Structure-from-motion (SfM) is the concept of estimating both sensor pose and three-dimensional (3D) scene structure from input images. The difficulty with synthetic aperture radar (SAR) SfM stems from the non-linearity of radar imaging, making it hard to decouple and calculate radar pose and structure. Existing methods typically address this issue by simplifying the imaging process or introducing auxiliary data. In this paper, we propose to jointly solve radar pose and structure by formulating an optimization problem, which only needs two-dimensional (2D) SAR observations as input. The objective function is written as the summation of all reprojection errors established by the precise range-Doppler (RD) imaging model, with radar poses embedded into the transformations between the sensor and scene coordinate systems. The rotational components in radar poses are represented as matrices and constrained on the special orthogonal groupSO(3). A special orthogonal Riemannian conjugate gradient algorithm (SO-RCG) is then proposed to solve the optimization problem. The proposed algorithm preserves the orthogonality of rotation matrices and updates all variables iteratively. Furthermore, we deduce that only five degrees of freedom (DoFs) in radar pose are involved in determining the imaging results of targets. We also discuss the ambiguity issue in multiview SAR observation leading to local minimums and introduce strategies against ambiguity. Experimental results on real-measured and simulated datasets show that the proposed algorithm is effective on both near- and far-field cases, and can be applied to both side-looking and squint SAR.

Despite notable advancements in remote sensing vision-language models (VLMs), existing models often struggle with spatial understanding, limiting their effectiveness in real-world applications. To push the boundaries of VLMs in remote sensing, we specifically address vehicle imagery captured by drones and introduce a spatially-aware dataset AirSpatial, which comprises over 206K instructions and introduces two novel tasks: Spatial Grounding and Spatial Question Answering. It is also the first remote sensing grounding dataset to provide 3DBB. To effectively leverage existing image understanding of VLMs to spatial domains, we adopt a two-stage training strategy comprising Image Understanding Pre-training and Spatial Understanding Fine-tuning. Utilizing this trained spatially-aware VLM, we develop an aerial agent, AirSpatialBot, which is capable of fine-grained vehicle attribute recognition and retrieval. By dynamically integrating task planning, image understanding, spatial understanding, and task execution capabilities, AirSpatialBot adapts to diverse query requirements. Experimental results validate the effectiveness of our approach, revealing the spatial limitations of existing VLMs while providing valuable insights. The model, code, and datasets will be released at https://github.com/VisionXLab/AirSpatialBot.

Synthetic aperture radar (SAR) images are inherently affected by speckle noise. Deep learning-based methods have shown good potential in image denoising task. Most deep learning methods for denoising focus on additive Gaussian noise removal. However, SAR images are usually contaminated by non-Gaussian multiplicative speckle noise. In this paper, we propose a novel deep unrolling network named SAR-DURNet to deal with the SAR image despeckling problem. We establish optimization problem of speckle noise removal by using the priori of noise distribution, which can be sovled by half-quadratic splitting (HQS) method with iterative steps. We unroll the iterative process into a trainable deep unrolling network(SAR-DURNet). The parameters of the SAR-DURNet are trained end-to-end with simulated SAR image dataset. Experimental results on simulated test data and real SAR data show that the proposed approach has superior results in terms of quantitative performance metrics and the preservation of intricate visual details, compared to several well-known SAR image despeckling methods.

Tensor completion has attracted increasing attention in signal processing, computer vision, and biomedical engineering. By using nuclear norm minimization, a tensor completion problem can be converted into a convex program and enjoys properties gained from matrix completion. The low rank property has been widely used for tensor/matrix completion. However, the prior subspace information can also be utilized, which has been ignored and does not exhibit its full power in the existing formulation. In this paper, we propose a new framework leveraging tensor subspace prior for the sum of nuclear norm (SNN) minimization, which supports a range of tensor decompositions. By using the knowledge of the self-prior (SP)/nonself-prior (NSP) and further designing an efficient algorithm based on the Alternating Direction Method of Multipliers (ADMM), the performance of tensor completion can be enhanced. The superiority of the proposed method is verified by extensive numerical experiments.

Hybrid precoding is considered in wideband mm-Wave massive MIMO-OFDM systems with beam squint. Traditional wideband hybrid precoding schemes cannot achieve near-optimal sum rate as digital precoding/beamforming (DBF) and may induce high hardware cost. Dynamic time-domain weighting hybrid precoding (DTW-HBF) updates the analog weights during an OFDM symbol, realizing equivalent frequency-dependent analog precoding and approximating DBF with a low cost. Directly reconstructing the time-domain signals, however, involves pseudo-inverse operations, which may cause numerical instability. In this work, the frequency-domain spectrum is reconstructed by introducing the optimal frequency-domain analog precoder and using the cyclic convolution property of Discrete Fourier Transform (DFT). The proposed method can approximately approach the performance of DBF while maintaining the hardware structure based on phase shifters (PSs). As shown by simulation results, an increased sum rate has been achieved.

This paper proposes a fast two-step method which aims to address the SAR pose estimation problem and enable Unmanned Aerial Vehicles (UAVs) the self-localization capability under harsh conditions. Firstly, the monocular SAR pose estimation is formulated as a Circular-n-Point (CnP) problem based on frequency-domain SAR imaging mechanism. Then, we propose to decouple the motion components of radar platform and solve the overdetermined equations of direction and location sequentially. Experimental results validate the effectiveness, accuracy, and efficiency of the proposed method.

