Low-rank And Sparse Matrix Decomposition Research Articles

SAR Jamming Suppression by Exploiting Polarized Similarity with Low-Rank and Sparse Matrix Decomposition

Optimal hyper-parameter selection for low-rank and sparse matrix decomposition (LRSMD) in synthetic aperture radar jamming suppression is usually challenging. This letter proposes an effective approach to LRSMD jamming suppression by exploiting the polarized similarity. A polarimetric ratio function is established to straightforwardly determine the rank hyper-parameter. The polarimetric ratio function is defined as the energy ratio of the decomposed low-rank jamming component to the sparse target signal, which is consistent across multiple polarized channels due to the equal jamming gain distinguished from the target polarized scattering. The algorithm optimally exploits the polarized similarity of jamming components to determine the rank hyper-parameter. It provides enhanced robustness and accuracy in SAR jamming removal, confirmed by synthetic experiments.

Hyperspectral Anomaly Detection with Auto-Encoder and Independent Target

As an unsupervised data representation neural network, auto-encoder (AE) has shown great potential in denoising, dimensionality reduction, and data reconstruction. Many AE-based background (BKG) modeling methods have been developed for hyperspectral anomaly detection (HAD). However, their performance is subject to their unbiased reconstruction of BKG and target pixels. This article presents a rather different low rank and sparse matrix decomposition (LRaSMD) method based on AE, named auto-encoder and independent target (AE-IT), for hyperspectral anomaly detection. First, the encoder weight matrix, obtained by a designed AE network, is utilized to construct a projector for generating a low-rank component in the encoder subspace. By adaptively and reasonably determining the number of neurons in the latent layer, the designed AE-based method can promote the reconstruction of BKG. Second, to ensure independence and representativeness, the component in the encoder orthogonal subspace is made into a sphere and followed by finding of unsupervised targets to construct an anomaly space. In order to mitigate the influence of noise on anomaly detection, sparse cardinality (SC) constraint is enforced on the component in the anomaly space for obtaining the sparse anomaly component. Finally, anomaly detector is constructed by combining Mahalanobi distance and multi-components, which include encoder component and sparse anomaly component, to detect anomalies. The experimental results demonstrate that AE-IT performs competitively compared to the LRaSMD-based models and AE-based approaches.

Speech Enhancement Based on Constrained Low-rank Sparse Matrix Decomposition Integrated with Temporal Continuity Regularisation

Speech enhancement in strong noise condition is a challenging problem. Low-rank and sparse matrix decomposition (LSMD) theory has been applied to speech enhancement recently and good performance was obtained. Existing LSMD algorithms consider each frame as an individual observation. However, real-world speeches usually have a temporal structure, and their acoustic characteristics vary slowly as a function of time. In this paper, we propose a temporal continuity constrained low-rank sparse matrix decomposition (TCCLSMD) based speech enhancement method. In this method, speech separation is formulated as a TCCLSMD problem and temporal continuity constraints are imposed in the LSMD process. We develop an alternative optimisation algorithm for noisy spectrogram decomposition. By means of TCCLSMD, the recovery speech spectrogram is more consistent with the structure of the clean speech spectrogram, and it can lead to more stable and reasonable results than the existing LSMD algorithm. Experiments with various types of noises show the proposed algorithm can achieve a better performance than traditional speech enhancement algorithms, in terms of yielding less residual noise and lower speech distortion.

Dictionary Learning-Cooperated Matrix Decomposition for Hyperspectral Target Detection

Hyperspectral target detection is one of the most challenging tasks in remote sensing due to limited spectral information. Many algorithms based on matrix decomposition (MD) are proposed to promote the separation of the background and targets, but they suffer from two problems: (1) Targets are detected with the criterion of reconstruction residuals, and the imbalanced number of background and target atoms in union dictionary may lead to misclassification of targets. (2) The detection results are susceptible to the quality of the apriori target spectra, thus obtaining inferior performance because of the inevitable spectral variability. In this paper, we propose a matrix decomposition-based detector named dictionary learning-cooperated matrix decomposition (DLcMD) for hyperspectral target detection. The procedure of DLcMD is two-fold. First, the low rank and sparse matrix decomposition (LRaSMD) is exploited to separate targets from the background due to its insensitivity to the imbalanced number of background and target atoms, which can reduce the misclassification of targets. Inspired by dictionary learning, the target atoms are updated during LRaSMD to alleviate the impact of spectral variability. After that, a binary hypothesis model specifically designed for LRaSMD is proposed, and a generalized likelihood ratio test (GLRT) is performed to obtain the final detection result. Experimental results on five datasets have shown the reliability of the proposed method. Especially in the Los Angeles-II dataset, the area under the curve (AUC) value is nearly 16% higher than the average value of the other seven detectors, which reveals the superiority of DLcMD in hyperspectral target detection.

