Low-rank Sparse Decomposition Research Articles

Ground penetrating radar clutter suppression based on the weighted tensor Schatten p-paradigm minimization of tensor principal components

Abstract Ground-penetrating radar (GPR) is an effective geophysical-electromagnetic method for detecting subsurface targets. However, target echoes are often flooded by strong clutter, which affects the detection performance. Clutter suppression is an active area in GPR research, and the current trend is to use methods based on low-rank sparse decomposition (LRSD), which has significant advantages over traditional low-rank methods. In recent years, the tensor robust principal component analysis (TRPCA) method has been proposed for use in GPR clutter suppression. Although good results have been achieved, TRPCA does not retain the information of the low-rank part well by shrinking all the singular values equally. There is a significant gap between all singular values in B-scan data in practical applications; therefore, different singular values should be treated differently. Therefore, this study proposes a TRPCA method (Schatten p-TRPCA, p-TRPCA) based on weighted tensor Schatten p-paradigm minimisation, which assigns different weights to different singular values and decomposes the B-scan image into a low-rank clutter matrix and a sparse target matrix. The method was evaluated using simulation experiments and real test data, and its performance was found to be better than those of TRPCA and traditional methods.

Shallow sea reverberation suppression based on a range azimuth patch matrix model.

Reverberation is the main background interference for active sonar detection in shallow sea. Reverberation suppression is crucial for enhancing the performance of active sonar. In this paper, a reverberation suppression method based on low-rank sparse decomposition is proposed. First, both the sparseness property of the targets and the non-local self-correlation property of the reverberation are used to construct a range azimuth patch matrix model. The reverberation suppression problem is then transformed into an optimization problem for the recovery of a low-rank sparse matrix. The validity of the proposed method is verified by using the measured data. Results show that, compared with the reverberation pre-whitening and sparse fractional Fourier transform methods, the proposed method significantly improves the reverberation suppression performance and achieves a better detection result when the signal-to-interference ratio is below -2 dB.

Robust PCA with Lw,∗ and L2,1 Norms: A Novel Method for Low-Quality Retinal Image Enhancement.

Nonmydriatic retinal fundus images often suffer from quality issues and artifacts due to ocular or systemic comorbidities, leading to potential inaccuracies in clinical diagnoses. In recent times, deep learning methods have been widely employed to improve retinal image quality. However, these methods often require large datasets and lack robustness in clinical settings. Conversely, the inherent stability and adaptability of traditional unsupervised learning methods, coupled with their reduced reliance on extensive data, render them more suitable for real-world clinical applications, particularly in the limited data context of high noise levels or a significant presence of artifacts. However, existing unsupervised learning methods encounter challenges such as sensitivity to noise and outliers, reliance on assumptions like cluster shapes, and difficulties with scalability and interpretability, particularly when utilized for retinal image enhancement. To tackle these challenges, we propose a novel robust PCA (RPCA) method with low-rank sparse decomposition that also integrates affine transformations τi, weighted nuclear norm, and the L2,1 norms, aiming to overcome existing method limitations and to achieve image quality improvement unseen by these methods. We employ the weighted nuclear norm (Lw,∗) to assign weights to singular values to each retinal images and utilize the L2,1 norm to eliminate correlated samples and outliers in the retinal images. Moreover, τi is employed to enhance retinal image alignment, making the new method more robust to variations, outliers, noise, and image blurring. The Alternating Direction Method of Multipliers (ADMM) method is used to optimally determine parameters, including τi, by solving an optimization problem. Each parameter is addressed separately, harnessing the benefits of ADMM. Our method introduces a novel parameter update approach and significantly improves retinal image quality, detecting cataracts, and diabetic retinopathy. Simulation results confirm our method's superiority over existing state-of-the-art methods across various datasets.

A two-stage multi-view partial multi-label learning for enhanced disambiguation

Multi-view partial multi-label (MVPML) problems are often encountered in our real life. Each training sample described by multi-view is associated with a set of candidate labels, including multiple ground-truth labels and noisy labels. Currently, to tackle the problem, some attempts are focusing on label enhancement. Moreover, disambiguation is a relatively valid method to recover the ground-truth label by disambiguating the candidate label for each sample. However, due to the complexity of the data, the one-stage disambiguation method is hard to fully recover the ground-truth label. To deal with the challenge, we propose a novel two-stage MVPML method motivated by feature-induced manifold disambiguation and low-rank sparse decomposition (TFMDD). Specifically, in the first stage, the KNN-based aggregate manifold structure adaptively fuses feature information from different views, and the obtained structure information is used to build a feature-induced manifold structure in the label space to remove the ambiguity of candidate labels. In the second stage, under the supervision of the disambiguated label matrix, multi-label classifiers and noise recognizers are simultaneously optimized in a unified framework by considering label correlation and low noise levels. Through the two stages, TFMDD attains satisfactory results. Extensive experiments on real-world datasets clearly confirm the method validity and give a validation in a statistical sense.

