# Generative Adversarial Networks for SAR Automatic Target Recognition and Classification Models Enhanced Explainability: Perspectives and Challenges

Héloïse Remusati, Jean-Marc Le Caillec, Jean-Yves Schneider, Jacques Petit-Frère, Thomas Merlet

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Héloïse Remusati, Jean-Marc Le Caillec, Jean-Yves Schneider, Jacques Petit-Frère, Thomas Merlet. Generative Adversarial Networks for SAR Automatic Target Recognition and Classification Models Enhanced Explainability: Perspectives and Challenges. Remote Sensing, 2024, 16 (14), pp.2569. 10.3390/rs16142569. hal-04655400

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Review

# Generative Adversarial Networks for SAR Automatic Target Recognition and Classification Models Enhanced Explainability: Perspectives and Challenges

Héloïse Remusati <fnref n="1" />,*,† D, Jean-Marc Le Caillec <fnref n="2" />,† D, Jean-Yves Schneider <fnref n="1" />, Jacques Petit-Frère <fnref n="1" /> and Thomas Merlet <fnref n="1" />

**Abstract:** Generative adversarial networks (or GANs) are a specific deep learning architecture often used for different usages, such as data generation or image-to-image translation. In recent years, this structure has gained increased popularity and has been used in different fields. One area of expertise currently in vogue is the use of GANs to produce synthetic aperture radar (SAR) data, and especially expand training datasets for SAR automatic target recognition (ATR). In effect, the complex SAR image formation makes these kind of data rich in information, leading to the use of deep networks in deep learning-based methods. Yet, deep networks also require sufficient data for training. However, contrary to optical images, we generally do not have a substantial number of available SAR images because of their acquisition and labelling cost; GANs are then an interesting tool. Concurrently, how to improve explainability for SAR ATR deep neural networks and how to make their reasoning more transparent have been increasingly explored as model opacity deteriorates trust of users. This paper aims at reviewing how GANs are used with SAR images, but also giving perspectives on how GANs could be used to improve interpretability and explainability of SAR classifiers.

**Keywords:** explanation; neural networks; radar target recognition; synthetic aperture radar

## 1. Introduction

Deep learning models have been increasingly employed for different applications and especially computer vision tasks. These kinds of algorithms have unlocked a huge advance in this area by enabling the automation of feature extraction and classification tasks, thanks to the powerful learning capabilities of such models.

In 2014, Goodfellow made a breakthrough with his idea of a novel architecture for generative models, called generative adversarial networks (GANs) [1]. The principle is fairly simple: the training needs two networks that play an adversarial game: one, referred as the discriminator, learns how to make the distinction between real and generated images by seeing both of them, while the other model, the generator, benefits from the feedback from the former to learn to generate more realistic data. At the end of the training step, the discriminator should not be able to differentiate between real and fake images any more. This process enables one to obtain a generator that can approximate real data distributions, such as common probability distributions in statistics or, in our case, distributions of pixels in images. In other terms, GANs intend to model high-dimensional distributions of data. Indeed, the generator learns to transform random noise (sampled from a chosen prior distribution) given to it as input into data, respecting the targeted real data distribution. This first architecture corresponds to the vanilla GAN. However, this initial framework is known to suffer from different drawbacks such as mode collapse, which has led researchers to invent novel architectures. We present some of them later in this paper.

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**Citation:** Remusati, H.; Le Caillec, J.-M.; Schneider, J.-Y.; Petit-Frère, J.; Merlet, T. Generative Adversarial Networks for SAR Automatic Target Recognition and Classification Models Enhanced Explainability: Perspectives and Challenges. *Remote Sens.* **2024**, *16*, 2569. https://doi.org/10.3390/rs16142569

Academic Editor: Dusan Gleich

Received: 4 June 2024

Revised: 3 July 2024

Accepted: 8 July 2024

Published: 13 July 2024

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**Copyright:** © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

<footnote n="1">¹ Thales LAS France SAS, 2 Avenue Gay Lussac, 78990 Elancourt, France</footnote>

<footnote n="2">² IMT Atlantique Bretagne-Pays de la Loire, Campus de Brest, Technopole Brest-Iroise, CS 83818, CEDEX 3, 29238 Brest, France; jm.lecaillec@imt-atlantique.fr</footnote>

<footnote>* Correspondence: heloise.remusati@thalesgroup.com; Tel.: +33-0614612301</footnote>

<footnote>† These authors contributed equally to this work.</footnote>
GANs can be and are often used to produce new data. This property is particularly desirable, especially for applications for which few data are available. In particular, we are going to focus on synthetic aperture radar (SAR) data in this article.

Synthetic aperture radar is a type of radar that can acquire remote-sensing data with a finer spatial resolution than usual radars. Its properties have made it a significant remote imaging technology, which has been used in many applications ranging from environment surveillance to target recognition. However, the complex mechanism of SAR image building strongly differs from human vision and makes SAR images difficult to interpret. Hence, manual interpretation is time consuming, challenging, and requires expertise. Strong attention has focused on SAR automatic target recognition (SAR ATR), which is an interpretation of SAR images aiming at associating labels to data. In particular, SAR ATR consists in identifying the class in which objects in an image belong; these targets can be terrestrial, aerial or maritime. It usually involves two steps: first, we need to extract features from the original images, and then we classify them by assigning the label. The number of papers and, consequently, techniques have been increasing since 1992, as we can see in Figure 1.

<figure><img src="image_6.png" /><figcaption>**Figure 1.** Evolution of the number of published papers found with the "SAR ATR" keywords in IEEE Xplore over the years.</figcaption></figure>

The acquisition cost constitutes one of the main drawbacks of this technique, along with the tedious task of labelling. This is where GANs come in. In 2017, Guo et al. [2] used a conditional GAN (its architecture is detailed later in this paper) to generate SAR target images and highlighted the difficulties of training GANs. In particular, they were confronted with failure modes that were, in part, characterised by the degradation of generated images. Indeed, their model ended up producing images only composed of noise. They suspected that this phenomenon was caused by speckle noise greatly present in SAR images. To make the model focus on the target instead of noise, they added a pre-processing step, called clutter normalisation. In addition, Zheng et al. [3] were among the first to explicitly use their generated images to improve SAR ATR model performances. They resorted to a model based on multiple discriminators (MGAN) to generate SAR target images and combined it with a CNN trained through semi-supervised learning and label smoothing regularisation [4] to improve target recognition results. They finally proved that using their model to expand the classifier training dataset increases its recognition accuracy up to 3%, especially in the context of a limited number of samples. One of the uses of GANs is thus to expand the amount of available data to improve recognition performances of SAR ATR deep learning-based models. This is the principle of data augmentation. Other generative models, such as autoencoders, are also used for this purpose but, in this paper, we choose to focus on GANs and SAR ATR, as previously stated. To perform ATR, two approaches are generally considered:
* Deep learning. The idea is to perform recognition via an end-to-end framework that includes both feature extraction and classification. In computer vision, the convolutional neural network (CNN) is a powerful tool known for its ability to extract relevant complex features from images thanks to its convolution and pooling layers. Chen et al. [5] proposed an all-convolutional network (ACconvNet) for SAR vehicle target classification, replacing all the fully connected layers with convolutional layers in order to reduce the computational burden while keeping the learning capabilities of the model. It is worth noting that other main CNN architectures such as VGGNet [6], ResNet [7], and DenseNet [8] are also used as backbone structures in SAR image interpretation methods [9]. On the other hand, in addition to CNNs, other major deep learning network architectures are also used. We can list recurrent neural networks (RNNs) [10] and long short-term memory (LSTM) [11], which is one of the most popular architectures in RNN. This structure is often used to deal with sequential data and thus is widely used in the research of multi-view SAR images [12].

* Scattering centres. In this case, the focus is on feature extraction. In fact, instead of automatically discovering the representation needed for classification from raw data (process also known as representation learning), we design features specially constructed for SAR data that tend to better reflect the characteristics of SAR images. Among them, we can name geometric features [13], transform domain features [14], and electromagnetic scattering features [15]. The later approach includes the use of the attributed scattering centres (ASCs) model that consists in approximating target scattering as the sum of the response of multiple canonical ASCs. In this example, we can convey the physical characteristics of the SAR target better than with features extracted in an end-to-end manner. For example, Fu et al. [16] proposed a template matching-based aircraft recognition method with a scattering structure feature (SSF) to improve classification accuracy in SAR images. This kind of target recognition algorithm makes the classification process more interpretable and robust by considering physical aspects.