Land cover (LC) classification via remote sensing is crucial for ecosystem monitoring and urban planning but faces the challenge of inconsistent multimodal data availability. Current techniques often falter with incomplete modalities, resulting in reduced performance and adaptability. Addressing these issues, this study propose the Transformer-based Incomplete Multi-Modal Learning (TIMML) framework. TIMML incorporates a Bernoulli indicator module during training to facilitate adaptation to missing modalities. This module, in tandem with a fusion token, is instrumental in enabling the model to handle the random omission of modalities by selectively nullifying data streams and effectively aggregates information from the remaining available modalities. Moreover, TIMML integrates a modality-aware regularization module designed to enhance the stability of the feature extraction process, especially when perturbed by the Bernoulli indicator during training. Our comprehensive experiments demonstrate that TIMML not only proficiently manages the challenge of missing modalities but also outperforms existing methods in LC classification tasks, marking a significant advancement in the field.

Change detection (CD) plays a crucial role in various physical applications. Recently, many studies have turned to semi-supervised semantic segmentation methods to alleviate the reliance on extensive annotations. However, these methods tend to neglect the presence of the cross-temporal background noise in bi-temporal remote sensing image (RSI) pairs, which can mislead model’s prediction. Therefore, this work introduces an innovative Multi-view Feature Enhancement (MFE) method for semi-supervised CD. To mitigate the influence of inherent cross-temporal background noise in RSI pairs, we design a multi-view strategy and temporal-perception data augmentation for feature enhancement. According to the experimental results on two publicly available datasets, our proposed method outperforms several state-of-the-art (SOTA) methods in terms of intersection over union (IoU) and overall accuracy (OA).

The utilization of unlabeled samples has contributed significantly to the achievements of semi-supervised methods in optical remote sensing image (ORSI) scene classification. However, existing methods face the challenge of effectively integrating labeled and unlabeled data during model training. To mitigate these challenges, a semi-supervised label and embedding consistency network (SS-LEC) is proposed for OSRI scene classification. Specifically, given an image, SS-LEC enables the high-confidence prediction from a weak-augmentation view consistent with the prediction from a strong-augmentation view, while also ensuring consistency in embeddings derived from middle-augmentation views. Moreover, a soft learning schedule is proposed to strategically focus on varied consistency tasks at different stages of training. Our experiments on two ORSI datasets showcase SS-LEC’s superior classification performance over existing semi-supervised methods. Notably, under label-scarce scenarios with only four labeled images per category, SS-LEC achieves classification accuracies of 92.04% on the EuroSAT dataset and 70.19% on the NWPU-RESISC45 dataset. These results set new benchmarks and demonstrating superior classification performance in challenging conditions with limited labeled data.

Generative diffusion models have recently shown impressive results in image restoration. However, the predicted noise from existing diffusion-based methods may be inaccurate, especially when the noise amplitude is small, thereby leading to sub-optimal results. In this letter, an unsupervised diffusion model with latent low-rank regularization is proposed to alleviate this challenge. In particular, we first create a latent low-rank space using self-supervised learning for each degraded images, from which we derive corresponding latent low-rank regularization. This regularization, combining with observed prior information and smoothness regularization, guides the reserve sampling process, resulting in the generation of high-quality images with fine-grained textures and fewer artifacts. In addition, by utilizing the pre-trained unconditional diffusion model, the proposed model reconstructs the missing pixels in a zero-shot manner, which does not need any reference images for additional training. Extensive experimental results demonstrate that our proposed method is superior to the self-supervised tensor completion methods and representative diffusion model-based image restoration methods.

In recent years, enormous studies have been conducted to improve the land cover (LC) classification performance of multimodal remote sensing (RS) data, which outperforms single-modal-based methods by a large margin due to information diversity. To go a step further, we develop a two-branch patch-based convolutional neural network (CNN) with an encoder–decoder (ED) module to fuse multimodal RS data information. A knowledge distillation in model (DIM) module is proposed to guild per-modality encoder learning with the final fused information to enable multimodal data fusion more effectively. Moreover, utilizing multimodal information to guide single-modal learning still remains to be explored. To this end, a knowledge distillation cross-model (DCM) module is designed to improve single-modal LC classification with multimodal knowledge distillation, which bridges the gap between single-modal-based and multimodal-based methods. In particular, the multimodal-based method is taken as a teacher to transfer knowledge to single-modal-based methods. Extensive experiments are carried out on two multimodal RS datasets, including hyperspectral (HS) and light detection and ranging (LiDAR) data, i.e., the Houston2013 dataset, and HS and synthetic aperture radar (SAR) data, i.e., the Berlin dataset. The results demonstrate the effectiveness and superiority of the proposed multimodal fusion strategy in comparison with several state-of-the-art multimodal RS data classification methods. Also, the proposed DCM module improves the LC classification performance of single-modal methods by a large margin.