FOC winding defect detection based on improved texture features and low-rank representation model.

The defect detection of fiber-optic coils (FOCs) plays an important role in the quality control of the FOC production. In order to overcome the problems of poor performance and low reliability of existing methods, this paper provides a solution for winding defect detection of FOCs based on low-rank representation (LRR) technology. First, we design a feature matrix, which represents the image. Then the LRR model is employed to formulate the defect detection task as a problem of low rank and sparse matrix decomposition. Meanwhile, Laplacian regularization is introduced as a smoothness constraint to expand the distance between defect regions and low-rank background. Experiments are performed on a real dataset to verify the algorithm. The results show that the proposed winding defect detection method of FOCs achieves the highest detection accuracy and lowest false alarm rate compared to other methods, verifying the effectiveness of the proposed method.

Spectral–Spatial Complementary Decision Fusion for Hyperspectral Anomaly Detection

Hyperspectral anomaly detection has become an important branch of remote–sensing image processing due to its important theoretical value and wide practical application prospects. However, some anomaly detection methods mainly exploit the spectral feature and do not make full use of spatial features, thus limiting the performance improvement of anomaly detection methods. Here, a novel hyperspectral anomaly detection method, called spectral–spatial complementary decision fusion, is proposed, which combines the spectral and spatial features of a hyperspectral image (HSI). In the spectral dimension, the three–dimensional Hessian matrix was first utilized to obtain three–directional feature images, in which the background pixels of the HSI were suppressed. Then, to more accurately separate the sparse matrix containing the anomaly targets in the three–directional feature images, low–rank and sparse matrix decomposition (LRSMD) with truncated nuclear norm (TNN) was adopted to obtain the sparse matrix. After that, the rough detection map was obtained from the sparse matrix through finding the Mahalanobis distance. In the spatial dimension, two–dimensional attribute filtering was employed to extract the spatial feature of HSI with a smooth background. The spatial weight image was subsequently obtained by fusing the spatial feature image. Finally, to combine the complementary advantages of each dimension, the final detection result was obtained by fusing all rough detection maps and the spatial weighting map. In the experiments, one synthetic dataset and three real–world datasets were used. The visual detection results, the three–dimensional receiver operating characteristic (3D ROC) curve, the corresponding two–dimensional ROC (2D ROC) curves, and the area under the 2D ROC curve (AUC) were utilized as evaluation indicators. Compared with nine state–of–the–art alternative methods, the experimental results demonstrate that the proposed method can achieve effective and excellent anomaly detection results.

Bi-Endmember Semi-NMF Based on Low-Rank and Sparse Matrix Decomposition

This article presents a bi-endmember semi-nonnegative matrix factorization (Semi-NMF) algorithm based on low-rank and sparse matrix decomposition (LRSMD), referred to as BLSNMF, to resolve the issues of endmember variability and nonlinear mixing. Given the fact that the hyperspectral images contain a large amount of redundant information, compressing sensing (CS) techniques can generally be used to randomly sense the effective information in an observed image according to the effective approximation of the bi-endmember components. In this article, the proposed BLSNMF integrates low-rank and sparse spaces decomposed by go decomposition (GoDec) or orthogonal subspace projection-based go decomposition (OSP-GoDec) with Semi-NMF to suppress interference between different components so as to improve the unmixing performance via a simple linear mixed model. Specifically, the observed data space is first decomposed by GoDec or OSP-GoDec to approximate four different attribute components, CS-sampled double low-rank components, structured sparse component, and noise component. Second, from the CS-sampled double low-rank components, the inherent and new endmembers along with their abundances are evaluated via Semi-NMF, and then, the double low-rank components are redescribed using the estimated endmembers and abundances. Finally, the serious interference entries in the structured sparse component space are removed from the data to better learn other attribute components. The experimental results show that BLSNMF can eliminate the interference of new endmembers and sparse noise so as to better evaluate the endmembers and abundances and effectively improve the ability to interpret the spectral information.

Declutter-GAN: GPR B-Scan Data Clutter Removal Using Conditional Generative Adversarial Nets

Clutter removal in ground-penetrating radar (GPR) B-scan data has been widely studied in recent years. In this letter, we propose a novel data-driven clutter suppression method in GPR data based on conditional generative adversarial nets (cGANs). The proposed method learns a function that maps the cluttered data to the clutter-free data from the training set. The training set consists of pairs of cluttered data and corresponding clutter-free data. Different from the traditional method that only uses the simulation training set, we simulate the clutter-free data and add the real collected non-target data to the simulated clutter-free data as cluttered data, so that the trained network can generalize well to the real GPR data. The proposed method is compared with the subspace method, sparse representation-based method, and low-rank and sparse matrix decomposition (LRSD) methods on both simulation data and real collected data. The results show that the proposed method has higher performance in terms of computational complexity, clutter suppression results, and applicability than those state-of-the-art methods.

