. The summary of the testing data is listed in
Table III and the recognition performance of EOC-D under limited training
samples are listed in Table IV.

TABLE III: Training and Testing dataset under EOCs Train | Number |  | Depression
---
Angle
Test(EOC-D) | Number |  | Depression
---
Angle
2S1 | 299 | $\text{17}{}^{\circ}$ | 2S1-b01 | 288 | $\text{30}{}^{\circ}$
BRDM2 | 298 | BRDM2-E71 | 287
T72 | 232 | T72-A64 | 288
ZSU234 | 299 | ZSU234-d08 | 288
Train | Number |  | Depression
---
Angle
Test(EOC-C) | Number |  | Depression
---
Angle
BMP2 | 233 | $\text{17}{}^{\circ}$ | T72-S7 | 419 | $\text{15}{}^{\circ}$, $\text{17}{}^{\circ}$
BRDM2 | 298 | T72-A32 | 572
BTR70 | 233 | T72-A62 | 573
T72 | 232 | T72-A63 | 573
|  | T72-A64 | 573
Train | Number |  | Depression
---
Angle
Test(EOC-V) | Number |  | Depression
---
Angle
BMP2 | 233 | $\text{17}{}^{\circ}$ | T72-SN812 | 426 | $\text{15}{}^{\circ}$, $\text{17}{}^{\circ}$
|  | T72-A04 | 573
BRDM2 | 298 | T72-A05 | 573
|  | T72-A07 | 573
BTR70 | 233 | T72-A10 | 567
|  | BMP2-9566 | 428
T72 | 232 | BMP2-C21 | 429
TABLE IV: Recognition Performance (%) under EOC-D on MSTAR Class | Labeled Number in Each Class
---|---
1 | 2 | 5 | 10 | 25 | 80
BRDM2-E71 | 63.76 | 63.41 | 70.03 | 99.28 | 98.94 | 99.31
2S1-b01 | 75.00 | 68.75 | 82.99 | 72.84 | 81.61 | 96.00
T72-132 | 59.72 | 69.10 | 63.19 | 99.31 | 98.69 | 99.55
ZSU234-d08 | 50.00 | 47.92 | 81.94 | 84.57 | 77.93 | 84.18
Average | 62.12 | 62.29 | 74.54 | 85.93 | 86.97 | 94.01
TABLE V: Recognition Performance (%) under EOC-C on MSTAR Class | Labeled Number in Each Class
---|---
1 | 2 | 5 | 10 | 25 | 80
T72-A32 | 58.74 | 63.99 | 84.09 | 81.12 | 81.12 | 87.24
T72-A62 | 69.11 | 70.68 | 71.55 | 78.88 | 78.88 | 88.48
T72-A63 | 67.36 | 71.38 | 69.11 | 69.98 | 69.98 | 81.33
T72-A64 | 58.29 | 60.73 | 59.69 | 73.47 | 73.47 | 90.92
T72-S7 | 59.67 | 60.38 | 90.21 | 94.27 | 94.27 | 100.00
Average | 62.80 | 65.72 | 74.06 | 78.71 | 84.10 | 89.00
TABLE VI: Recognition Performance (%) under EOC-V on MSTAR Class | Labeled Number in Each Class
---|---
1 | 2 | 5 | 10 | 25 | 80
BMP2-9566 | 22.43 | 29.21 | 51.40 | 62.38 | 80.61 | 96.50
BMP2-C21 | 19.35 | 23.54 | 48.25 | 63.40 | 77.39 | 97.44
T72-SN812 | 76.76 | 81.22 | 89.44 | 92.72 | 94.84 | 96.71
T72-A04 | 68.41 | 61.95 | 78.01 | 76.44 | 83.25 | 88.66
T72-A05 | 57.94 | 61.08 | 79.23 | 85.34 | 89.35 | 95.64
T72-A07 | 65.45 | 63.35 | 74.69 | 82.20 | 91.80 | 96.16
T72-A10 | 53.62 | 64.55 | 82.72 | 91.36 | 95.06 | 98.59
Average | 53.49 | 56.21 | 67.16 | 79.85 | 87.84 | 95.52