Patch-based adversarial attacks have increasingly aroused concerns due to their application potential in military and civilian fields. In aerial imagery, numerous targets exhibit inherent directionality, such as vehicles and ships, giving rise to the emergence of oriented object detection tasks; similarly, adversarial patches also exhibit intrinsic orientation due to their lack of perfect symmetry. Existing methods presuppose a static alignment between the adversarial patch’s orientation and the camera’s coordinate system – an assumption that is frequently violated in aerial images, whose effectiveness degrades in real-world scenarios. In this paper, we investigate the often-neglected aspect of patch orientation in adversarial attacks and its impact on camouflage effectiveness, particularly when the orientation is not congruent with the target. A new Directional Guided Attack (DGA) framework is proposed for deceiving real-world aerial detectors, which shows robust and adaptable attack performance in camera shooting direction agnostic (CSDA) scenarios. The core idea of DGA is to utilize affine transformations to constrain the relative orientation of the patch to the target and introduce three types of loss to reduce target detection confidence, make the color printable, and smooth the patch color. We introduce a direction-guided evaluation methodology to bridge the gap between patch performance in the digital domain and its actual real-world efficacy. Moreover, we establish a drone-based vehicle detection dataset (SJTU-4K), which labels the orientation of the target, to assess the robustness of patches under various shooting altitudes and views. Extensive proportionally scaled and 1:1 experiments are performed in physical scenarios, demonstrating the superiority and potential of the proposed framework for real-world attacks.

Remote sensing (RS) images are unavoidably contaminated by thick clouds, greatly limiting their subsequent application and exploration. Most existing conventional thick cloud removal methods are based on hand-crafted priors, which utilize the low-rank or smoothness property to regularize the latent RS images. However, these hand-crafted priors are failed to describe the rich structure that many RS images exhibit. Deep learning (DL) methods achieve their performance owing to extensive labeled training data while large-scale labeled data are expensive to acquire in the RS scene. In this paper, a thick cloud removal method named Spectral-Temporal Low-Rank regularization with Deep Prior (STLR-DP) is proposed to tackle these issues, solely using a single cloud-contaminated image without any extra external training data or pre-trained models, which utilizes an untrained neural network to capture the rich characteristic of RS images rather than hand-crafted priors. The spectral-temporal low-rank regularization is further incorporated into the model to avoid the over-fitting problem. Benefiting from the deep intrinsic image characteristic captured by the neural network and its self-supervised nature, our method can effectively simultaneously reconstruct the contour and details of contaminated regions, and can be adaptive to various RS images with strong generalization ability. Experimental results on simulated and real datasets demonstrate that the proposed STLR-DP method outperforms the representative thick cloud removal and tensor completion methods.

Structure-from-Motion (SfM) is the process of estimating 3D scene structure and sensor pose from a set of 2D inputs. In this paper, we present a matrix factorization scheme for solving SAR SfM problem. First, SAR imaging model is linearized at local scene and the SfM problem is converted to a problem that decomposes data matrices into the product of two kinds of matrices, one of which satisfies Stiefel constraint. We then propose a Riemannian conjugate gradient descent algorithm leveraging the Stiefel constraint. SAR SfM is solved by the proposed algorithm via alternating iteratively estimating radar pose and scene structure. Finally, the feasibility and accuracy of the proposed scheme are verified through experiments.

Object detection in remote sensing images is an essential application of deep learning. However, due to the vulnerability of deep learning models, they are susceptible to adversarial attacks, which can undermine their reliability and accuracy. While significant progress has been made in the field of adversarial attacks, most of the work has focused on image classification tasks due to the complexity of object detection. In this paper, we propose a target camouflage method based on adversarial attacks that can mislead detectors and hide targets with minimal pixel perturbations. Experiments on the DIOR dataset demonstrate the effectiveness of our approach. Our method generates adversarial examples that can successfully fool Faster R-CNN into failing to detect objects with minimal perturbations.

Recently, fully supervised deep learning has achieved excellent success in remote sensing (RS) scene classification and segmentation. However, supervised learning requires tremendous labels, which are difficult to obtain in the field of RS. Self-supervised contrastive methods alleviate this problem by learning impressive transferable representations invariant to different data augmentations, e.g. color jittering. Such invariance could be harmful to RS scene classification and segmentation, which is sensitive to color changes. Therefore, we introduce a color-aware self-supervised learning framework (ColorSelf) for RS scene classification and segmentation. Our model encourages to preserve color-aware information in learned representation to improve their transferability. Extensive experiments on two challenging RS datasets demonstrate the proposed ColorSelf brings a significant performance improvement in both RS scene classification and segmentation task.

Most existing works on lightweight SAR ship detectors sacrifice a lot of detection accuracy to reduce model size. In this letter, we propose an ultra-lightweight detector based on distillation technology, which can reduce the parameter quantity of the model while minimizing the damage to the model’s detection accuracy. Due to the scattering interference and speckle noise in SAR images, directly applying the existing ultra-lightweight detectors cannot achieve satisfactory performance for ship detection. As a result, we design a global relationship distillation (GRD) algorithm for the ultra-lightweight SAR ship detector. This algorithm can preserve more global relationships from the teacher and mitigate the accuracy degradation caused by the noise and interference, especially in complex inshore scenarios. Besides, the features learned by this algorithm are robust, and the pruned model is more stable. The superiority of the GRD method over several state-of-the-art distillation methods has been evaluated on the HRSID dataset.

In this paper, we propose a novel dictionary learning model based on the idea of deep unrolling to deal with the synthetic aperture radar (SAR) image change detection problem. Deep unrolling aims at unrolling the iterative algorithm into a trainable neural network. In our proposed method, the idea of unrolling is applied to the Iterative Shrinkage Threshold Algorithm (ISTA), which is one of classic algorithms for dictionary learning. Then, the proposed Unrolling Iterative Shrinkage Threshold Algorithm (UR-ISTA), is utilized to obtain the sparse codes of the difference results. Finally, the change map is computed by k-means clustering algorithm. The advantage of UR-ISTA method is relatively low time cost, which makes it possible to add dictionary updating step to calculate specific feature vectors. Experimental results show that the proposed approach has superior accuracy and precision compared to several well-known change detection techniques. The proposed UR-ISTA algorithm shows more robustness than another sparse representation algorithm.