Infrared Small Target Detection Via Two-Stage Feature Complementary Improved Tensor Low-rank Sparse Decomposition

Infrared Small Target Detection Via Two-Stage Feature Complementary Improved Tensor Low-rank Sparse Decomposition

Infrared Dim and Small Target Detection Based on Superpixel Segmentation and Spatiotemporal Cluster 4D Fully-Connected Tensor Network Decomposition

The detection of infrared dim and small targets in complex backgrounds is very challenging because of the low signal-to-noise ratio of targets and the drastic change in background. Low-rank sparse decomposition based on the structural characteristics of infrared images has attracted the attention of many scholars because of its good interpretability. In order to improve the sensitivity of sliding window size, insufficient utilization of time series information, and inaccurate tensor rank in existing methods, a four-dimensional tensor model based on superpixel segmentation and statistical clustering is proposed for infrared dim and small target detection (ISTD). First, the idea of superpixel segmentation is proposed to eliminate the dependence of the algorithm on selection of the sliding window size. Second, based on the improved structure tensor theory, the image pixels are statistically clustered into three types: corner region, flat region, and edge region, and are assigned different weights to reduce the influence of background edges. Next, in order to better use spatiotemporal correlation, a Four-Dimensional Fully-Connected Tensor Network (4D-FCTN) model is proposed in which 3D patches with the same feature types are rearranged into the same group to form a four-dimensional tensor. Finally, the FCTN decomposition method is used to decompose the clustered tensor into low-dimensional tensors, with the alternating direction multiplier method (ADMM) used to decompose the low-rank background part and sparse target part. We validated our model across various datasets, employing cutting-edge methodologies to assess its effectiveness in terms of detection precision and reduction of background interference. A comparative analysis corroborated the superiority of our proposed approach over prevailing techniques.

Infrared Small-Target Detection Based on Background-Suppression Proximal Gradient and GPU Acceleration

Patch-based methods improve the performance of infrared small target detection, transforming the detection problem into a Low-Rank Sparse Decomposition (LRSD) problem. However, two challenges hinder the success of these methods: (1) The interference from strong edges of the background, and (2) the time-consuming nature of solving the model. To tackle these two challenges, we propose a novel infrared small-target detection method using a Background-Suppression Proximal Gradient (BSPG) and GPU parallelism. We first propose a new continuation strategy to suppress the strong edges. This strategy enables the model to simultaneously consider heterogeneous components while dealing with low-rank backgrounds. Then, the Approximate Partial Singular Value Decomposition (APSVD) is presented to accelerate solution of the LRSD problem and further improve the solution accuracy. Finally, we implement our method on GPU using multi-threaded parallelism, in order to further enhance the computational efficiency of the model. The experimental results demonstrate that our method out-performs existing advanced methods, in terms of detection accuracy and execution time.

TVRPCA＋: Low-rank and sparse decomposition based on spectral norm and structural sparsity-inducing norm

Traditional low-rank sparse decomposition algorithms have trouble obtaining a clear and complete foreground representation in foreground–background separation due to the complex video environment and the noise. For this issue, We propose a more robust and higher-performance low-rank and sparse decomposition algorithm named TVRPCA＋ based on spectral norm, structured sparse norm and total variation (TV) regularization. The structured sparse norm and TV regularization are exploited to suppress noise and obtain much cleaner foregrounds. Spectral norm is used in our algorithm for the low-rank component to address the issue of over-punishment and restore more foreground information. Moreover, an efficient algorithm based on the inexact augmented Lagrange multiplier method is designed to solve the proposed optimization problem. Experimental results show that TVRPCA＋ obtained five top F-measures and three of the second-highest F-measures in eight noise-free test video sequences with complex backgrounds, while the highest average F-measure was also achieved in all ten experimental groups with noise.