Reweighted Nuclear Norm and Total Variation Regularization With Sparse Dictionary Construction for Hyperspectral Anomaly Detection

Hyperspectral anomaly detection is an important technique in the field of remote sensing image processing. Over the last few years, low rank and sparse matrix decomposition (LRSMD) has played an increasingly significant role in hyperspectral anomaly detection. The detection performance of the LRSMD-based anomaly detectors is primarily determined by prior constraints and the background dictionary construction method. To increase the detection accuracy, we proposed the reWeighted Nuclear Norm and total variation regularization with Sparse Dictionary construction for hyperspectral Anomaly Detection (WNNSDAD), which incorporated reweighted nuclear norm and total variation regularizations as the prior constraints into the LRSMD model, and constructed a sparse background dictionary without the need of clustering. Compared to the standard nuclear norm, the reweighted nuclear norm helped to overcome the challenge of an unbalanced penalty for a singular value and ensure a more effective low rank approximation. Simultaneously, total variation regularization was introduced as a piecewise smoothing constraint, which helped to maintain the spatial correlation of the hyperspectral image. Additionally, we proposed a background dictionary construction method, by which a relatively complete background dictionary could be obtained without clustering, and the background part could be represented more reliably. The experiments on seven real-world hyperspectral datasets show that in comparison to eight state-of-the-art anomaly detection methods, the proposed WNNSDAD method demonstrated greater accuracy.

Hyperspectral Anomaly Detection via Integration of Feature Extraction and Background Purification

Anomaly detection (AD) has become a hotspot in hyperspectral imagery (HSI) processing due to its advantage in detecting potential targets without prior knowledge, and a variety of algorithms are proposed for a better performance. However, they usually either fail to extract intrinsic features underlying HSIs, or suffer from the contamination of noise and anomalies. To address these problems, we propose a new anomaly detector by integrating fractional Fourier transform (FrFT) with low rank and sparse matrix decomposition (LRaSMD). First, distinctive features of HSI data are extracted via FrFT. Then, row-constrained LRaSMD (RC-LRaSMD), which is more practical and stable than the traditional LRaSMD, is employed to separate background from noise and anomalies. Finally, we implement an atom-selection strategy to construct the background covariance matrix for detection. The experimental results with several HSI data sets demonstrate satisfying detection performance compared with other state-of-the-art detectors.

FrHPI: A Discriminative Patch-Image Model for Hyperspectral Anomaly Detection

Anomaly detection is now a significantly important part of hyperspectral image analysis to detect targets in an unsupervised manner. Traditional hyperspectral anomaly detectors fail to consider spatial information, which is vital in hyperspectral anomaly detection. Moreover, they usually take the raw data without feature extraction as input, limiting the detection performance. We propose a new anomaly detector based on the fractional Fourier transform (FrFT) and a modified patch-image model called the hyperspectral patch-image (HPI) model to tackle these two problems. By combining them, the proposed anomaly detector is named fractional hyperspectral patch-image (FrHPI) detector. Under the assumption that the target patch-image is a sparse matrix while the background patch-image is a low-rank matrix, we first formulate a matrix by sliding a rectangle window on the first three principal components (PCs) of HSI. The matrix can be decomposed into three parts representing the background, targets, and noise with the well-known low-rank and sparse matrix decomposition (LRaSMD). Then, distinctive features are extracted via FrFT, a transformation which is desirable for noise removal. Background atoms are selected to construct the covariance matrix. Finally, anomalies are picked up with Mahalanobis distance. Extensive experiments are conducted to verify the proposed FrHPI detector’s superiority in hyperspectral anomaly detection compared with other state-of-the-art detectors.

SAR Interference Suppression Algorithm Based on Low-Rank and Sparse Matrix Decomposition in Time–Frequency Domain

Radio frequency electromagnetic interference is a relatively common phenomenon, especially for synthetic aperture radar (SAR) systems working in P- or L-band. Compared with the suppression of narrowband interference, that of wideband interference, particularly of those whose signal parameters have frequently changing property, is still a sophisticated problem. In this letter, a suppression algorithm for interference with wideband and complicated parameters is proposed, based on low-rank and sparse matrix decomposition (LRSMD) in time–frequency domain (TFD) of the signal. The proposed algorithm begins with transforming the SAR signal into TFD. After that, LRSMD based on bilateral random projection (BRP) is applied to decompose the time–frequency spectrum matrix into three parts, a low-rank matrix standing for interference, a sparse matrix standing for SAR signal, and a noise matrix. Finally, inversely transform the sparse matrix into the time domain to obtain SAR signal without interference. The proposed algorithm is applied to a single look complex (SLC) SAR data of Sentinel-1 to validate its effect and efficiency.