In fact, even though using deep learning models can improve automatic target recognition performances, they remain black-box models, which is problematic in safety-critical applications, for example defence applications. Recent papers aim at improving explainability of such algorithms via different approaches, such as attention mechanisms or even injecting physical knowledge into networks. For instance, Feng et al. [17] built an electromagnetic scattering feature module embedded network to perform robust and interpretable ATR. Indeed, they trained a CNN-based model to extract ASC parameters in order to learn how to extract target features related to the physical model. This model, called physics-guided deep learning, is then used to construct a classifier. Conversely, Belloni et al. [18] proposed another approach by studying pre-trained CNNs and presented tools aiming at explaining their reasoning. First, via different occlusion techniques, they studied the critical features used by the model to make predictions and highlighted the contribution of the shadow, the target, and the clutter to classification performances. Finally, they showed that features are increasingly activated along the CNN depth in accordance with the target type and its orientation, even though there is no explicit regularisation of pose during training.

In parallel, researchers try to lift the veil on the mystery of GANs. In particular, Bau et al. [19] proposed GAN dissection to attempt to explain what concepts GANs have learned and to evaluate the presence of semantic units in them. They succeeded in identifying specific groups of neurons that correspond to trees, for example. Playing with such entities allows interactive image editing: enabling them permits one to add trees in a scene, while ablating them makes tree erasure possible.

Through the study of these various aspects, we believe that it would be useful to give an overall vision of the use of GANs for SAR images and, in particular, with respect to SAR ATR, in order to give a new perspective on how to use GANs to improve explainability of SAR classifiers.
As seen below, the SAR ATR and the GANs architecture, training, and understanding are not easily affordable topics. The two require much investment to be at least understood and possibly handled. We conceive this paper as a milestone in the interest and the difficulty of using GANs for the SAR ATR purpose. Obviously, as usual in machine learning, we base our reflection on numerous results obtained on optical images, since the number and diversity of the databases with these kind of images substantially overwhelm the few databases of active sensors (in particular SAR), first promising then producing results as a possible spark to transfer GANs to SAR ATR. Indeed, transposing results from RGB images to the very less informative images of grey-scale intensity (but possibly complex valued) is a gap to be bridged, requiring also some involvement.

Then, the main contributions of this paper are fourfold:

* A review of GANs for SAR images.
* A categorisation grouping GANs approaches according to their potential contribution for improving explainability of SAR classifiers, and particularly for terrestrial targets.
* New perspectives of classifier explainability through GANs.

Section 2 introduces the theory useful for this paper, Section 3 considers related surveys, and Section 4 is the main body of our work. Finally, we mention some of the challenges related to our approach in Section 5 and conclusions are given in Section 6.

## 2. A Brief Background on GAN, Explainability, and SAR Images

In this first section, we expose the three domains tackled in this paper, as concisely as possible, before focusing on their interaction.

### 2.1. GAN Theory

As previously mentioned, GANs were first proposed by Goodfellow et al. [1]. The architecture of GANs consists of a deconvolutional network and a convolutional network, as presented in Figure 2.

<figure><img src="image_7.png" /><figcaption>**Figure 2.** GAN Architecture.</figcaption></figure>

The deconvolutional network, called generator *G*, is trained to generate samples from data distribution $P_r(x)$, by transforming the noise, *z*, from noise distribution $P_z(x)$ to $P_r(x)$, with *x* = *G*(*z*). The convolutional network, called discriminator *D*, is trained to determine whether its input sample is a real or fake image during the process of training. Indeed, *D* outputs a score between 0 and 1, representing the probability that the seen sample is a real data point. 0 corresponds to an image that *D* considers as fake whereas *D* outputs 1 when it is sure that the considered sample is real. Concretely, we can roughly consider this scalar as a "realism" score.
While the generator tries to deceive *D* by generating realistic images, *D* attempts to maximise the probability of assigning the correct label to both training and generated samples. In fact, *D* and *G* look like playing the two-player minimax game on the condition of the following function *V*(*D*, *G*):

$$ \min_G \max_D V(D, G) = E_{X \sim P_r(x)}[\log(D(x))] + E_{Z \sim P_z(z)}[\log(1 - D(G(z)))] \quad (1) $$

with $E_{X \sim P_r(x)}$ the expected value under distribution $P_r(x)$, and $D(x)$ the probability that sample $x$ comes from the data distribution, $P_r(x)$, rather than the generator distribution, $P_g(x)$. In practice, there are two alternative steps to training a GAN:

* While the generator weights are frozen, the discriminator is trained. Specifically, it is trained on real data to check whether it can properly forecast them as real, and, conversely, it is taught on the generator false-generated data to determine whether it can properly forecast them as fake.

* While the discriminator is fixed, the generator is being trained. The discriminator gives its feedback to the network and the generator tries to become better at misleading the discriminator.

The aforementioned technique is replicated over a few epochs, after which false data are carefully checked to determine whether they appear as real. In case of satisfactory results, the training is ended. Otherwise, it proceeds for extra epochs. As seen below, jointly with GANs, the latent space is a key concept to open the black box, as stated in introduction. Latent space is a high-dimensional space in which lie the vectors inputted into the generator. After training, the generator provides an image from a point in latent space. In other words, one vector in latent space corresponds to an image in image space. Thus, latent space can be seen as a reduced dimension representation of the considered data and the generator as the bridge between them. Figure 3 intends to illustrate this definition.

<figure><img src="image_8.png" /><figcaption>Figure 3. Latent and data space representation (SAR image from the MSTAR Dataset [20]).</figcaption></figure>

## 2.2. eXplainable Artificial Intelligence (XAI)

At the appearance of deep learning methods, great amounts of attention and wonderment were produced at the learning capabilities and accuracy performances of such methods. The number of learning parameters combined with the non-linearities layers enabled one to solve complex problems in an end-to-end manner only thanks to the power of optimization. Their breathtaking performances enticed researchers to apply them to their domains. This overperformance also caught the eye of industry, since adopting these models could automate, improve, and hasten many processes while reducing operators'
cognitive load. However, not all the applications are equivalent. In fact, generating art with deep models does not have the same impact as identifying a target, and such critical utilisations raise ethical questions. In addition to the creation of new laws intending to regulate, or at least control, AI implementations, users have begun asking questions about what models learn, what concepts are learnt, and to what extent models are trustworthy and dependable. Indeed, deep learning-based algorithms are black-box and opaque models, which make them unintelligible and undermine users' trust. To alleviate this issue, a new research approach has surfaced: explainable artificial intelligence, or XAI. To lay the foundation of our paper, we want to begin by defining terms.

Explainability. This concept is relatively new, and it is kind of delicate since there is no consensus over the definition of an explanation, interpretability, or explainability. We can roughly name two trends:

* Some authors, like Guidotti et al. [21], use interpretability and explainability interchangeably, defining interpreting as the fact of making sense, being explicit, and presenting concepts and results via intelligible terms;

* Others, like Marcinkevics et al. [22], on the other hand, make a distinction between explainability and interpretability. In their opinion, interpretability is a property of a model that is intelligible and self-sufficient enough to be understandable. In other terms, it is an intrinsic property of white-box models such as decision trees. Explainability is the extent to which it is possible to explain, in a post-hoc manner, a black-box model. In this paper, we prefer this definition because we need to have this nuance.

For both propositions, explanations can be local or global.

Local explanations generally refer to explanations that aim at answering "Why did the model make this prediction for this instance?". The idea is to justify the decision for a particular input, for example, revealing the features participating the most in the prediction.

Secondly, global explanations produce larger scope explanations. They tend to "whiten" the model by answering "How does the trained model make predictions?". They can, e.g., unveil concepts learnt by the model.

Obviously, distinct types of deep learning models require different explainability methods: explaining CNNs is different from explaining RNNs due to their architecture specificities. In our paper, we only focus on those related to GANs.