The average recognition ratios are more than 94.00% when the training samples
are equal to or larger than 80. It means that the SCDR achieves a superior
performance of recognition when the training samples are not particularly
limited. The average recognition ratios achieve 87.48%, 86.96% and 85.92%,
respectively, when the training samples are 40, 20 and 10. When the training
samples are decreasing from 80 to 10, the performance of SCDR is robust to the
influence of the decreasing training samples. When the training samples are
limited to 5-shot and 2-shot, the recognition ratios can still achieve 74.54%
and 62.29%.

The recognition performance at the variance of target configuration and
version (EOC-C and EOC-V) is also evaluated. The training data and the testing
data for EOC-C and EOC-V are listed in Table III. Two different serial types
of BMP2 and five different serial types of T72 captured at
$\text{17}{}^{\circ}$ and $\text{15}{}^{\circ}$ depression angles are employed
to evaluate the recognition performance under EOC-C. The recognition
performance of EOC-C under limited training samples are listed in Table V. The
average recognition ratios achieve above 84.00% when the training samples are
ranging from 25 to 80. It is noted that when the training samples are limited
to 10 for each class, the recognition ratios achieve 78.70%. Furthermore, when
the samples are decreasing to 5-shot, the SCDR gets the recognition ratio of
74.06%, which means it is robust to decrease training samples in the range
from 5 to 10. When it is limited to 2-shot, the recognition ratio is 65.72%.
The results of EOC-C have illustrated the SCDR has the capability of handling
the large variance of serial types with limited training samples.

There are four different serial type versions of T72 in the testing dataset
being captured at $\text{17}{}^{\circ}$ and $\text{15}{}^{\circ}$ depression
angles and utilized to evaluate the recognition performance under EOC-V. The
recognition performance of EOC-V under limited training samples are listed in
Table VI. The average recognition ratios achieve above 95.50% when the
training samples are equal to or larger than 80 for each class. Even the
training samples are greatly decreasing to 25, the recognition ratios still
obtain 87.84%. The recognition ratios are close to 80.00% when there are 10
images for each class. In other words, the SCDR classifies most of the testing
samples correctly. When the training samples are limited in the range from 5
to 80, the recognition ratios decrease gradually. It is illustrated that the
SCDR alleviate the problem of the limited training samples.

From the recognition performance of EOCs, it is clear that facing the larger
variance of depression angels, configurations and type versions, the SCDR can
still achieve good recognition performance. In other words, the SCDR are
robust to the large variance between the imaging scenes of the training and
testing samples, which increases the practical application capability of SAR
ATR.

As shown by the recognition performance under SOC and EOCs in MSTAR data set,
the proposed SCDR is robust and effective when confronting the large
depression angle variant, configuration variant, and version variant, staying
at a high-level recognition accuracy.

####  IV-C3 Recognition Results under OpenSARShip

Following [39], [50], we choose three-class objects, bulk carrier, container
ship, and tanks, from OpenSARShip. The distribution of training and testing
data is listed in Table VII. To avoid the effects of the imbalance of the
number of three-class objects, concerning the least number of samples in all
three classes with the training-testing ratio as $4:6$, we make the number of
training samples the same for each class. The remaining samples are used for
testing. In the experiments, the training images are adjusted to the size of
$224\times 224$ by bi-linear interpolation.