A working video synthetic aperture radar (VideoSAR) can obtain continuous observations of a region of interest from different viewpoints, meaning those observations naturally contain 3D information for positioning. This paper reports our preliminary studies on SAR scene structure-from-motion using several frames extracted from a VideoSAR sequence. In contrast to classic stereo-radargrammetric workflow, the radar pose is estimated only with information measured by radar. The coordinates of each scattering point are calculated by least-square optimization. We also develop an affine transformation aware dense matching framework to accurately measure pixel-level correspondence between frames. Experiments on real VideoSAR data demonstrate the validity of our approach.

With the development of deep learning, SAR target rotating detection has become a research hotspot. However, the regression process of the rotated boxes is challenging, especially for the rotating detection in target gathering areas such as docks and airports. This is because the regions of interest corresponding to adjacent targets have a relatively large overlap, which may cause data misalignment during the regression and classification process. To solve this problem, we propose a three-stage cascaded rotating regression network (3SCR2Net). Specifically, a horizontal anchor will be rotated and corrected three times continuously. 3SCR2Net overcomes the original problem of information misalignment caused by rotation detection in a complex background. In addition, two decoders are designed in this paper to decode the regression parameters. Experimental results on the SSDD+ dataset demonstrate that the proposed network outperforms five state-of-the-art methods in mean average accuracy (mAP).

A growing number of researchers have begun to use arbitrary-oriented detectors to detect ships. Because in the remote sensing dataset, ships are shown to be narrow and dense. Most of the deep learning methods used in synthetic aperture radar (SAR) ship detection are the same as or variants of those of optical remote sensing. However, the experimental settings of different papers are different. Therefore, various arbitrary-oriented target detectors can not be compared fairly on the SAR dataset. To solve this problem, we developed an arbitrary-oriented SAR ship detection benchmark, which provides strong baselines and state-of-the-art methods in rotation detection. All benchmark methods are tested on RSSDD datasets, and the code is publicly released at https://github.com/open-mmlab/mmrotate. Meanwhile, this paper further explores the role of ImageNet pretrained weight in SAR target detection and tries to train the SAR pretrained weight through unsupervised learning.

We present an open-source toolbox, named MMRotate, which provides a coherent algorithm framework of training, inferring, and evaluation for the popular rotated object detection algorithm based on deep learning. MMRotate implements 18 state-of-the-art algorithms and supports the three most frequently used angle definition methods. To facilitate future research and industrial applications of rotated object detection-related problems, we also provide a large number of trained models and detailed benchmarks to give insights into the performance of rotated object detection. MMRotate is publicly released at https://github.com/open-mmlab/mmrotate.

In a multichannel synthetic aperture radar (SAR) system, because of the target uncooperative motion, a ground moving target (GMT) is usually smeared, distorted, and shifted in an SAR image. In this article, a novel approach for multichannel SAR-GMT indication (GMTI) processing is proposed. The main innovations of this method are that a GMT can be well refocused and relocated since the target high-order Doppler parameters can be precisely estimated based on a high-order polynomial phase signal (PPS) model, and the target statistical amplitude and phase information is jointly applied to improve the radial velocity estimation robustness. Compared with the current SAR-GMTI algorithms, the improvements of this method over the existing methods are: 1) the topography interferometric phase can be effectively compensated by applying an adaptive 2-D spectrum filtering technique via iterative processing; 2) a GMT can be well imaged since the target Doppler chirp rate and the quadratic chirp rate can be well estimated via the 2-D coherent integration in the time–frequency plane; and 3) a GMT can be precisely relocated into its original position by applying the generalized amplitude and phase weighting technique. Real-measured SAR data processing results are presented to validate the effectiveness and feasibility of the proposed method.

In inverse synthetic aperture radar (ISAR) imaging for a uniformly moving rigid-body target, a finely focused ISAR image can be obtained by using the conventional range-Doppler algorithm. However, the ISAR image quality may significantly deteriorate when the time-vary Doppler phases in virtue of target maneuvering motions are present, such as an airplane with nonuniformly rotation and a ship with fluctuation. This has become a challenging task, especially under nonhigh signal-to-noise ratio (SNR) environment. In this article, a novel ISAR imaging algorithm for a maneuvering target with moderate reflection intensity is proposed. After motion compensation, the radar echo signal in a range cell is modeled as a multicomponent cubic phase signal (CPS), in which the chirp rate and the quadratic chirp rate are two important physical quantities that may determine the target ISAR focusing quality. Based on a symmetrical instantaneous autocorrelation function, the received CPSs are transformed into the time and lag-time plane, and then a 2-D coherent integration can be realized after the generalized time-scaled transform and 1-D maximization. This forms a high-quality ISAR image. The effectiveness and superiority of the proposed algorithm are validated by the ISAR imaging results of simulated and real measured data.

In this paper, a convolutional neural network based hierarchical kernel dictionary learning, which consists of convolutional neural networks (CNN) and dictionary learning (DL) parts, is proposed for synthetic aperture radar (SAR) target recognition. Compared with conventional DL methods, which use the raw images for training, the CNN part with three convolution layers is utilized to extract the SAR image's hierarchical features. The hierarchical features are introduced into the objective function of DL part. To handle the resulting nonlinear problem, we utilize a nonlinear mapping function to map the dimension-reduced hierarchical features into a higher Hilbert space and perform DL in the space such that the features can be represented linearly. A classification error term is added into the objective function to train a linear classifier. We use the kernel trick to solve the optimization problem. Experiments performed on the MSTAR dataset show that the proposed method outperforms the representative DL methods.