## 3. Previous Surveys

In this section, we briefly compare this paper to different existing surveys dealing with the tackled topics, depicted in Figure 4. First, we can enumerate several surveys giving a general overview and review of GANs [23–40]. These papers present the training procedure, the different architectures, their applications, and limitations but without focusing on any specific applications or data type, whereas other papers [41–46] give an overview of GAN applications for specific domains, such as medical imaging or anomaly detection (but none on SAR images). Ref. [47] is the closest to our intent, since it presents GANs’ remote sensing context. Yet, it differs from ours in the sense that the authors give a more general overview: they do not focus on SAR data and do not consider the explainability aspect. No survey specifically deals with explainable GANs, but we can find different reviews interested in explainability definitions and methods, such as [21,22,48–55]. Similarly, few surveys try to review methods for explainable SAR ATR models but [56] proposes a comprehensive comparison of explainability methods, usually used on optical data and transferred in the SAR image domain. Moreover, we cannot count the number of papers reviewing deep learning methods used for SAR ATR (e.g., [57–60]), with some references to the use of GANs. To the authors’ knowledge, this paper is the first to jointly tackle the three aforementioned fields: SAR ATR, GANs, and explainable AI.
<figure><img src="image_9.png" /><figcaption>Figure 4. Considered topics and existing surveys.</figcaption></figure>

4. GANs for SAR Images

As previously said, the central idea of our work is to review some potential uses of GANs for SAR images, and in particular ATR, and see how it has been or how it could be used to improve explainability of SAR ATR classifiers. Firstly, it is important to emphasis the fact that GANs learn to approximate the real distribution of data. This is the main asset of this type of architecture in our opinion. In fact, they are consequently used to learn a representation of existing data and inevitably can be exploited to provide new samples. Thanks to our literature compiling, we identified three approaches to use GANs and this special attribute to enhance SAR ATR models’ explainability:

* Using GANs to improve classifier performances;

* Using GANs as a post-hoc method to understand classifiers;

* Using GANs' explainability to improve classifiers' intrinsic explainability.

The structure of this section can be seen in Figure 5.

<figure><img src="image_10.png" /><figcaption>Figure 5. Structure of Section 4.</figcaption></figure>
In Table 1, we gather the different approaches (for enhancing SAR ATR model explainability) discussed in our paper with their related references (papers using GANs).

<table><caption>**Table 1.** Brief summary of proposed approaches and related works.</caption><thead><tr><th colspan="3">Approaches</th><th rowspan="2">Related Works</th><th colspan="2">SAR Classification</th><th colspan="2">Usages</th></tr><tr><th></th><th></th><th></th><th>SAR ATR</th><th></th><th>Enhancing GAN Explainability</th><th>Enhancing Classifier Explainability</th></tr></thead><tbody><tr><td rowspan="10">Improve classifier performance (Section 4.1)</td><td rowspan="5">Data generation (Section 4.1.1)</td><td rowspan="3">Improve image quality</td><td>Constrained Naive-GAN [61]</td><td></td><td>x</td><td></td><td></td></tr><tr><td>Dual GAN [62]</td><td></td><td>x</td><td></td><td></td></tr><tr><td>Shi et al. [63]</td><td></td><td>x</td><td></td><td></td></tr><tr><td rowspan="2">Generate new data</td><td>Sun et al. [64]</td><td>x</td><td>x</td><td></td><td></td></tr><tr><td>MS-GAN [65]</td><td></td><td>x</td><td></td><td></td></tr><tr><td rowspan="5">Enhance feature extraction (Section 4.1.2)</td><td>CVCGAN [66]</td><td></td><td>x</td><td></td><td></td></tr><tr><td>MGAN [3]</td><td></td><td>x</td><td></td><td></td></tr><tr><td>WGAN-GP [67]</td><td></td><td>x</td><td></td><td></td></tr><tr><td>WGAN-GP</td><td></td><td></td><td></td><td></td></tr><tr><td>Hinge Loss [68]</td><td></td><td>x</td><td></td><td></td></tr><tr><td rowspan="10">Understand classifier (Section 4.2)</td><td rowspan="5">Identify classifier failure modes (Section 4.2.1)</td><td rowspan="2">Generate counterfactual explanations (4.2.2)</td><td>Zhang et al. [69]</td><td>x</td><td>x</td><td></td><td></td></tr><tr><td>cGAN</td><td></td><td>x</td><td></td><td></td></tr><tr><td>Open Set Recognition [70]</td><td></td><td>x</td><td></td><td></td></tr><tr><td>AEN [71]</td><td></td><td>x</td><td></td><td></td></tr><tr><td>DCGAN-MCAE [72]</td><td></td><td>x</td><td></td><td></td></tr><tr><td rowspan="5">Generate counterfactual explanations (4.2.2)</td><td>Le Coz et al. [73]</td><td></td><td></td><td></td><td>x</td></tr><tr><td>TUAN [74]</td><td></td><td>x</td><td></td><td></td></tr><tr><td>CounteRGAN [75]</td><td></td><td></td><td></td><td>x</td></tr><tr><td>GANMEX [76]</td><td></td><td></td><td></td><td>x</td></tr><tr><td>XAI for Automotive Radar Targets Classification [77]</td><td></td><td>x</td><td></td><td>x</td></tr><tr><td rowspan="20">Ensure classifier explainability thanks to GAN explainability (Section 4.3)</td><td rowspan="10">Explainability for GANs (Section 4.3.1)</td><td rowspan="5">Post-hoc methods</td><td>GAN Dissection [19]</td><td></td><td></td><td>x</td><td></td></tr><tr><td>GANSpace [78]</td><td></td><td></td><td>x</td><td></td></tr><tr><td>Voynov et al. [79]</td><td></td><td></td><td>x</td><td></td></tr><tr><td>InterFaceGAN [80]</td><td></td><td></td><td>x</td><td></td></tr><tr><td>PCAAE [81]</td><td></td><td></td><td>x</td><td></td></tr><tr><td>IIN [82]</td><td></td><td></td><td>x</td><td></td></tr><tr><td rowspan="10">Ante-hoc methods</td><td>infoGAN [83]</td><td></td><td>x</td><td></td><td></td></tr><tr><td>Feng et al. [84]</td><td></td><td>x</td><td></td><td>x</td></tr><tr><td>DDGAN [85]</td><td></td><td>x</td><td></td><td></td></tr><tr><td>PGGAN [86]</td><td></td><td>x</td><td></td><td></td></tr><tr><td>Li et al. [87]</td><td></td><td>x</td><td></td><td></td></tr><tr><td>MCGAN [88]</td><td></td><td>x</td><td></td><td></td></tr><tr><td>TripleGAN [89]</td><td></td><td>x</td><td></td><td></td></tr><tr><td>PeaceGAN [90]</td><td></td><td>x</td><td></td><td></td></tr><tr><td>AAE [91]</td><td></td><td>x</td><td></td><td></td></tr><tr><td rowspan="5">Components of latent space</td><td>GAN-Control [92]</td><td></td><td></td><td>x</td><td></td></tr><tr><td>Sparsified spike and slab distribution [93]</td><td></td><td></td><td>x</td><td></td></tr><tr><td>ClusterGAN [94]</td><td></td><td></td><td>x</td><td></td></tr><tr><td rowspan="2">Clustering in latent space</td><td>SIMI-ClusterGAN [95]</td><td></td><td></td><td>x</td><td></td></tr><tr><td>Soft Nearest Neighbour Loss [96]</td><td></td><td></td><td>x</td><td></td></tr><tr><td>Perspectives on how to use GAN explainability for classifier explainability (Section 4.3.2)</td><td></td><td></td><td>Garg et al. [97]</td><td></td><td>x</td><td>x</td></tr></tbody></table>

We chose our related works according to two criteria:

* GANs dealing with SAR data (purple);

* GANs dealing with explainability (orange).

We state their different application domain (SAR classification refers to texture recognition, forest for example, whereas SAR ATR consists in recognising a man-made target in an image) and their aim (GAN explainability, classifier explainability). Table 1 shows that no paper joins the three considered topics (GANs, XAI, and SAR ATR). As far as we know, using GANs to enhance SAR ATR model explainability has never been explored in detail: it justifies our motivation to show how existing methods could be used and to propose new perspectives to improve SAR classifier explainability through GANs. We want to demonstrate that the discussed approaches are thus strategies that came to our mind during literature compiling. To the best of our knowledge, none of the approaches have been tried on SAR ATR models and are our proposals. Related works are then illustrations of our suggestions based on the referred papers. Consequently, a significant number of papers have not been tested on SAR data (only on optical images). Nevertheless, we believe that the motivation behind these approaches is still of interest and can be seen as domain-agnostic, such that it would be worthwhile to explore their adaptation to the SAR domain.

## 4.1. Use of GANs to Improve Classifier Performance

Usually, GANs are used to improve classifier performances, with data augmentation for example. Similarly, we think that GANs could be used to improve the explainability of the classifiers during training. The idea is to improve the training process and the classifier learning by:

* Enhancing the training dataset [3,4,61–64,67,98,99]. The dataset quality is undeniably essential to the relevant learning of the classifier. Adding more data could overcome
the lack of data and/or data diversity, which could improve the concepts learnt by the SAR ATR model. For instance, it would enable one to guide the invariances acquired by the algorithm.

