**1. Introduction**

Synthetic aperture radar (SAR) imagery has become a significant research object in many areas, such as civilian and military fields [1–3]. It takes advantage of acquiring images in all weather conditions and during the night as well as the day. Image target recognition is a basic step in understanding and interpreting SAR images [4]. In this context, it is important to develop discriminative and robust methods for automatic target recognition (ATR) systems, and tremendous research attention has been paid to the study of ATR for SAR images [5–9].

Recently, sparse representation (SR) has become a focus and has been used in many areas [10]. It is robust to noise and can maintain natural discrimination without any prior information. Even in SAR target recognition, SR could remove the need for the pose estimating process. Recently, Thiagarajan et al. [11] applied SR to realize SAR image target recognition and applied a local linear approximation to generate a classification prediction for every target class manifold. This algorithm did not demand any specific pose estimation or preprocessing, but the use of random projections in the high-dimensional space discarded some discriminative locality information, thus making occlusion handling more difficult. In another study [12], descriptors from local patches were extracted, and an image was treated as a collection of the unordered descriptors; then, sparse representation was applied to represent the local patches for SAR image target classification in the framework of SPM. Additionally, the application of spatial pyramids was confirmed to be an effective classification method for SAR images.

This model of spatial pyramid matching [13] for image classification is a statisticsbased model with the objective of providing a better image representation. In order to obtain discriminant details of the images, the SPM needs to extract the low-level local

**Citation:** Wang, S.; Liu, Y.; Li, L. Sparse Weighting for Pyramid Pooling-Based SAR Image Target Recognition. *Appl. Sci.* **2022**, *12*, 3588. https://doi.org/10.3390/ app12073588

Academic Editors: Pingjuan Niu, Li Pei, Yunhui Mei, Hua Bai and Jia Shi

Received: 4 March 2022 Accepted: 29 March 2022 Published: 1 April 2022

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features through, for example, scale-invariant feature transform (SIFT) [14] and histogram of oriented gradient (HOG) [15]. However, the local features are not provided directly to image classifiers due to their sensitivity to noise and computational complexity. One solution is to represent the images by integrating the local features into the midlevel features. This image representation works well with linear classifiers, and the results have achieved a competitive performance in many image classification tasks. Nonetheless, the SPM model is not perfect when implemented on SAR images. This is attributed to the fact that the variety of targets posed in SAR images hinders the advantages of SPM. Noteworthy, locality is more essential than sparsity [16], locality-constrained linear coding was presented in place of the vector quantization (VQ) coding, and a good approximation was obtained. Recently, Zhang et al. [17] proposed to apply a locality constraint to ensure similar patches shared similar codes in the coding scheme for SAR image target recognition. However, its complete codebook was obtained after preprocessing of the estimation of target poses.

In a literature study [5], a complementary spatial pyramid coding method was used in change detection, and good performance was gained. The SAR targets suffer from the effects of the speckle noise and the background; therefore, different parts of an image play different roles in image representation. Combining the advantages of SPM and SR, a novel SAR image target recognition method is proposed herein, which makes use of the dependability obtained by SR to obtain weighted sub-regions at every pyramid level. Some sub-regions in each level of the spatial pyramid may consist of background noise, and other ones represent the target. Based on the sparse representation theory, the target parts could be represented by the training samples from the same class [18]. Therefore, there could be a small residual value corresponding to its class, which shows the dependability of the sub-region. We apply the dependability to weight the pooling features obtained from the SPM sub-regions [19]. Therefore, the pooling feature located in the target is enhanced. Meanwhile, the pooling feature located in the background is suppressed. The results obtained using real SAR Moving and Stationary Target Acquisition and Recognition (MSTAR) database demonstrate that the method presented herein is more robust to variant unconstrained conditions than the methods reported in other recent related studies.

The organization of this paper is as follows: Section 2 introduces the presented subregions weighting method. Section 3 reports the experimental results of the presented algorithm and compares the approach used herein with some classical approaches. Finally, Section 4 includes the conclusion.

## **2. SAR Image Recognition with Sparse Weighting Spatial Pyramid Pooling**

The method proposed herein simultaneously utilizes the SPM model and SR to deal with SAR image recognition. Enlightened by the idea that different parts of an image play different roles, a sparse weighting spatial pyramid pooling method is proposed to extract a new type of feature. The main objective of utilizing this method is to reduce the influence of background clutter and enhance the target. Figure 1 exhibits the flowchart of the proposed SAR image target recognition method. Firstly, an image was divided into gradual fine sub-regions; then, the dense local features were calculated, followed by coding and pooling according to SPM, in order to obtain feature vectors of the sub-regions, respectively. Additionally, the pooling feature vector of the sub-regions at each pyramid level was weighted based on the dependability, which was determined according to the residuals obtained by the SR. Finally, the representation for SAR images was built by systematically concatenating the weighted feature vectors. With sparse representation classification, the method is robust, in particular, in dealing with the speckle noise and large clutter background.

**Figure 1.** Overview of the SAR image target recognition flowchart.