A growing number of researchers begin to use the arbitrary-oriented detector to detect ships. Because in the remote sensing dataset, ships are shown to be narrow and dense. Most of the deep learning methods used in synthetic aperture radar (SAR) ship detection are the same as or variants of those of optical remote sensing. However, due to the relatively low resolution and signal-to-noise ratio, the amplitude information in SAR image becomes more contaminated than that in optical image. Therefore, it is very difficult to train the arbitrary-oriented target detection task based on SAR dataset. In order to solve this problem, we attempt to further extract the frequency domain features of the SAR image by introducing a frequency attention module. The discrete cosine transform (DCT) to converts SAR image from spatial domain to frequency domain. Experimental results on HRSID datasets show that the proposed method can significantly improve the performance of arbitrary-oriented SAR ship detection.

This letter deals with the motion parameter estimation and focusing for ground moving targets in synthetic aperture radar (SAR) imagery. In the proposed algorithm, after range compression, the echo signal of a moving target is first transformed into the range-frequency and Doppler domain. Then, the target signal is characterized as an inclined trajectory after applying the correlation operation with respect to the divided Doppler subaperture data. Finally, target motion parameter estimation and focusing can be effectively accomplished based on the Doppler axis rotation transform (DART). The effectiveness of the proposed algorithm is validated by both simulated and real airborne/spaceborne SAR data.

In this letter, a novel convolutional neural network (CNN)-based dictionary learning (DL) method is proposed for synthetic aperture radar (SAR) target recognition. Different from conventional target recognition schemes, which consist of the hand-crafted feature extraction followed by a classifier, the proposed scheme utilizes a well-designed ConvNet as the feature extractor, and it can automatically learn hierarchies of features from the training data set. The outputs of the ConvNet are regarded as multifeature and are used for the following multi-DL. For a classification task, we take into consideration the mean-squared error (MSE) combined with a regularization term as the loss function. As a result, the whole architecture combines the ConvNet and DL as an end-to-end framework. We show the back propagation of the loss and update the variables using the stochastic gradient descent with the momentum method. Experiments performed on the moving and stationary target automatic recognition (MSTAR) data set exhibit that the proposed method outperforms many state-of-the-art DL and CNN methods in terms of recognition performance.

Matrix and tensor completion aim to recover the incomplete two- and higher-dimensional observations using the low-rank property. Conventional techniques usually minimize the convex surrogate of rank (such as the nuclear norm), which, however, leads to the suboptimal solution for the low-rank recovery. In this paper, we propose a new definition of matrix/tensor logarithmic norm to induce a sparsity-driven surrogate for rank. More importantly, the factor matrix/tensor norm surrogate theorems are derived, which are capable of factoring the norm of large-scale matrix/tensor into those of small-scale matrices/tensors equivalently. Based upon surrogate theorems, we propose two new algorithms called Logarithmic norm Regularized Matrix Factorization (LRMF) and Logarithmic norm Regularized Tensor Factorization (LRTF). These two algorithms incorporate the logarithmic norm regularization with the matrix/tensor factorization and hence achieve more accurate low-rank approximation and high computational efficiency. The resulting optimization problems are solved using the framework of alternating minimization with the proof of convergence. Simulation results on both synthetic and real-world data demonstrate the superior performance of the proposed LRMF and LRTF algorithms over the state-of-the-art algorithms in terms of accuracy and efficiency.

An outlier-resistance phase retrieval algorithm based on alternating direction method of multipliers (ADMM) is devised in this paper. Instead of the widely used least squares criterion that is only optimal for Gaussian noise environment, we adopt the least absolute deviation criterion to enhance the robustness against outliers. Considering both intensity- and amplitude-based observation models, the framework of ADMM is developed to solve the resulting non-differentiable optimization problems. It is demonstrated that the core subproblem of ADMM is the proximity operator of the ℓ1-norm, which can be computed efficiently by soft-thresholding in each iteration. Simulation results are provided to validate the accuracy and efficiency of the proposed approach compared to the existing schemes.

A novel ℓp-greedy pursuit (GP) algorithm for robust matrix completion, i.e., recovering a low-rank matrix from only a subset of its noisy and outlier-contaminated entries, is devised. The ℓp-GP uses the strategy of sequential rank-one update. In each iteration, a rank-one completion is solved by minimizing the ℓp-norm of the residual. Unlike the existing greedy methods that use the principal singular vectors of the residual matrix as the solution to the rank-one completion with the index information of the observed entries being ignored, the ℓp-GP employs alternating minimization to obtain an improved solution by fully exploiting the index information. More importantly, it achieves outlier-robustness by setting p = 1. For p = 1, only computing the weighted medians is involved, which yields that the complexity is near-linear with the number of observations. The low complexity enables the ℓ1-GP to be applicable to very large-scale problems. Simulation results demonstrate the superiority of the ℓp-GP over other approaches.

The deep convolutional neural networks (CNNs) have achieved the state of art performance in synthetic aperture radar (SAR) automatic target recognition (ATR). However, these networks often provide sub-optimal recognition results in the case of imbalanced SAR data distribution. In this paper, a synthetic minority class data method for improving imbalanced SAR target recognition using the generative adversarial network (GAN) is proposed. The minority class SAR data is first over-sampled by optimized data augmentation policies from automatic search method, which enlarge the training set for GAN. The progressive growing of GANs (PGGAN) is then trained on these data and generates high quality and diverse minority class SAR data to alleviate imbalanced data distribution. Experimental results on the designed imbalanced distributed Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset indicate that our method can effectively improve the recognition accuracy of minority class by approximately 11.68%.