* Guiding feature extraction [68,69]. Adding GANs as part of the classifier training process changes and can make the features extracted by the classifier richer.

Obviously, there is not any guarantee that adding more data images into the training, or even improving learning in the sense of increasing the model accuracy, would improve the classifier explainability (even though it is interesting to note that, philosophically speaking, Durán and Jongsma [100] state that accuracy is enough to trust AI models); we only think that it would be an interesting direction to study the differences undergone by the classifier implied by the modification of the original dataset. Consequently, it could be possible to use off the-shelf explainability methods, such as heatmaps [101], to compare the modified and unmodified models.

### 4.1.1. Data Generation

We first study how to enhance the training dataset with GANs.

* Improving image quality

The first approach consists in improving the quality of the images fed to the classifier. In this case, we are dealing with image-to-image translation kind of problems. In [61], Mao et al. proposed an architecture called constrained naive GAN, whose aim is to denoise images. They wanted to deal with the recurrent issues encountered with SAR images, i.e., speckle noise and scarce data. First, they use the principle of image-to-image translation to despeckle noisy SAR images: they feed them to the trained generator that has learnt to produce high-quality synthetic images. Next, they use a shallow CNN dedicated to classification. They shown that their expansion method (adding denoised images to the initial noisy dataset) improves the recognition rate of their classifier.

Similarly, Guo et al. designed a polyvalent and compact ATR model that jointly includes denoising, feature extraction, and classification in [62]. Their framework is presented in Figure 6.

<figure><img src="image_11.png" /><figcaption>**Figure 6.** Guo et al. model architecture [62].</figcaption></figure>

By using a dual GAN, they constructed a symmetrical bridge between low and high signal-to-noise ratio (SNR) data, while incorporating a classifier for the recognition part that works on denoised data. They showed the interest of despeckling images in terms of classification.

Conversely, Shi et al. [63] considered that low-resolution images were pre-processed SAR images masked with a computed binary mask intending to remove background. They trained a GAN to teach it to produce high-resolution images before feeding high-quality inputs to a deep CNN.
Different again, Sun et al. [64] innovatively proposed using a conditional GAN (cGAN-[98])-based model to translate SAR images to the optical domain as a pre-processing step. In fact, the automatically translated images are then fed to a classifier. Their architecture is shown in Figure 7.

<figure><img src="image_12.png" /><figcaption>**Figure 7.** Sun et al. model architecture [64]. (a) Creation of the SPH4 dataset; (b) Training of the translation and recognition networks.</figcaption></figure>

In the same manner, Guo et al. [65] resorted to SAR-to-optical image translation via their architecture called MS-GAN. However, their framework does not require any data pairs to learn the conversion between SAR and optical domains. Indeed, they used a generative cycle adversarial network, which also enabled them to perform transfer between the two domains in both directions (see also [102]). On another note, they ensured that their generated images were of satisfactory quality by:

- Denoising SAR images with a sub-bands shrinkage denoising (SSD) module;

- Designing a multiscale representation generator (MRG) and a multireceptive field discriminator (MFD), which can respectively memorize and generate subtle details of the scenes.

In [66], Kim et al. proposed a technique for adapting synthetic SAR images to measured SAR images using a complex value conditional generative adversarial network. This method aims to reduce the disparities between synthetic SAR images, which are generated by simulations and often used for training recognition models, and measured SAR images from real sensors. In the end, they proved that their adapted images can improve classifier accuracy compared with a classifier trained on real data.

* **Generating new data**

The second approach involves generating new data points after training on real data. In this case, we deal with “classical” types of data for the generator: we input noise into the generator in order to obtain images as outputs. In addition, in this paragraph, we are only going to focus on GANs that can “traditionally” generate SAR images and not on variants such as models based on a conditional GAN or InfoGAN [99] since they affect latent space (see Section 2.1).
In [3], Zheng et al. proposed to train a dynamically adjustable multi-discriminator GAN in order to produce unlabelled images that are then labelled through label smoothing regularisation [4]. Then, these images are jointly used with real images to train a CNN devoted to SAR ATR. This work innovatively resorts to a multi-discriminator framework in a dynamic manner, enabling the generator to be exposed to the ensemble average of all discriminators and gradually to the best one during the rest of the training as the discriminators' performances increase. This paper highlights the interest of using GANs to perform data augmentation for SAR ATR, especially in a case of semi-supervised learning.

Conversely, Cui et al. [67] used a GAN variant called the Wasserstein generative adversarial network with gradient penalty (WGAN-GP-[103,104]) to generate new data. This model aims at improving the initial GAN architecture by:

- Stabilising training through the addition of a Wasserstein distance metric;

- Improving the quality of training and images thanks to the penalisation of the norm of gradient of the critic (discriminator) with respect to its input, instead of using weight clipping.

After several images are generated, they are filtered via classification and azimuth estimation, with a pre-trained support vector machine (SVM) and an azimuth filter, respectively, in order to limit randomness in the expanded dataset.

### 4.1.2. Enhance Feature Extraction

During training, classical ATR models are shown images with a corresponding label that they must be able to predict. Consequently, training them in an end-to-end manner leads the classifier to focus on relevant features for the classification task. However, depending on the training dataset and on the architecture of the model, the classifier can learn features enabling it to obtain high-accuracy, but not necessarily relevant, extract features, at least human-relevant for the application. Indeed, since deep learning relies on optimisation methods, models take the path giving the best results for resolving problems. For example, this can lead to learn biases but also to deterioration of the generalisation ability. To circumvent this, we can guide the features learnt by the classifier. There are several ways to make it occur, but we focus here on how using GANs can enhance (at least change) the feature extraction learning. As GANs are used to learn to approximate the real data distribution, using this purpose as an auxiliary task can lead the models to learn more general features, which are richer than only learnt classification features but sufficient to succeed in classifying images. This can be done thanks to transfer learning or even multi-task learning.

In [68], He et al. proposed using a WGAN-GP to be trained on SAR data. The first layers of the discriminator are then extracted and used as a feature extractor. A convolutional classifier is then added to this pre-trained encoder, and its parameters are fine-tuned via a hinge loss. According to them, this transfer learning combined with the hinge loss enables the model to extract a more complete feature representation and improves the generalisation ability of the finally obtained classifier.

Similarly, Zhang et al. [69] built an InfoGAN (Chen et al. [99])-inspired model. InfoGAN is a variant of GAN introducing structured latent variables into the information flow. Generator input is now the concatenation of *c*, structured latent variables, and *z*, the standard random noise. To come back in feature space, an auxiliary model, *Q*, is added to retrieve this label from the provided image. This last task is performed using the mutual information maximisation lower bound between *c* and the generated data, while the real/fake task is performed in a classical manner. This architecture is used to learn disentangled representation in an unsupervised manner. It is presented in Figure 8.
<figure><img src="image_13.png" /><figcaption>**Figure 8.** InfoGAN architecture.</figcaption></figure>

After having trained this GAN on a huge amount of unlabelled SAR images, Zhang et al. extracted the encoder, or even the feature extractor, to build a classifier by adding a supplementary fully connected layer. Hence, the encoder first learns the generic features of the SAR images through an auxiliary task and is then fine-tuned on the classification task (see also [105]).

On the other hand, Ma et al. in [70] do not resort to transfer learning but rather to multi-task learning. They built a model inspired by the conditional GAN (cGAN) architecture and added another output branch to the discriminator dedicated to ATR (see also [106]). cGAN is a variant of its predecessor GAN, in which information, such as category or source, is added along the data flow. In this type of architecture, the discriminator does not only evaluate images, as with a vanilla GAN, but also pairs of data samples: data concatenated with c, the piece of information of interest. The architecture is shown in Figure 9.

<figure><img src="image_14.png" /><figcaption>**Figure 9.** conditional GAN (cGAN) architecture.</figcaption></figure>

Thus, the features extracted by the model core are influenced by both outputs and tasks.

However, Ma et al. are not directly dealing with a classification task but with an open set recognition task. In other words, they want to identify whether the considered target is known or unknown. To do so, they make the non-negligible assumption whereby the real/fake task of the discriminator can be seen as a regression task and represents the confidence score of the model. In other words, known classes, hence known distributions, are synonyms of high confidence scores and inversely for unknown classes. Open set recognition (OSR) can then be simply performed by choosing a threshold on the output score.