TABLE VII: Image Number of Different Targets of OpenSARShip Class | Training | Testing | Total
---|---|---|---
Bulk Carrier | 300 | 374 | 674
Container Ship | 300 | 710 | 1010
Tanks | 300 | 253 | 553
TABLE VIII: Recognition Performance (%) under OpenSARship Class | Labeled Number in Each Class
---|---
10 | 50 | 60 | 75 | 100 | 150
Bulk Carrier | 57.77 | 55.39 | 64.34 | 65.10 | 66.11 | 74.13
Container Ship | 81.45 | 92.36 | 87.60 | 83.76 | 83.71 | 85.69
Tanks | 75.60 | 76.64 | 76.33 | 83.20 | 82.81 | 92.77
Average | 73.19 | 73.57 | 78.07 | 78.52 | 78.75 | 83.93

The recognition results of the proposed SCDR under OpenSARShip are presented
in Table VIII. The recognition performance achieves above 78.75% when training
samples are sufficient, equal to or more than 100, 83.92% under 150 for each
target, and 78.75% under 100 for each target. From 10 to 100 training images
for each class, the recognition ratios are ranging from 73.19% to 78.75%. More
thoroughly, the recognition ratios are 78.75% under 100 for each class, 78.52%
under 75 for each class, 78.06% under 60 for each class, and 73.57% under 50
for each class. Even when the training samples are limited to 10 training
samples for each class, the recognition ratio still obtains 73.19%. Therefore,
the recognition performance is robust to the decreasing training samples from
100 to 10.

By analyzing the experimental results under the MSTAR and OpenSARShip
datasets, our proposed SCDR shows the capabilities of robustness and
effectiveness. It can be seen that when encountering cases of limited training
samples and large variances in the experiments, the SCDR is capable of
remaining good recognition performance even for different SAR datasets. To
better and fairly illustrate the improvements in the recognition performance,
the following subsection gives a quantitative comparison with other SAR ATR
methods.

TABLE IX: Comparison of Performance (%) under SOC of MSTAR. Algorithms | Image Number for Each Class
---|---
20 | 40 | 80 | All data
PCA+SVM [51] | 76.43 | 87.95 | 92.48 | 94.32
ADaboost [51] | 75.68 | 86.45 | 91.45 | 93.51
LC-KSVD [51] | 78.83 | 87.39 | 93.23 | 95.13
DGM [51] | 81.11 | 88.14 | 92.85 | 96.07
DNN1 [52] | 77.86 | 86.98 | 93.04 | 95.54
DNN2 [53] | 79.39 | 87.73 | 93.76 | 96.50
CNN1 [51] | 81.80 | 88.35 | 93.88 | 97.03
CNN2 [50] | 75.88 | - | - | -
CNN+matrix [50] | 82.29 | - | - | -
GAN-CNN [51] | 84.39 | 90.13 | 94.91 | 97.53
MGAN-CNN [51] | 85.23 | 90.82 | 94.91 | 97.81
Semisupervised [39] | 92.62 | 97.11 | 98.65 | -
Ours | 94.97 | 97.81 | 98.72 | -