A Spatial–Temporal Block-Matching Patch-Tensor Model for Infrared Small Moving Target Detection in Complex Scenes

Detecting infrared (IR) small moving targets in complex scenes quickly, accurately, and robustly remains a challenging problem in the current research field. To address this issue, this paper proposes a novel spatial–temporal block-matching patch-tensor (STBMPT) model based on a low-rank sparse decomposition (LRSD) framework. This model enhances the traditional infrared patch-tensor (IPT) model by incorporating joint spatial–temporal sampling to exploit inter-frame information and constructing a low-rank patch tensor using image block matching. Furthermore, a novel prior-weight calculation is introduced, utilizing the eigenvalues of the local structure tensor to suppress interference such as strong edges, corners, and point-like noise from the background. To improve detection efficiency, the tensor is constructed using a matching group instead of using a traditional sliding window. Finally, the background and target components are separated using the alternating direction method of multipliers (ADMM). Qualitative and quantitative experimental analysis in various scenes demonstrates the superior detection performance and efficiency of the proposed algorithm for detecting infrared small moving targets in complex scenes.

One-bit SAR imaging algorithm based on MC function and TV norm

Synthetic Aperture Radar (SAR) imaging is generally characterized by a large amount of data and a high sampling rate. The traditional one-bit compressed sensing will generate virtual targets when recovering images at a low SNR, resulting in low reconstruction accuracy and obvious noise impact of the algorithm. In this paper, a one-bit SAR imaging algorithm based on the Minimax Concave (MC) penalty function and the Total Variation (TV) norm is proposed, which can potentially improve the reconstruction accuracy. At the same time, to solve the problem of speckle noise generated in the imaging process, this paper proposes a Fast Low-rank Sparse Decomposition (FLRSD) algorithm based on the one-bit contaminated image, which potentially improves the anti-noise performance and reconstruction efficiency. The results of simulation and measured data show that the proposed algorithms have better reconstruction accuracy and focusing performance than other algorithms. Even at low SNR, they also have good reconstruction effect.

Infrared Cirrus Detection Using Non-Convex Rank Surrogates for Spatial-Temporal Tensor

Infrared small target detection (ISTD) plays a significant role in earth observation infrared systems. However, some high reflection areas have a grayscale similar to the target, which will cause a false alarm in the earth observation infrared system. For the sake of raising the detection accuracy, we proposed a cirrus detection measure based on low-rank sparse decomposition as a supplementary method. To better detect cirrus that may be sparsely insufficient in a single frame image, the method treats the cirrus sequence image with time continuity as a tensor, then uses the visual saliency of the image to divide the image into a cirrus region and a cirrus-free region. Considering that the classical tensor rank surrogate cannot approximate the tensor rank very well, we used a non-convex tensor rank surrogate based on the Laplace function for the spatial-temporal tensor (Lap-NRSSTT) to surrogate the tensor rank. In an effort to compute the proposed model, we used a high-efficiency optimization approach on the basis of alternating the direction method of multipliers (ADMM). Finally, final detection results were obtained by the reconstructed cirrus images with a set threshold segmentation. Results indicate that the proposed scheme achieves better detection capabilities and higher accuracy than other measures based on optimization in some complex scenarios.

Video SAR Moving Target Shadow Detection Based on Intensity Information and Neighborhood Similarity

Video Synthetic Aperture Radar (SAR) has shown great potential in moving target detection and tracking. At present, most of the existing detection methods focus on the intensity information of the moving target shadow. According to the mechanism of shadow formation, some shadows of moving targets present low contrast, and their boundaries are blurred. Additionally, some objects with low reflectivity show similar features with them. These cause the performance of these methods to degrade. To solve this problem, this paper proposes a new moving target shadow detection method, which consists of background modeling and shadow detection based on intensity information and neighborhood similarity (BIIANS). Firstly, in order to improve the efficiency of image sequence generation, a fast method based on the Back-projection imaging algorithm (f-BP) is proposed. Secondly, due to the low-rank characteristics of stationary objects and the sparsity characteristics of moving target shadows presented in the image sequence, this paper introduces the low-rank sparse decomposition (LRSD) method to perform background modeling for obtaining better background (static objects) and foreground (moving targets) images. Because the shadows of moving targets appear in the same position in the original and the corresponding foreground images, the similarity between them is high and independent of their intensity. Therefore, using the BIIANS method can obtain better shadow detection results. Real W-band data are used to verify the proposed method. The experimental results reveal that the proposed method performs better than the classical methods in suppressing false alarms, missing alarms, and improving integrity.