To come back to the classification task, Du et al. [71] proposed a model combining an adversarial encoding network and a classifier. This model consists of an encoder and a discriminator that outputs three components. The shared layers perform feature extraction, which is influenced by:

* A decoding component reconstructing the image, which assures that a complete representation of the image is contained in the feature vector;
* A classifier component simply labelling the image, which ensures that category information is contained in this feature vector;

* Finally, the real/fake component that aims at recognising real and generated images. Their work is original in the sense that they use real and simulated SAR images. By using data that are extracted from two distinct domains, the model tends to pay more attention to features that are common to the two: the “physical-related features”. Their architecture is illustrated in Figure 10.

<figure><img src="image_15.png" /><figcaption>**Figure 10.** Du et al. [71] framework.</figcaption></figure>

Similarly, in [72], Zhang et al. designed a deep convolutional GAN-multi-classifier autoencoder to perform SAR ATR. The principle of their work is to improve the extracted features as much as possible. To do so, they use the same architecture several times but at different scales. One unit is composed of a generator and a discriminator; the discriminator outputs once again three elements: the real/fake score, the classification prediction, and an autoencoder that pushes the generator to extract richer features. Then, the trained discriminators extract the features that are next concatenated and classified. Finally, they used an explainability method (adjacent super pixel patch gradient-weighted class activation map visualisation), which aims at visualising the importance of different image regions in making predictions, in order to show that their proposed network activates the correct categories more than other models.

## 4.2. Use of GANs to Understand Classifiers

Instead of using GANs to enhance classifier performances or feature extraction, another trail we can think about is using GANs to understand ATR models. More clearly, in this paragraph, we do not focus on GANs used during training neither on GANs whose aim is to indirectly improve explainability for classifiers but rather on architecture that straightforwardly intends to give explanations or provide explainability for the considered models. As far as we know, none of these techniques have been applied on SAR ATR models.

### 4.2.1. Identify Classifier Failure Modes

An idea can be to use trained generators to produce data and identify the classifier failures. In other words, we first need to train a generator, via adversarial training, to obtain a functional model that can produce data obeying real data distribution. Then, the model can provide as many data as wanted. By providing these images to the classifier, it is possible to search for trends of the ATR model: for example, we could find similar images always leading the model to make a mistake. This could highlight concepts that the model does not know or that it has learnt in an incorrect way. For example, Le Coz et al. [73] identified directions in a StyleGAN2 latent space that led to strong classifier performance degradation. Thus, they considered these directions as failure conditions and they discovered that some of them, such as image quality, can affect all classes, whereas other ones, such as shape, are more class-specific.
Another idea is to directly train a generator to produce samples that will cause the classifier to fail. Roughly, these examples are known as adversarial attacks. In [74], Wan et al. proposed a GAN-based architecture called TUAN, whose aim is to produce black-box universal adversarial attacks for SAR ATR models (see also [107]). Their generator-like network aims at producing adversarial samples, while their discriminator-like network, referred as an attenuator in the paper, tries to weaken the attack effectiveness of the adversarial examples. They argue that this last aspect is the key to generate universal adversarial attacks as it makes the generator produce adversarial samples that are more robust to the perturbations produced by the attenuator.

### 4.2.2. Counterfactual Explanations Generation

Aside from being empirical, this last approach does not ensure that we retrieve general concepts or even logical reasoning for the classifier. To alleviate this issue, it could be interesting to produce fewer global explanations, and try to generate one-versus-one explanations answering the question “Why this class prediction and not this other one?”. To do so, GANs can help produce counterfactual explanations, which are data similar to an original input, but leading the classifier not to predict the same class as the initial image. This explainability method allows one to explain the classifier prediction for a specific input, to a certain extent, but also to learn how the classifier pictures different classes.

Nemirovsky et al. in [75] proposed a framework called CounteRGAN, presented in Figure 11, based on their proposed residual GAN (RGAN).

<figure><img src="image_16.png" /><figcaption>Figure 11. Nemirovsky et al. [75] framework.</figcaption></figure>

The latter aims to produce images called residuals. Adding these residuals to initial inputs lead the target classifier to predict a desired class, different from the original one. By definition, the sum of the initial images with the perturbation images provided by the generator are counterfactuals. In fact, the discriminator is fed with real images and with the obtained counterfactuals instead of only generated images, as in a vanilla GAN. The generator receives the feedback of two components during training:

* The discriminator, making *G* produce more realistic residuals, and thus counterfactuals;

* The trained classifier *C* that we want to explain, guaranteeing that the produced counterfactuals belong well to the desired class.

Not only does this model help with more visibility at the ATR model level, but also permits one to identify potential biases in the training dataset.
The authors of [77] used a similar architecture as in [75] to produce counterfactual
explanations. However, they applied it on automotive radar targets and succeeded in
providing information on classifier reasoning. Indeed, thanks to their counterfactual
examples, they revealed that some vehicle parts are decisive for predicting a specific class.
Finally, they also used different metrics on the generated counterfactual images to assess
the performance of their framework.

In [76], Shih et al. proposed a model called GANMEX (GAN-based model explainabil-
ity), adapted from the StarGAN model [108], including a generator and two discriminators
during training. One is for the classical real/fake task and the other is the trained classifier
that we want to explain. However, their work is different in the sense that they use the
provided counterfactuals to constitute baselines for attribution methods. In fact, these
methods, consisting in highlighting the features of a specific input image relevant for a
classifier, rely on baselines by definition. Nevertheless, they realised that these baselines
are often chosen by default, and this can be problematic since a poor baseline choice can
lead to completely incorrect results. Thus, they designed a GAN that is able of generating
baselines tailored for a precise classifier: based on image-to-image translation, it produces
personalised baselines starting from a standard baseline. Then, they simply use attribution
methods with these novel baselines which:

* Belong to a specific class (different from the initial one and that we want to confront to the original one) according to the considered classifier;

* Are realistic;

* Are similar to the original input to provide 1-vs-1 explanations and justify misclassified samples.
Thus, this method can help starting to open the black-box model.

4.3. Ensure Classifier Explainability through GAN Explainability

The last approach involves the use of GAN explainability. As explained before,
there has been increased attention on explainability methods for deep learning-based
models. Obviously, GAN-based works [19,78–82] have been published proposing different
approaches. However, to the best of our knowledge, no work has been carried out on
enhancing (SAR ATR) classifier explainability through GAN explainability.

We first present different approaches drawn from the literature to explain GANs,
and we then try to propose several methods to use this knowledge to suggest explainability
techniques for SAR ATR models.

4.3.1. Explainability for GANs

In this paragraph, we focus on some explainability methods applied on GANs. We
can divide them into two categories: post-hoc and ante-hoc explainability methods.

* Post-hoc methods

Post-hoc methods refer to techniques applied a posteriori on the trained model and
aimed at opening the black-box model.

In [19], Bau et al. introduced an analytical framework for visualising GANs, called
GAN dissection. The idea is to manipulate neurons to identify units in the model that
are related to semantic and human-friendly concepts. As presented in the introduction,
their work found out that:

- GANs learn concepts in an unsupervised way;

- Enabling or ablating such units can enable one to edit images meaningfully.

Different from Bau et al., other authors focused their attention on latent space rather
than on the network itself.

In [78–80], authors discovered that, just as internal units are correlated to concepts,
semantic and meaningful directions in latent space are learnt in an unsupervised
way by GANs. Meaningful directions can be seen as specific walks or traversals in
latent space, leading to modifying only one attribute or aspect in the outputted image,
independently from the other attributes.
Härkönen et al. [78] introduced a technique called GANSpace in order to identify controls and use them to allow one to edit images finely. They used principal component analysis (PCA) to discover important directions in feature and latent spaces of a pre-trained GAN. By only intervening on some layers, they show that we can modify images and only change one semantic element, such as pose and glass presence, without affecting the others.

Similarly, Voynov et al. [79] discovered semantically meaningful directions in latent space of pre-trained GANs in order to enable one to edit images. To do so, they produced image pairs: original images and images obtained after modifying one particular direction. Next, a model, called a reconstructor, aimed at getting back to the shift and the direction index from these images. By doing this, they succeeded in finding non-trivial transformations such as background removal. However, the number of directions that they want to unveil are a hyper-parameter defined by the user. Their results and framework can be found in Figures 12 and 13, respectively.

<figure><img src="image_17.png" /><figcaption>**Figure 12.** Voynov et al. [79] results.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>**Figure 13.** Voynov et al. [79] framework.</figcaption></figure>

Different from the previously presented works, Shen et al. [80] found meaningful directions in latent space in a supervised manner. In their paper, they resort to SVMs (instead of PCA) to identify important directions. Indeed, they consider each binary attribute (for example glasses or not glasses) separately and make the assumption that they are linearly separable in latent space so they can use a SVM in order to determine the frontier between the considered semantics. When the hyperplane is discovered, computing the unit normal vector gives the direction of a specific attribution. Then, it is sufficient to manipulate the original latent space code along the normal direction to obtain meaningful modifications in the initial image.