###  IV-D Comparison

TABLE X: Comparison of Performance (%) under SOC and EOCs of MSTAR.
(Other methods employed an additional dataset (SARSIM [54]) in training
besides MSTAR.) SOC
---
Algorithms | 10-way 1-shot | 10-way 2-shot | 10-way 5-shot | 10-way 10-shot | 10-way 25-shot
DeepEMD [55] | 36.19±0.46 | 43.49±0.44 | 53.14±0.40 | 59.64±0.39 | 59.71±0.31
DeepEMD grid [56] | 35.89±0.43 | 41.15±0.41 | 52.24±0.37 | 56.04±0.31 | 57.89±0.24
DeepEMD sample [56] | 35.47±0.44 | 42.39±0.42 | 50.34±0.39 | 52.36±0.28 | 55.02±0.22
DN4 [57] | 33.25±0.49 | 44.15±0.45 | 53.48±0.41 | 64.88±0.34 | 79.28±0.22
Prototypical Network [58] | 40.94±0.47 | 54.54±0.44 | 69.42±0.39 | 78.01±0.29 | 84.96±0.22
Relation Network [59] | 39.16±0.46 | 43.49±0.44 | 53.14±0.40 | 59.64±0.39 | 59.71±0.31
DKTS-N [60] | 49.26±0.48 | 58.51±0.42 | 72.32±0.32 | 84.59±0.24 | 96.15±0.08
Ours | 43.75 | 48.74 | 74.64 | 88.58 | 96.74
EOC-D
Algorithms | 4-way 1-shot | 4-way 2-shot | 4-way 5-shot | 4-way 10-shot | 4-way 25-shot
DeepEMD [55] | 56.81±0.99 | 62.80±0.78 | 65.16±0.61 | 67.58±0.49 | 70.22±0.35
DeepEMD grid [56] | 55.95±0.43 | 57.46±0.41 | 63.81±0.37 | 65.72±0.31 | 68.85±0.24
DeepEMD sample [56] | 49.65±0.44 | 54.00±0.42 | 58.19±0.39 | 60.34±0.28 | 62.51±0.22
DN4 [57] | 46.59±0.83 | 51.41±0.69 | 58.11±0.49 | 62.15±0.43 | 65.14±0.37
Prototypical Network [58] | 53.59±0.93 | 56.57±0.53 | 61.94±0.48 | 65.13±0.43 | 69.81±0.36
Relation Netwrok [59] | 43.21±1.02 | 46.93±0.81 | 54.97±0.56 | 38.62±0.49 | 44.42±0.43
DKTS-N [60] | 61.91±0.91 | 63.94±0.73 | 67.43±0.48 | 71.09±0.41 | 78.94±0.31
Ours | 62.11 | 62.29 | 74.54 | 85.93 | 86.98
EOC-C
Algorithms | 4-way 1-shot | 4-way 2-shot | 4-way 5-shot | 4-way 10-shot | 4-way 25-shot
DeepEMD [55] | 38.39±0.86 | 45.65±0.75 | 54.53±0.60 | 62.13±0.50 | 63.71±0.36
DN4 [57] | 46.13±0.69 | 51.21±0.62 | 58.14±0.54 | 63.08±0.51 | 69.66±0.46
Prototypical Network [58] | 43.59±0.84 | 51.17±0.78 | 59.15±0.70 | 64.15±0.61 | 69.95±0.50
Relation Netwrok [59] | 42.13±0.90 | 48.24±0.82 | 53.12±0.71 | 36.28±0.59 | 39.81±0.42
DKTS-N [60] | 47.26±0.79 | 53.61±0.70 | 62.23±0.56 | 68.41±0.51 | 74.51±0.36
Ours | 62.80 | 65.72 | 74.06 | 78.71 | 84.10
EOC-V
Algorithms | 4-way 1-shot | 4-way 2-shot | 4-way 5-shot | 4-way 10-shot | 4-way 25-shot
DeepEMD [55] | 40.92±0.76 | 49.12±0.65 | 58.43±0.51 | 67.64±0.42 | 67.03±0.21
DN4 [57] | 47.00±0.72 | 52.21±0.61 | 58.87±0.55 | 63.93±0.52 | 70.64±0.47
Prototypical Network [58] | 45.13±0.72 | 52.86±0.65 | 62.07±0.52 | 67.71±0.40 | 73.41±0.31
Relation Netwrok [59] | 40.24±0.91 | 46.32±0.82 | 54.22±0.68 | 35.13±0.52 | 33.18±0.46
DKTS-N [60] | 48.91±0.70 | 55.14±0.58 | 65.63±0.49 | 70.18±0.42 | 76.97±0.35
Ours | 53.49 | 56.21 | 67.16 | 79.85 | 87.84

In this subsection, the performance of the SCDR are compared with other
methods under two different ranges of training sample numbers. As described in
related works, the methods for the limited SAR data only employ K-shot from
MSTAR in training. If one method for the limited SAR data employs other images
as unlabeled images or other usages, we will present more detail about the
usages of the method.