A ViSAR Shadow-Detection Algorithm Based on LRSD Combined Trajectory Region Extraction

Shadow detection is a new method for video synthetic aperture radar moving target indication (ViSAR-GMTI). The shadow formed by the target occlusion will reflect its real position, preventing the defocusing or offset of the moving target from making it difficult to identify the target during imaging. To achieve high-precision shadow detection, this paper proposes a video SAR moving target shadow-detection algorithm based on low-rank sparse decomposition combined with trajectory area extraction. Based on the low-rank sparse decomposition (LRSD) model, the algorithm creates a new decomposition framework combined with total variation (TV) regularization and coherence suppression items to improve the decomposition effect, and a global constraint is constructed to suppress interference using feature operators. In addition, it cooperates with the double threshold trajectory segmentation and error trajectory elimination method to further improve the detection performance. Finally, an experiment was carried out based on the video SAR data released by Sandia National Laboratory (SNL); the results prove the effectiveness of the proposed method, and the detection performance of the method is proved by comparative experiments.

Wavelet-Based Weighted Low-Rank Sparse Decomposition Model for Speech Enhancement Using Gammatone Filter Bank Under Low SNR Conditions

Estimating noise-related parameters in unsupervised speech enhancement (SE) techniques is challenging in low SNR and non-stationary noise environments. In the recent SE approaches, the best results are achieved by partitioning noisy speech spectrograms into low-rank noise and sparse speech parts. However, a few limitations reduce the performance of these SE methods due to the use of overlap and add in STFT process, noisy phase, due to inaccurate estimation of low rank in nuclear norm minimization and Euclidian distance measure in the cost function. These aspects can cause a loss of information in the reconstructed signal when compared to clean speech. To solve this, we propose a novel wavelet-based weighted low-rank sparse decomposition model for enhancing speech by incorporating a gammatone filter bank and Kullback–Leibler divergence. The proposed framework differs from other strategies in which the SE is carried entirely in time domain without the need for noise estimation. Further, to reduce the word error rate, these algorithms were trained and tested on a typical automatic speech recognition module. The experimental findings indicate that the proposed cascaded model has shown significant improvement under low SNR conditions over individual and traditional methods with regard to SDR, PESQ, STOI, SIG, BAK and OVL.

ANLPT: Self-Adaptive and Non-Local Patch-Tensor Model for Infrared Small Target Detection

Infrared small target detection is widely used for early warning, aircraft monitoring, ship monitoring, and so on, which requires the small target and its background to be represented and modeled effectively to achieve their complete separation. Low-rank sparse decomposition based on the structural features of infrared images has attracted much attention among many algorithms because of its good interpretability. Based on our study, we found some shortcomings in existing baseline methods, such as redundancy of constructing tensors and fixed compromising factors. A self-adaptive low-rank sparse tensor decomposition model for infrared dim small target detection is proposed in this paper. In this model, the entropy of image block is used for fast matching of non-local similar blocks to construct a better sparse tensor for small targets. An adaptive strategy of low-rank sparse tensor decomposition is proposed for different background environments, which adaptively determines the weight coefficient to achieve effective separation of background and small targets in different background environments. Tensor robust principal component analysis (TRPCA) was applied to achieve low-rank sparse tensor decomposition to reconstruct small targets and their backgrounds separately. Sufficient experiments on the various types data sets show that the proposed method is competitive.

A Modified 2-D Notch Filter Based on Image Segmentation for RFI Mitigation in Synthetic Aperture Radar

Synthetic aperture radar (SAR), as an active microwave sensor, can inevitably receive radio frequency interference (RFI) generated by various electromagnetic equipment. When the SAR system receives RFI, it will affect SAR imaging and limit the application of SAR images. As a kind of RFI mitigation method, notch filtering method is a classical method with high efficiency and robust performance. However, the notch filtering methods pay no attention to the protection of useful signals. This paper proposed a modified 2-D notch filter based on image segmentation for RFI mitigation with signal-protected capability. (1) The adaptive gamma correction (AGC) approach was utilized to enhance the SAR image with RFI in the range-frequency and azimuth-time domain. (2) The modified selective binary and Gaussian filtering regularized level set (SBGFRLS) model was utilized to further process the image after AGC to accurately extract the contour of the useful signals with interference, which is more conducive to protecting the useful signals without interference. (3) The Generalized Singular Value Thresholding (GSVT) based low-rank sparse decomposition (LRSD) model was utilized to separate the RFI signals and the useful signals. Then, the useful signals were restored to the raw data. The simulation experiments and measured data experiments show that the proposed method can effectively mitigate RFI and protect the useful signals whether there are RFI with single source or multiple sources.