Instead of directly exploring the latent space, other authors look at transforming it in order to organise it and make it more interpretable.
For example, Pham et al. in [81] used PCA and autoencoders to create an interpretable latent space. In more detail, they iteratively train an autoencoder on a specific input image (the autoencoder being only valid locally) while increasing the latent space by one at each time, fixing the previous trained components and requiring that they are independent. It is important to note that the latent space is a hyperparameter defined by the user. This permits them to have a latent space that is well organised and interpretable. Then, they can use the decoder to obtain the perturbation latent code that has to be added to the original latent code in order to obtain an image similar to the initial image but with only one factor of variation changed.

Esser et al. [82] used a network called an invertible interpretation network (IIN), with the aim of being able to transform the latent space, $z$, of a pre-trained model (either as an autoencoder $E-D$ or as a classifier) into an interpretable space, $\tilde{z}$. They consider an interpretable space as a space in which each dimension only encodes one interpretable concept and is invariant with respect to all other variations. The invertibility of its transformation, $T$, enables reversible translation between the initial and interpretable latent spaces. Once again, the dimension of the interpretable representation depends on the application of the decoding model. They considered two use cases: one in which each concept can be represented by image pairs, meaning a supervised context, and the other one in which we do not have this type of dataset and where we want the network to learn by itself the different semantics contained in the data, which is the non-supervised context. Their architecture can be seen in Figure 14.

<figure><img src="image_19.png" /><figcaption>Figure 14. Esser et al. [82] framework.</figcaption></figure>

This type of work is particularly interesting since it maintains the model performance, as it is not modified, while enhancing model explainability.

*   Ante-hoc methods

On the other hand, we can find ante-hoc methods aimed at modifying the considered GAN or its latent space before training in order to make them more explainable.

Indeed, when training a GAN without any constraint on latent space, we do not have any guarantee on its structure. Mukherjee et al. [94] showed that learnt data representation can be not well organised according to the chosen latent space distribution.

For example, data belonging to the same class can be totally spread over the latent space, as illustrated in Figure 15, and, instead of being close to each other, they can find themselves near to data points that represent images from other categories. One could hope that data structure in image space is conserved in latent space and that the spacing in it reflects similarities and dissimilarities.
<figure><img src="image_20.png" /><figcaption>Figure 15. Unorganised latent space (latent space representation extracted from [94]).</figcaption></figure>

To rectify this, there exist several ways to enforce constraints on the latent space.

1. Components of latent space

One way to disentangle latent space involves applying constraints on components. Here, we focus on disentangled representation learnings that are deeply studied by Higgins et al. [109] and comprehensively reviewed by Liu et al. [110] in the medical domain. We first define some vocabulary with definitions produced by Liu et al.

In the upcoming definitions, we will use the following notations: $f$ performs a mapping between domains $X$ and $Y$, such that $f: X \to Y$. $f$ can be split into two components, an "encoder", $E_\Phi$, and a "decoder", $D_\Theta$ ($f: E_\Phi \circ D_\Theta$). Thus, $E_\Phi$ maps to an intermediate latent representation, $Z$ ($E_\Phi: X \to Z$) and $D_\Theta$ maps to the output ($D_\Theta: Z \to Y$).

Generating factors. Be a domain, $X$, characterised by a distribution, $P$. The gener- ating factors are the underlying variables that fully characterise the data variation that we want the model to learn. In fact, it can be unrealistic to hope that a model discovers all these factors. Thus, many works only consider the main ones and argue that domain knowledge can help the model training.

Equivariance. A function $E_\Phi: X \to Z$ is said to be equivariant with respect to $\Omega$ if there is a transformation $\omega \in \Omega$ of the input $x \in X$ that affects the output $z \in Z$ in the same way. More formally, $\Omega$-equivariance of $E_\Phi$ is obtained when there exists a mapping $M_\omega: R^d \to R^d$ applying $\omega$ to an input such that:

$$E_{\Phi}(M_{\omega} \circ X) = M_{\omega} \circ E_{\Phi}(X), \forall \omega \in \Omega. \quad (2)$$

Concretely, in a detection task, it means that if the target object moves in the image then we would like the bounding box output to change location accordingly. In this case, we want the model to be translation equivariant.

Invariance. Invariance is a special case of equivariance for which $M_\omega$ is the identity map. Formally, $E_\Phi$ is invariant to transformations of $\Omega$ if:

$$E_{\Phi}(M_{\omega} \circ X) = E_{\Phi}(X), \forall \omega \in \Omega. \quad (3)$$

More practically, it means that a certain transformation of the input image should not have any impact on the corresponding output. For example, in the case of SAR ATR, target orientation should not affect the classification output. The rep- resentation should be orientation invariant, because changing the azimuth angle of the target does not change its category.

Disentangled representations. Disentangled representations are not yet well defined but Liu et al. [110] explain that disentangling is the idea of separating the main factors of variation that are present in the considered data distribution. More formally, they use the Higgins et al. [109] definition:
Consider a compositional world, W, and a set of transformations, Ω. They consider a function $f: W \to Z$ that can induce Ω in the latent representation $z \in Z$ in an equivariant manner. The representation Z can be considered as "disentangled" if a decomposition of $Z = Z_1 \times Z_2 \times \dots \times Z_n$ exists such that a transformation, $\omega$, applied on $Z_i$ causes an equivariant transformation in the input domain, X, while all other aspects controlled by $Z_{(i \neq j)}$ remain intact. For instance, if $Z_1$ encodes the target orientation attribute, changing it should not impact the other attributes of the image, such as category or width.

Liu et al. highlight the fact that this definition respects two desired properties defined by other works on disentanglement:

- Modularity. In fact, each latent dimension should encode no more than one generative factor;

- Informativeness. All underlying generative factors are encoded in the representation.

We emphasize that we focus on disentanglement performed on latent space and not on intermediate latent spaces like W space [111].

In practice, Xie et al. [83] tried to apply InfoGAN (Chen et al. [99]) on SAR images and succeeded in controlling the generated category. Indeed, in their paper, the discrete component, *c*, aims at representing the category label and the continuous one, *z*, must embody the other factors of variation and image diversity.

In the same way, Feng et al. [84] proposed employing an InfoGAN-based model to generate SAR images. Yet, they wanted to make the most of this model, so they also analysed the latent codes in order to bring clarity in the relationships between latent codes and SAR image properties.

Thanks to reasoning through several works [112–115], Cao et al. [85] succeeded in developing a GAN that can produce labelled images. To do so, they base their model on an auxiliary classifier GAN (ACGAN), asking the discriminator to determine both target source and class. ACGAN [116] is another variant of the original GAN, which also deals with conditional image generation. In this architecture, categorical information is concatenated to images (both real and generated) and a classifier head is added to the discriminator. This framework can be visualised in Figure 16.

<figure><img src="image_21.png" /><figcaption>**Figure 16.** ACGAN architecture.</figcaption></figure>

Specifically, they consider the condition of imbalanced data. They add a demand matrix at the end of the classification model, which aims at making the GAN aware of minority classes and preventing the discriminator mistaking the less represented samples for fake images.

Similarly, Luo et al. [86] considered the imbalanced data condition. However, instead of adding a customised layer like Cao et al. [85], they simply oversample minority categories through to a Bayesian optimiser, aiming at rebal-
ancing the training dataset. Then, they trained a progressive growing GAN (PGGAN—[111]) with this augmented dataset to alleviate the loss of generation quality of underrepresented target samples.

These last two works emphasise the fact that SAR ATR data are also challenging by their imbalanced nature. In addition to being scarce, operating conditions generally lead to disparities between considered target classes. Cao et al. understood well that imbalanced data make GAN training more difficult, as the discriminator tends to pay less attention to minority categories and even to consider underrepresented samples as fake/generated images. Thus, the generator is penalised when generating minority classes. Consequently, using GANs to compensate the data lack for some categories can be counterproductive when we precisely need sufficient samples to teach the generator to produce plausible images. The use of simulated images is highly considered, even though differences between these and real images are still not negligible.