In Table IX, the comparison with state-of-the-art methods for the limited SAR
data is presented. MGAN-CNN [39] improves the generated image quality of GAN
by multi-discriminator architecture for the improvement of the recognition
performance. CNN1 and GAN-CNN are the simplified versions of MGAN-CNN.
Semisupervised [39] proposed the self-consistent augmentation to utilize the
unlabeled data. For a fair comparison, we used the results of recognition
without sufficient unlabeled images in this paper. The methods used in the
above papers are also compared with the SCDR, including PCA+SVM, ADaboost, LC-
KSVD, DGM, DNN-based methods (DNN1 and DNN2), and CNN-based methods (CNN2 and
CNN+matrix) [39].

From the comparison, the recognition performance decreases obviously when the
image number for each class is changed from all data to 20 samples. MGAN-CNN
increased the performance lightly under 20 and 40 samples. Semisupervised
boost the performance under 20, 40, and 80 samples with its self-consistent
augmentation and training resources. From the quantitative comparison, it has
illustrated that the SCDR obtain higher recognition performance than others
under any number of training images in each class.

In Table X, the comparison with state-of-the-art methods from 1-shot to
25-shot is presented. DeepEMD [55] employed the earth mover’s distance (EMD)
as a metric to compute a structural distance between image representations to
determine image relevance for classification. DeepEMD-Grid and DeepEMD-
Sampling were novel structures with DeepEMD for slightly higher recognition
performance. Deep nearest neighbor neural network (DN4) [57] employed a local
descriptor-based image-to-class measure via a k-nearest neighbor searching
over the deep local descriptors of convolutional feature maps. Prototypical
network [58] learns a metric space in which classification can be performed by
computing distances to prototype representations of each class. By using both
SARSIM [54] and MSTAR, domain knowledge-powered two-stream deep network
(DKTS-N) [60] proposed a two-stream deep network for better recognition
performance.

It should be noted that the other methods in Table X employed an additional
dataset (SARSIM) [54] in training besides K-shot from MSTAR. From the
comparison of SOC, the results of the SCDR are higher than other methods when
the training samples for each class are larger than 2. Under the extreme
conditions, like 1-shot and 2-shot, there are few training samples used in our
method and no additional training datasets, which lead to the recognition
ratios of the SCDR being relatively lower than the DKTS-N. When the training
samples are increasing, like 5-shot or 10-shot, the effectiveness of our
method is also becoming more apparent. From the comparison of EOCs, the SCDR
outperforms other methods under the recognition of the 4-way, even without
additional training datasets. Clearly, the SCDR has a distinct improvement of
4-way 5-shot, 4-way 10-shot, and 4-way 25-shot under all three EOCs. Under
extreme conditions, the SCDR is still higher than other methods, only with
1-shot and 2-shot to train the model.

From the comparison with methods of the limited SAR data under SOC and EOCs in
MSTAR, it has illustrated that the SCDR has achieved state-of-the-art
performance among the methods of the limited SAR data, facing extreme few
training samples and a large variance between the training and testing
samples.

TABLE XI: Comparison of Performance (%) under OpenSARShip Methods | Number range of training images in each class
---|---
1 to 50 | 51 to 100 | 101 to 240
Semi-Supervised [39] |  | 61.88 (20)
---
64.73 (40)
68.67 (80) |  | 71.29 (120)
---
74.96 (240)
Supervised [39] |  | 58.24 (20)
---
62.09 (40)
65.63 (80) |  | 68.75 (120)
---
70.83 (240)
CNN[50] | 62.75 (50) | 68.52 (100) | 73.68 (200)
CNN+Matrix[50] | 72.86 (50) | 75.31 (100) | 77.22 (200)
Ours |  | 73.19 (10)
---
73.57 (50)
| 78.07 (60)
---
78.52 (75)
78.75 (100)
83.93 (150)

The comparison with other state-of-the-art methods under OPENSARShip is also
presented in Table XI. In different number ranges of the training sample for
each class, the SCDR outperforms other methods. When the training samples are
10 for each class, the performance of the SCDR is higher than the performance
of others with 50 for each class. It has illustrated that the SCDR has
increased obviously the recognition performance under OPENSARShip dataset.