Privacy-Preserving Video Fall Detection via Chaotic Compressed Sensing and GAN-Based Feature Enhancement

Currently, falling is the primary cause of injury and death of the elderly due to accidents, which seriously threatens the health and life of the elderly. Considering the phenomenon of video privacy disclosure in recent years, this article proposes a computer vision fall detection method to meet the needs of video privacy protection. The innovation here lies in compressed sensing (CS) visual privacy protection and GAN-based feature enhancement. There are three main steps, the video frame visual privacy protection with chaotic pseudo-random CS mechanism, the foreground extraction with improved low rank sparse decomposition theory, and the temporal and spatial feature enhancement and fall detection with improved-ACGAN `architecture. The experimental results on three open fall datasets show that the method can not only effectively detect the fall behavior in video, but also has high accuracy. At the same time, the overall operation speed of the algorithm increases with the increase of the number of compression layers.

A Patch-Based Flow Field Reconstruction Method for Particle Image Velocimetry Data of Multistage Centrifugal Pumps

Abstract Particle image velocimetry (PIV) technology, which performs the full-field velocity measurement on the laser plane, plays a crucial role in studying complex flow structures in multistage centrifugal pumps. In particle image cross-correlation analysis, the flow field could be corrupted with outliers due to the background Gaussian imaging noise, insufficient illumination caused by optical obstruction, and particle slip caused by centrifugal forces. In this study, we propose a patch-based flow field reconstruction (PFFR) method for PIV data of multistage centrifugal pumps. Since natural images contain a large number of mutually similar patches at different locations, the instantaneous PIV data with a symmetric property is segmented to multiple patches. The flow field reconstruction is achieved by low-rank sparse decomposition, which exploits the information about similar flow characteristics present in patches. Furthermore, we illustrated the proposed PFFR on a large eddy simulation vorticity field and experimental data of a multistage centrifugal pump to evaluate its effectiveness. We also performed the three other data analysis methods. The results show that the proposed PFFR has a strong reconstruction ability to improve data reliability for the instantaneous flow field with outliers. When the outliers account for 20% of the total flow vectors, the average normalized root-mean-square error of PFFR-reconstructed data is 0.143, which is lower than the three other data methods by 21.9%–48.1%. The structural similarity is 0.702, which is higher than the three other data methods by 2.1%–9%.

An Improved RFI Mitigation Approach for SAR Based on Low-Rank Sparse Decomposition: From the Perspective of Useful Signal Protection

As an open system, synthetic aperture radar (SAR) inevitably receives radio frequency interference (RFI) generated by electromagnetic equipment in the same band. The existence of RFI seriously affects SAR signal processing and image interpretation. In recent years, many algorithms and models related to RFI mitigation have been proposed. However, most of that focus on effectively mitigating the RFI is insufficient to protect the useful signals. This article proposes a mitigation method of RFI with a signal-protected capability. (1) The kurtosis coefficient is used to detect RFI pulse-by-pulse, and the echoes containing RFI are stored in matrix form. (2) The preliminary extraction of RFI is complete by low-rank sparse decomposition of the echo matrix containing RFI. (3) For the secondary separation of RFI, the accurate position of RFI in the preliminary extraction results is located by the fuzzy C-means clustering; then, we separate the RFI and the remaining useful signals again and reconstruct the useful signals to complete the mitigation work. The proposed method can further protect useful signals while effectively removing interference through the secondary separation of RFI. Experimental results based on simulated and measured data verify the performance and potential of the proposed method.

Infrared Small Target Detection Algorithm Based on Local Spatial Gradient Peak

A sparse infrared small target detection algorithm based on local spatial gradient peaks is proposed to deal with the problem of slow running speed and edge sensitivity in low-rank decomposition methods.The detection steps are as follows. In the first step, the image expansion operation is used for preprocessing. We use the circular structure element to sharpen the edges of targets and smooth the background noise. Then, the saliency gradient features of the target local region are applied to calculate the overlapping gradient information of the image after expansion. The local area with a larger gradient peak is located in the original image, and the selected local area is considered to be the region of interest with candidate targets. Finally, we use the advanced accelerated proximal gradient algorithm to perform matrix decomposition in the extracted local regions of interest to extract sparse infrared small targets. Extensive experimental results under real scenarios illustrated that compared with the baseline low-rank sparse decomposition method, the proposed approach runs faster and shows superior detection performance in the comprehensive evaluation index.