Like Cao et al. [85], Li et al. [87] proposed performing data augmentation for ship recognition tasks also using an ACGAN-based model. They upgraded it by adding residual connections in the generator and using the Wasserstein loss and the gradient penalty of WGAN-GP. The specificity of their work is that they feed the discriminator with generated and real images but also with merged images. Du et al. [88] wanted to produce high-quality images by implementing a WGAN-GP based model called the multiconstraint GAN (MCGAN). It is composed of four components:

- A usual generator;

- A pre-trained classifier ensuring that the different generated images belong to the correct category;

- A standard discriminator;

- Finally, an encoder, which makes their work innovative. Indeed, in order to help the training and make more realistic images, they train an encoder to produce features that are next fed to the generator concatenated with the corresponding category label and noise.

Conversely, Hwang et al. [89] do not use a pre-trained classifier. Indeed, they improved a GAN-based model by also adding a classifier, but it is trained at the same time as the rest of the GAN. This model, called TripleGAN, enables one to perform data augmentation and tolerates labelled and unlabelled data during training.

In these different works, only one component of latent space is controlled and interpretable. Other works seek to monitor more components, which leads to more interpretable variables in latent code since it corresponds to more known latent dimensions.

In [90], Oh et al. designed PeaceGAN, a deep convolutional GAN (DCGAN—[117])-based model, presented in Figure 17. They impose different constraints on latent variables. Indeed, one is for the category label, another is for pose estimation, while the last part is the traditional random noise. They succeeded in implementing a model that is able to provide images in a desired pose and category by adding several branches to the discriminator. In fact, authors use multi-task learning to train the discriminator to perform source recognition tasks, classification, and pose estimation. On the contrary, Song et al. [91] used numerical variables but also other types of data. They trained a PGGAN-based model that is called an adversarial autoencoder and is composed of two components:

- A discriminator that aims at determining source target, category label, and pose value;

- A generator that is fed with random noise, pose values, category label, and a semantic map on the desired image.
<figure><img src="image_22.png" /><figcaption>**Figure 17.** Oh et al. [90] framework.</figcaption></figure>

Then, they used the trained network to produce new images and expand the initial training dataset in order to train a target recognition network.

In [92], Shoshan et al. propose GAN control. Their idea is to consider different latent variables, which represent concepts such as person identity, pose, and angle, except the last component that aims at containing the non-controllable attributes. In the first step, a GAN is trained to generate realistic images. Their work is innovative in the sense that they consider an intermediate latent space, between the original latent space and the generator. This embedding is learnt via contrastive learning [118], knowing that the dataset is pre-processed by making pairs of images sharing an attribute, and consequently part of their latent vector. The idea is to have similar data (sharing an attribute) relatively close in the intermediate space. The second step of the training consists in training several encoders (one for each attribute) to translate latent vectors into feature vectors in the intermediate space, in order to be fed to the trained generator.

In [93], Li et al. proposed an unsupervised learning approach to enforce sparsity on the latent space of the generator model. To do so, they used a gradually sparsified spike and slab distribution as latent space prior, which pushes non-informative latent dimensions toward zero. Next, they led numerous experiments to show that the learned sparse latent representations can retain the majority of the information while learning disentangled semantics. These features enabled an increased latent code explainability, and an enhanced robustness regarding classification and denoising tasks.

These different works lead to the obtaining of disentangled representations and components of latent vectors that are semantically interpretable. In our view, related to SAR ATR models for terrestrial targets, an example of the seeking decomposition is illustrated in Figure 18.

<figure><img src="image_23.png" /><figcaption>**Figure 18.** Semantically understandable latent code with different variables.</figcaption></figure>
Ideally, changing one component of the latent code results in the modification of an attribute, leaving the others intact. This allows a fine edition of data and customised image generation. In fact, a particular component value, the category label for example, corresponds to a specific attribute state and according to the considered latent code. Then, we can predict in advance which features the output image will contain.

In addition, as we have seen, latent space can be considered as a reduced dimension representation of data. This means that the latent code can be interpreted, in a way, as a feature vector. In this case, the feature extraction process is explainable since extracted features are identifiable and the distance geometry in the latent space respects similarities within the training dataset. Indeed, two similar data points share mutual attributes, such as the same class or even the same orientation. Consequently, some part of their latent code will be comparable and, as their latent code values are their corresponding coordinates, it means that these two points will be close in this space.

This last section is illustrated in Figure 19 for our application.

<figure><img src="image_24.png" /><figcaption>**Figure 19.** Principle of our idea to organise latent space with latent code constraints (SAR images from the MSTAR Dataset [20]).</figcaption></figure>

On the one hand, the latent space is structured, with understandable dimensions, as previously illustrated in Figure 18. With one specific latent code, z₁, we would produce one desired image, x₁. By only changing the component, c₁, of this latent code, we would obtain another image, x'₁ in which only the corresponding factor of variation, for example the azimuth, is modified. On the other hand, these latent codes, z₁ and z'₁, are the coordinates in the latent space of the representations of x₁ and x'₁. Since they are almost the same, the similarities of these two images are reflected by their closeness in the latent space.

## 2. Clustering in latent space

Another way of structuring data in the latent space is to cluster or, at least, make close data points that are similar in latent space. This can be done with additional loss terms.

For example, in [94], Mukherjee et al. propose a model called ClusterGAN, which succeeded in clustering data in latent space using a mixture of discrete and continuous components in the latent vector and a clustering-specific loss. They also used an encoder to perform explicit inverse mapping, aiming at obtaining latent codes' given images. Their architecture is depicted in Figure 20.
<figure><img src="image_25.png" /><figcaption>Figure 20. Mukherjee et al. [94] framework.</figcaption></figure>

In [95], Dam et al. propose to improve the ClusterGAN model by learning the different distributions of the latent variables directly from data in order to replace the uniform distribution used in the first version. To do so, they resort to a principle called self-augmented information maximisation, combining mutual information maximisation between data and self-augmented training [119]. In a slightly different approach Agarap et al. in [96] proposed improving the k-means clustering of disentangled representations by pushing similar pairs of points to be close via a soft nearest neighbour loss term [120].

### 4.3.2. Perspectives on How to Use GAN Explainability for Classifier Explainability

In the previous sections, we presented some ideas of methods aiming at enhancing GAN explainability. In this section, we detail how we could potentially use them to improve SAR ATR model explainability. The motivation behind this paragraph is the same as in [97], in which the authors proposed an ante-hoc explainable classification model using GANs. Inspired by self-explaining neural networks (SENNs), developed in [121], they presented a framework performing classification based on a latent space whose dimensions are meant to be concepts. In detail, in order to learn these concepts, they resort to:

* A base encoder, which aims at extracting features from images;

* A concept encoder, which extracts visual concepts from the classifier's latent representations;

* A generator, which reconstructs an image from concept encodings;

* A discriminator, which must determine if images are real or generated;

* A classifier, which performs classification on base encodings;

* A classifier, which performs classification in concept encodings.

The objective of this joint training scheme is to implicitly align the model's internally learned concepts with human-interpretable visual properties. The authors stated that using a GAN-based architecture can help create more refined concepts compared with the autoencoders initially used in [121].

To integrate the classification task (Figure 21) into a GAN framework (Figure 22), we split the discriminator into two different components: the feature extractor and the other layers aiming at performing the desire task, such as computing the “realism score”. Consequently, we designate the first component named above as an encoder, since it extracts features from initial images to project them into a reduced dimension representation, also called feature space. This step can be likened to the process of usual ATR methods (such as ASC), as described in the Introduction. The second discussed model is the standard traditional discriminator and performs the well-known real/fake task. In fact, we want the classification step to be performed in the feature space. This corresponds to the baseline of our two following proposals.
<figure><img src="image_26.png" /><figcaption>**Figure 21.** Classification framework.</figcaption></figure>

<figure><img src="image_27.png" /><figcaption>**Figure 22.** GAN framework.</figcaption></figure>

In fact, regarding the previously presented GAN explainability techniques, we propose two strategies to enhance classifier explainability: a model-based and latent space-based one.

*   **Model-based method**

The motivation behind this proposed method is to take benefit from internal visualisa-
tion of GANs for classification explainability.

GAN dissection [19] gives an insight into the generator model. Yet, the classifica-
tion task is performed on the encoding part, so we need enhanced explainability
on this pathway. Consequently, to exploit this method, we propose to make sure
that the encoder uses the same reasoning as the generator by tying their weights.
Tying weights consists in computing decoder weights as the transpose of the encoder
weights, for autoencoders. This technique is often used to reduce the number of model
parameters and to reduce computational cost. To do so, we can adopt an adversarial
encoder network (inspired by [71]). In the end, we obtain two models, the encoder
and the decoder networks, making the bridge between feature and image space. We
would like to resort to interpretable models to perform classification, such as k-nearest
neighbours (kNNs).