In this paper, a fusion of linear and nonlinear classification errors is introduced into kernel dictionary learning and is applied for SAR target recognition. Different from linear dictionary and classifier learning, we utilize a nonlinear mapping function to map the SAR data into a higher dimensional space for nonlinear reconstruction. Inspired by neural networks, a multilayer nonlinear classification structure combined with a linear classification is introduced into the objective function such that the reconstruction error and the two classification errors are optimized simultaneously. In addition, we also use the Gaussian function to filter the noise in SAR images and perform the principal component analysis (PCA) algorithm to extract the main components of the samples. An optimization method is developed to solve the resulting problem. Experimental results performed on the MSTAR dataset demonstrate that the proposed method outperforms some representative dictionary learning and sparse representation schemes.

With the rapid development of deep learning, more and more deep neural networks with strong discrimination have come up. One reason why deep learning models can achieve such good results is the abundant annotation data. However, obtaining such considerable amount of annotation data is costly, especially in the field of synthetic aperture radar (SAR). High-quality SAR dataset cannot be constructed without the support of the specialists and institutes in the related field, which leads to the limited amount of labeled training data of SAR. In order to solve the problem that deep neural networks (DNNs) may face under limited labeled training data, researchers often use data augmentation methods to increase the number of labeled samples to boost model performance. But in fact, a large number of augmented training samples not only introduce extra noise, but also additional training time. In this paper, we introduce the active learning into SAR target recognition, which used to help specialists select the samples that are most worth labeling. Moreover, we propose a data-driven active learning scheme named Ranking Loss Module (RLM), which does not rely on artificially strategies to select samples. In contrast to data augmentation, it can improve the performance of the model while reducing the number of training data samples. Experimental results based on MSTAR dataset demonstrate the superiority of the proposed scheme. Using the RLM, better performance can be achieved with only one third of the full training samples.

With the development of synthetic aperture radar (SAR) system, automatic target recognition (ATR) has attracted wide attention in many decision-making tasks, in which an enhanced feature of SAR image is a powerful tool to improve the recognition accuracy. However, the presence of speckle noise and natural clutter inevitably contaminates SAR images and, thus, degrades image features. In this article, we explicitly address the speckle reduction problem for the circular SAR system, in which the motion of aircraft platform causes continuous angular variations so that different SAR images can be captured with the high interrelationship. By exploiting the underlying low-rank and continuous properties among different SAR images, a method called the ℓp-regularized low-rank and space-angle continuity extraction (ℓp-LSCE) is proposed to suppress the noise and enhance the target feature. Taking into account the interrelationship between SAR images, we arrange the images in a 3-D tensor to investigate the space-angle continuity of the targets. Furthermore, we develop a robust ℓp-regularized scheme to incorporate the low-rank property of targets. Then, the joint optimization problem is solved via the framework of augmented Lagrange multiplier (ALM) with efficient computation of each ALM subproblem. The experimental results of circular SAR data sets of the moving and stationary target acquisition and recognition (MSTAR) and the VideoSAR demonstrate that the proposed method can efficiently despeckle SAR images with well-preserved target features, which is conducive to the improvement of ATR performance.

In this article, a supervised nonlinear dictionary learning (DL) method, called multiscale supervised kernel DL (MSK-DL), is proposed for target recognition in synthetic aperture radar (SAR) images. We use Frost filters with different parameters to extract an SAR image's multiscale features for data augmentation and noise suppression. In order to reduce the computation cost, the dimension of each scale feature is reduced by principal component analysis (PCA). Instead of the widely used linear DL, we learn multiple nonlinear dictionaries to capture the nonlinear structure of data by introducing the dimension-reduced features into the nonlinear reconstruction error terms. A classification model, which is defined as a discriminative classification error term, is learned simultaneously. Hence, the objective function contains the nonlinear reconstruction error terms and a classification error term. Two optimization algorithms, called multiscale supervised kernel K-singular value decomposition (MSK-KSVD) and multiscale supervised incremental kernel DL (MSIK-DL), are proposed to compute the multidictionary and the classifier. Experiments on the moving and stationary target automatic recognition (MSTAR) data set are performed to evaluate the effectiveness of the two proposed algorithms. And the experimental results demonstrate that the proposed scheme outperforms some representative common machine learning strategies, state-of-the-art convolutional neural network (CNN) models and some representative DL methods, especially in terms of its robustness against training set size and noise.

Tensor robust principal component analysis via tensor nuclear norm (TNN) minimization has been recently proposed to recover the low-rank tensor corrupted with sparse noise/outliers. TNN is demonstrated to be a convex surrogate of rank. However, it tends to over-penalize large singular values and thus usually results in biased solutions. To handle this issue, we propose a new definition of tensor logarithmic norm (TLN) as the nonconvex surrogate of rank, which can decrease the penalization on larger singular values and increase that on smaller ones simultaneously to preserve the low-rank structure of a tensor. Then, the strategy of tensor factorization is combined into the minimization of TLN to improve computational performance. To handle impulsive scenarios, we propose a nonconvex 'p-ball projection scheme with 0 < p < 1 instead of the conventional convex scheme with p = 1, which enhances the robustness against outliers. By incorporating the TLN minimization and the 'p-ball projection, we finally propose two low-rank recovery algorithms, whose resulting optimization problems are efficiently solved by the alternating direction method of multipliers (ADMM) with convergence guarantees. The proposed algorithms are applied to the synthetic data recovery and image and video restorations in real-world. Experimental results demonstrate the superior performance of the proposed methods over several state-ofthe- art algorithms in terms of tensor recovery accuracy and computational efficiency.