From the comparisons of the two benchmark datasets, MSTAR and OPENSARShip, the
effectiveness and practicality of the SCDR have been validated. Meanwhile,
under different imaging conditions of different datasets, the SCDR can achieve
state-of-the-art performance. Furthermore, under extremely few training
samples and large variance between the training samples and testing samples,
the SCDR is robust for various experimental conditions, which will boost the
practical application of SAR ATR methods.

##  V Conclusion

The limited training SAR images hinder the practical application of SAR ATR
methods. Based on crucial feature capture and discrimination module, our SCDR
is proposed to capture and enhance the golden key of image to improve the
performance of SAR ATR under limited training data. Through the novel
framework and feature capture module, the SCDR automatically searches and
captures the discriminative local image regions in the whole image while
discarding other useless or even harmful image regions. The discrimination
module is proposed to enhance the overall and local features with more intra-
class compactness and inter-class separateness. Finally, the overall and local
features cooperated with learnable voting weights to finish the final
recognition. The experimental results and comparisons on MSTAR and OPENSAR
show that our method has achieved the best recognition performance to date. It
has also illustrated that the SCDR is robust to the different large variances
between the training samples and testing samples.

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|  Chenwei Wang received the B.S. degree from the School of Electronic
Engineering, University of Electronic Science and Technology of China (UESTC),
Chengdu, China, in 2018. He is currently pursuing the Ph.D. degree with the
School of Information and Communication Engineering, University of Electronic
Science and Technology of China, Chengdu, China. His research interests
include radar signal processing, machine learning, and automatic target
recognition.
---|---
|  Siyi Luo received the B.S. dual degree from Chongqing University (CQU),
Chongqing, China, in 2021. She is currently pursuing the M.S. degree with the
School of Information and Communication Engineering, University of Electronic
Science and Technology of China, Chengdu, China. Her research interests
include machine learning, target detection, and automatic target recognition.
---|---
|  Jifang Pei (M’19) received the B.S. degree from the College of Information
Engineering, Xiangtan University, Hunan, China, in 2010, and the M.S. degree
from the School of Electronic Engineering, University of Electronic Science
and Technology of China (UESTC), Chengdu, China, in 2013. He received the
Ph.D. degree from the School of Information and Communication Engineering,
UESTC, in 2018. From 2016 to 2017, he was a joint Ph.D. Student with the
Department of Electrical and Computer Engineering, National University of
Singapore, Singapore. He is currently an Associate Research Fellow with the
School of Information and Communication Engineering, UESTC. His research
interests include radar signal processing, machine learning, and automatic
target recognition.
---|---
|  Yulin Huang (M’08) received the B.S. and Ph.D. degrees from the School of
Electronic Engineering, University of Electronic Science and Technology of
China (UESTC), Chengdu, China, in 2002 and 2008, respectively. He is currently
a Professor at the UESTC. His research interests include radar signal
processing and SAR automatic target recognition.
---|---
|  Yin Zhang (M’16) received the B.S. and Ph.D. degrees from the School of
Electronic Engineering, University of Electronic Science and Technology of
China (UESTC), Chengdu, China, in 2008 and 2016, respectively. From September
2014 to September 2015, he had been a Visiting Student with the Department of
Electrical and Computer Engineering, University of Delaware, Newark, USA. He
is currently an Associate Research Fellow at the UESTC. His research interests
include signal processing and radar imaging.
---|---
|  Jianyu Yang (M’06) received the B.S. degree from the National University of
Defense Technology, Changsha, China, in 1984, and the M.S. and Ph.D. degrees
from the University of Electronic Science and Technology of China (UESTC),
Chengdu, China, in 1987 and 1991, respectively. He is currently a Professor at
the UESTC. His research interests include synthetic aperture radar and
statistical signal processing. Prof. Yang serves as a Senior Editor for the
Chinese Journal of Radio Science and the Journal of Systems Engineering and
Electronics.
---|---