After training, the encoder should be able to extract relevant features for classification.
Investigating the inner reasoning of the decoder via the GAN dissection principle [19]
could indirectly unveil the different concepts learnt by the encoder. This idea is
illustrated in Figure 23.

*   **Latent-based method**

After considering diverse ways to organise GAN latent space, we propose two methods
to enhance SAR ATR explainability through latent space explainability.

The concept is to use this understanding of the latent space that we can see as a
meaningful feature extraction to perform comprehensible classification in it. In fact,
we would want to:

- Learn a meaningful latent space by means of a GAN-based model;

- Allow the return in the latent space with the use of an encoder network in order to perform classification in this interpretable space.
<figure><img src="image_28.png" /><figcaption>**Figure 23.** Model-based explainability method (tied weights are represented by the chain).</figcaption></figure>

However, before doing this, we need to be able to come back in this latent space, which is not systematic in usual GAN training. This is called the GAN inversion problem. Creswell et al. in [122] proposed to invert a pre-trained generator by resorting to a minimisation problem that aims at recovering a latent representation generating a similar image to the initially considered one.

In IGAN [123], Vignaud directly learns a bidirectional mapping between data space and latent space using multiple components inspired by the DCGAN model. The use of a sort of cyclic structure enables him to directly obtain an invertible GAN that surprisingly creates an organised latent space without any kind of regularisation or supervision.

Finally, we would have a bidirectional connection between latent and data spaces, which is useful since it would be possible to encode an unseen input image into relevant features. Conversely, we would generate desired images by choosing latent variables values. This part is the encoding/decoding component.

Ideally, when the GAN is trained, we would only have to use the encoder to encode the image into the organised latent space and then perform classification. The global idea is presented in Figure 24.

<figure><img src="image_29.png" /><figcaption>**Figure 24.** Latent-based explainability method.</figcaption></figure>

The first proposed strategy is based on unsupervised representation learning. We do not supervise the different features learnt by the model but rather intend to structure the latent space and let the model discover the relevant features by itself. For instance, we could look for learning decorrelated latent variables. However, since we want to perform classification in the latent space and use an interpretable classifier, it might be useful to also add regularisation on clustering. In fact, we want to conserve the distance geometry of the training dataset in the latent space.

When the model is trained, an analysis of its latent space, such as latent traversals, could reveal features learnt from the SAR images.

The second approach relies on supervised learning of the different extracted features. This method is a little more expensive than the former because it requires human
labelling. Effectively, we want the model to extract human-aligned features, such as
width or barrel presence. Thus, we have to gather the different concepts that are used
in practice to perform ATR. We want them to be the dimensions of the latent space, so
we could use the same approach as PeaceGAN for doing so: the multi-task learning
framework (Figure 25). In this case, other heads, such as a classification module, can
simply be added at the end of the feature extractor. Each module owns its own loss
function and corresponds to a latent variable.

<figure><img src="image_30.png" /><figcaption>**Figure 25.** Multi-task learning framework.</figcaption></figure>

After training, this constraint gives us a semantically understandable latent space.
For example, thanks to the different heads, we could roughly project images in this
space, in which we could perform classification with an interpretable model such as a
kNN classifier.

Both procedures are illustrated in Figures 26 and 27.

<figure><img src="image_31.png" /><figcaption>**Figure 26.** First proposed approach.</figcaption></figure>

<figure><img src="image_32.png" /><figcaption>**Figure 27.** Second proposed approach.</figcaption></figure>

**5. Discussion and Challenges**

As we have seen in this paper, the approach combining GANs, XAI, and SAR ATR is
not particularly delved into, whereas it could unveil unsuspected knowledge. However,
training GANs still remains a challenge, especially with complex data like SAR images.
## 5.1. *Advantages of Using GANs for Explainability Improvement*

GANs can be a useful tool to improve SAR ATR model explainability. In fact, adding further information and knowledge of the models or their behaviour can only lead to beneficial insight. By definition, GAN applications are different from classifiers. The latter aim at labelling images whereas GANs intend to produce samples following the original data distribution. Thus, they learn a global representation of the data instead of only focusing on relevant features for classification. Taking advantage of both tasks can improve our comprehension of the data.

In addition, GANs can simulate different environmental conditions and target variations, as well as give the opportunity to investigate their latent space and explore the different variation factors learnt from data. These features are an unquestionable asset for enhancing classifier transparency and, consequently, improving trust in them. These are also the reasons why they can be more powerful than other standard generative models. Indeed, ASC modelling and SAR simulators can also generate SAR images. However, these traditional generative methods require a wealth of knowledge and human input contrary to GANs that can directly learn information from data. In addition, the latter have shown in practice that they produce more realistic and diversified samples. On another note, compared with other deep learning-based generative models, GANs are rather efficient at generating realistic and diversified data.

Moreover, as exposed in this paper, we can use GANs differently in order to improve SAR ATR models' explainability directly using GANs during training or as a post-hoc method.

## 5.2. *Perspectives*

GANs are a very interesting architecture as they were proposed long enough ago to mature, but also recent enough for research to maintain an interest in improving them. We can expect future work on methods to improve GAN training stability and explainability.

We also have to remember that, in this article, we deal with different degrees of explainability. For example, counterfactual explanations (considered as local explanations) permit us to slightly understand black-box models but not as much as identifiable extracted features and an interpretable latent space (approaching *global* explanations, see Section 2.2). It is really a question of knowing for which configurations GANs are the most beneficial.

Furthermore, as developed throughout the article, how to combine GANs and classifiers remains a key challenge.

We believe that next steps could be to perform a benchmark with the different methods and potentially a comparison with other generative models such as transformers, variational autoencoders, or diffusion models.

## 5.3. *Challenges*

Finally, proposed strategies are ideas, reflections, and lines of approach coming up through literature reading, and putting them into practice will necessarily result in new challenges. However, an already existing challenge concerns the evaluation of the different approaches. Indeed, especially when it comes to benchmarking, evaluation metrics will be required, both for image quality and explainability. As a matter of fact, one way of assessing GAN quality is to make sure that generated images are realistic. However, SAR image quality assessment remains research in progress. Similarly, there is still no consensus on an explainability metric that would enable reliable performance comparisons between other interpretable deep learning network methods and GAN methods.

## 5.4. *Drawbacks*

GANs are notoriously tedious to train. Between non-convergence, collapse mode, and instability, they are very sensitive models requiring special handling. They also need an considerable amount of data, which is a key problem in the SAR domain.
Plus, in order to exploit GAN explainability for SAR ATR model explainability, we need to add constraints and regularisation (e.g., loss terms or constraints on latent space dimensions) on the different models, which, according to literature, leads to more stable training and higher quality images. Nevertheless, it is tough to anticipate the architecture behaviour, and these constraints may result in an impossible training because of a lack of degrees of freedom. In particular, we cannot predict the viability of our last two proposed methods (see Section 4.3.2).

However, we have to keep in mind that SAR images are difficult to visually interpret, which also means that some methods, like latent traversals or GAN dissection [19], could possibly not be as decodable and understandable as desired. Consequently, we have to consider the risk of obtaining unintelligible explanations, whether for developers or operators.

## 6. Conclusions

While GANs, explainability, and SAR ATR models have drawn much attention lately, they are generally considered separately. That is why we present several works on GANs (aggregated in Table 1), applied on SAR data or not, with the idea of potential use for enhancing SAR ATR model explainability.

We show in this work that some methods extracted from one field and applied to another could present powerful improvements. In fact, while we make more explainable SAR ATR models and GANs, few works, at least to our knowledge, have tried to take advantage of all three research domains. By presenting several works with this in mind, we highlight gaps between these areas and propose strategies to fill them.

**Author Contributions:** Conceptualization, H.R.; methodology, H.R.; validation, H.R., J.-M.L.C., J.-Y.S. and J.P.-F.; investigation, H.R.; writing—original draft preparation, H.R.; writing—review and editing, J.-M.L.C. and J.-Y.S.; visualization, H.R.; supervision, J.-M.L.C. and J.-Y.S.; project administration, J.-M.L.C., J.-Y.S. and T.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Association Nationale de la Recherche et de la Technologie (CIFRE N° 2021/1298).

**Acknowledgments:** The authors want to thank Cécile Baudry for the stimulating discussions on this subject.

**Conflicts of Interest:** Authors Héloïse Remusati, Jean-Yves Schneider, Jacques Petit-Frère and Thomas Merlet were employed by the company Thales LAS France SAS. The remaining author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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