A phase-only robust minimum dispersion (PO-RMD) beamformer is devised for non-Gaussian signals. The proposed PO-RMD employs a constant-modulus constraint on the weights, which is equivalent to simply phase shifting at each antenna. It adopts the minimum dispersion criterion to utilize the non-Gaussianity of the signals while employing the worst-case constraint to achieve the robustness against model uncertainty. A gradient projection algorithmic framework is developed to solve the resulting nonconvex optimization problem. In order to find a feasible point in the intersection of the constant-modulus and robustness constraint sets, an alternating projection algorithm is devised. More importantly, the closed-form expressions of the projection onto the two sets are derived, respectively. Simulation results demonstrate the effectiveness, accuracy and robustness of the PO-RMD.

Azimuth superresolution for real beam scanning radar aims to recover the high-resolution image from low-resolution echo. Among superresolution techniques, regularization-based methods are widely used, but most existing methods lead to the blurring of scattering targets and thus are difficult to distinguish between close targets. In this paper, we propose to employ the nonconvex ℓp-regularization with 0 <; p <; 1 to achieve the sparsity-driven superresolution, which further enhances the azimuth resolution. Furthermore, the resultant optimization problem is efficiently solved using an unified framework via incorporating different proximity operators. Simulation results validate the accuracy and efficiency of the proposed algorithm.

This paper proposes a method that can enhance the features of synthetic aperture radar images based on the exploitation of intrinsic target structure to improve the performance of automatic target recognition (ATR). We take advantage of the interrelationship between images and arrange them into a three-dimensional tensor. Then, by incorporating the joint low-rank and continuity constraints, the intrinsic target structure is extracted and enhanced with the reasonable suppression of speckle noise. Experiments on the moving and stationary target acquisition and recognition public database demonstrate the high quality of feature enhancement of the proposed algorithm, which efficiently improves the ATR performance.

In processing of large scene synthetic aperture radar (SAR) images, the first step is to split them into tiles in order to reduce the load of computer's computation effort and memory, which is crucial in the follow-up procedures of building radar footprints detection or reconstruction. Compared to the traditional cockamamie gridding method, we propose an automatic sub-images extraction approach based on the density and distance-based (DD) clustering algorithm and the connected-component labeling (CCL) algorithm of the graph theory which can avoid a mass of unnecessary least error finding work. According to our method, the original image can be split without introducing excessive subjective operation, which can remain the primary information of buildings' images efficiently. Meanwhile, automatic area searching reduces manpower effectively.

The existing approaches for synthetic aperture radar (SAR) automatic target recognition (ATR) based on deep neural network models have achieved promising performances. However, they cannot give satisfactory detection results when dealing with challenging scenarios, because the performance is influenced by multiple stages. We propose a simple yet powerful method that implements fast and accurate target recognition in SAR image. The system integrates intermediate steps with a single neural network, which can directly predict object of arbitrary orientations in full images. Comparing to the traditional methods, our system can eliminate the influence of previous stage and components in the process. The proposed method is applied to SAR imagery of (moving and stationary target acquisition and recognition) MSTAR dataset and the simulated data. Experimental results used demonstrate the potential of the developed approach in terms of high accuracy and efficiency.

In this paper, a novel robust multiscale dictionary learning algorithm is proposed for SAR object recognition. By extracting an SAR image's multiscale features and introducing them into the objective function, there are several reconstruction error terms. In addition, each reconstruction error term is calculated according to the sum of the absolute values of matrix entries instead of the Frobenius norm, and it is more robust against noise. An alternating minimization strategy is proposed to optimize the objective function. Experiments on the MSTAR dataset show that the proposed scheme outperforms some representative dictionary learning methods in terms of recognition performance and robustness against noise, especially under small training set size condition.

High-resolution images with abundant detailed information are necessary elements for various applications of synthetic aperture radar (SAR). In this paper, a novel super-resolution image reconstruction method based on self-normalizing generative adversarial network (SNGAN) is proposed. Compared with other published GAN-based super-resolution algorithms, the proposed method reflects its superiority in two aspects. First, the scaled exponential linear units (SeLU) is introduced as the activation function of generator to give the GAN system self-normalization ability and make it more suitable for SAR images. Second, the batch normalization layers after convolution are canceled to reduce the computational requirement and model oscillation. Experiment results on the images of TerraSAR and MSTAR dataset demonstrate that the proposed method acquires satisfactory performance on the resolution enhancement and target recognition of SAR images.

This letter addresses the coherent integration problem for the moving target detection in a frequency agile radar system. Due to the random phase fluctuation caused by the carrier frequency random hopping, the complex range-azimuth coupling effects will significantly deteriorate the target integration performance. In this letter, echoes are classified into different bursts according to the carrier frequencies, and then keystone transform (KT) is applied to correct range walk in every burst. After compensating the range offsets among different bursts and rearranging the signal returns, the scaled transform is constructed to remove the residual coupling between the agile carrier frequency and slow-time. Finally, a moving target can be well-focused in the frequency-velocity domain. Simulated results are provided to validate the effectiveness of the proposed algorithm.

In this letter, a novel method is proposed to estimate the along-track baseline for a multichannel high-resolution and wide-swath (HRSW) synthetic aperture radar (SAR) system. First, a spatial correlation function is constructed to remove the range cell migration and Doppler broadening of ground static targets. Then, the iterative adaptive approach (IAA) is applied to iteratively estimate the along-track baseline with high precision. Finally, a high-resolution SAR image can be obtained based on the estimated baseline. The effectiveness of the proposed algorithm is validated by both simulated and real SAR data.

In this letter, a novel nonlinear supervised dictionary learning (DL) scheme called multiscale incremental DL, whose objective function contains reconstruction error terms and a classification error term, is proposed for synthetic aperture radar (SAR) object recognition. In the reconstruction error terms, considering the local and global features of SAR images, Gaussian functions with different blurring parameters are exploited to extract SAR images' multiscale features, and all features can be reconstructed according to the weights assigned to these features at different scales. In the classification error term, a linear combination of classification vectors close to the labels of samples restricts sparse codes from different classes to be almost independent. Furthermore, an incremental method is utilized to address the memory consumption problem, and the optimal solution is obtained. Experiments on the moving and stationary target automatic recognition database demonstrate that the proposed algorithm outperforms several representative DL, support vector machine, and k-nearest neighbor methods in the case of a small training sample set size and exhibits strong antinoise performance.

In this paper, a new algorithm is presented to image ground moving targets in a synthetic aperture radar (SAR) system based on range frequency reversal transform-fractional Fourier transform (RFRT-FrFT). In this algorithm, a range compressed signal is initially transformed into the range frequency domain and then RFRT is proposed to directly compensate the range migration via multiplying the signal in the range frequency domain by its reversed data according to the equal interval sampling of range frequency variable, which can significantly decrease the computational complexity in target envelope migration elimination. Then, FrFT is applied to accomplish the target motion parameter estimation after range migration alignment. Finally, a ground moving target is well focused after motion compensation. The effectiveness of the proposed algorithm is validated by both simulated and real SAR data.

Matrix completion aims to find the missing entries from incomplete observations using the low-rank property. Conventional convex optimization based techniques for matrix completion minimize the nuclear norm subject to a constraint on the Frobenius norm of the residual. However, they are not robust to outliers and have a high computational complexity. Different from the existing schemes based on solving a minimization problem, we formulate matrix completion as a feasibility problem. An alternating projection algorithm (APA) is devised to find a feasible point in the intersection of the low-rank constraint set and fidelity constraint set. To achieve resistance to outliers, the fidelity constraint set is modeled as an ℓp-ball, where the ball center corresponds to the observed data. Furthermore, there is no stepsize within the framework of APA. Convergence of the APA is analyzed and the local linear convergence rate is established. Simulation results demonstrate the efficiency, accuracy, and outlier robustness of the APA.

The recently reported Wirtinger flow (WF) algorithm has been demonstrated as a promising method for solving the problem of phase retrieval by applying a gradient descent scheme. An empirical choice of stepsize is suggested in practice. However, this heuristic stepsize selection rule is not optimal. In order to accelerate the convergence rate, we propose an improved WF with optimal stepsize. It is revealed that this optimal stepsize is the solution of a univariate cubic equation with real-valued coefficients. Finding its roots is computationally simple because a closed-form expression exists. Furthermore, compared with obtaining the coefficients of the cubic equation, calculating the gradient is still the leading cost. Therefore, the proposed approach has the same dominant cost as WF in each iteration. Simulation results are provided to validate its efficiency compared to the existing technique.

Beamforming is a fundamental technique in array signal processing. Many existing approaches are based on second-order statistics. However, their performance degrades significantly due to outliers in the received signal. In this letter, we propose an outlier-resistant beamformer design criterion based on minimizing the expectation of the modulus of the array output with an${\ell _1}$-regularization term being added for sidelobe suppression. By using the${\ell _1}$-modulus of complex numbers instead of the standard modulus, the resulting optimization problem can be efficiently solved by a simple iterative algorithm or linear programming. Simulation results in the presence of impulsive signals are provided to demonstrate its robustness and accuracy compared to existing techniques.

Channels with a sparse impulse response arise in a variety of wireless communication applications, such as high definition television (HDTV) terrestrial transmission and underwater acoustic communications. By exploiting the sparsity of the channel, this paper proposes a fast algorithm for sparse channel estimation based on a greedy algorithm called orthogonal matching pursuit (OMP). The proposed fast OMP-based channel estimation algorithm has a low computational complexity of O (K N log N) with K and N the channel sparsity level and signal length, respectively. The fast OMP is competitive to the ℓ1-minimization based methods in terms of estimation accuracy. In addition, the fast OMP is faster and easier to implement. Therefore it is an attractive alternative to the ℓ1-minimization approaches. Simulation results are provided to demonstrate the performance of the fast OMP algorithm.

A new signal-selective direction finding algorithm which exploits the property of the cyclostationarity of incoming signals is proposed. After dimensionality reducing by projecting the observed array data onto the signal subspace, the array manifold matrix is identified by the simultaneous diagonalization structure of the matrix pencil consisting of the cyclic correlation matrix and the cyclic conjugate correlation matrix. Then the direction-of-arrivals (DOAs) are obtained from the phase-differences of the estimated array manifold matrix. Simulation results demonstrate that the proposed algorithm is superior to the cyclic-MUSIC and cyclic-ESPRIT in terms of the root mean squares errors (RMSEs) of the DOA estimates.