Anomaly Detection in Airborne Fourier Transform Thermal Infrared Spectrometer Images Based on Emissivity and a Segmented Low-Rank Prior

Although hyperspectral anomaly detection is commonly conducted in the visible, near-infrared, and shortwave infrared spectral regions, there has been less research on hyperspectral anomaly detection in the longwave infrared (LWIR) hyperspectral region. The radiance of thermal infrared hyperspectral imagery is determined by the temperature and emissivity. To avoid the detection uncertainty caused by the single factor of temperature, emissivity can be introduced to detect anomalies. However, in the emissivity domain, the spectral contrast and signal-to-noise ratio (SNR) are low, which makes it difficult to separate the anomalies from the background. In this paper, an anomaly detection method combining emissivity and a segmented low-rank prior (EaSLRP) is proposed for use with thermal infrared hyperspectral imagery. The EaSLRP method is divided into three parts—1) temperature/emissivity retrieval, 2) extraction of the thermal infrared hyperspectral background information, and 3) Mahalanobis distance detection. A homogeneous region generation method is also proposed to solve the problem of the complex global background leading to inaccurate background estimation. The GoDec method is used for matrix decomposition and background information extraction and to remove some of the noise. The proposed Mahalanobis distance detector then uses the background component and original image for anomaly detection, while highlighting the spectral difference between the anomalies and background. This method can also suppress the influence of noise, to some extent. The experimental results obtained with airborne Fourier transform thermal infrared spectrometer hyperspectral images demonstrate that the EaSLRP method is effective when compared with the Reed–Xiaoli detector (RXD), the segmented RX detector (SegRX), the low-rank and sparse representation-based detector (LRASR), the low-rank and sparse matrix decomposition (LRaSMD)-based Mahalanobis distance method (LSMAD), and the locally enhanced low-rank prior method (LELRP-AD).

Orthogonal Subspace Projection Using Data Sphering and Low-Rank and Sparse Matrix Decomposition for Hyperspectral Target Detection

Orthogonal subspace projection (OSP) has been widely used in many applications for hyperspectral data exploitation. However, its performance is sensitive to its used prior target knowledge, which is significantly affected by target background (BKG). To resolve this issue, this article develops three approaches to extend OSP in improving its performance. One is data sphering which can suppress BKG via removing the first- and second-order data statistics. Another takes advantage of a recently developed low-rank and sparse matrix decomposition (LRaSMD) to separate BKG and target signal sources in two subspaces characterized by the low-rank matrix and sparse matrix, respectively, and then annihilates BKG via the low-rank matrix, referred to as BKG-annihilated OSP (BA-OSP). A third approach combines data sphering and LRaSMD to further improve OSP over target detectability and BKG suppressibility. Experiments show that implementing OSP in conjunction with data sphering and LRaSMD significantly improves OSP in target detection and BKG suppression, and also performs as well as a widely used constrained energy minimization (CEM)-based subpixel target detection.

A Low-Rank and Sparse Matrix Decomposition- Based Dictionary Reconstruction and Anomaly Extraction Framework for Hyperspectral Anomaly Detection

As one of the important applications of hyperspectral imagery (HSI) processing, the Mahalanobis distance-based detector in anomaly detection used to extract knowledge from the background and then calculate the Mahalanobis distance to obtain the detection result. Different from the previous work, a novel low-rank and sparse matrix decomposition (LRaSMD)-based dictionary reconstruction and anomaly extraction framework constructs the detector by a comprehensive combination of the low-rank and sparse matrix for hyperspectral anomaly detection. We use the LRaSMD to fully exploit the background and sparse information to construct the detector. For the low-rank part, we use atom usage probability to reconstruct the dictionary for follow-up collaborative representation (CR). For the sparse part, we calculate the Euclidean distance and get the result by using a ratio to add these two parts. The proposed algorithm was tested on three real-world HSI data sets and demonstrated outstanding detection performance when compared with other state-of-the-art detectors.

An Improved Low Rank and Sparse Matrix Decomposition-Based Anomaly Target Detection Algorithm for Hyperspectral Imagery

Anomaly target detection has been a hotspot of the hyperspectral imagery (HSI) processing in recent decades. One of the key research points in the HSI anomaly detection is the accurate descriptions of the background and anomaly targets. Considering this point, we propose a novel anomaly target detector in this article. Improving upon the low-rank and sparse matrix decomposition (LRaSMD) approach, the proposed method assumes that the low-rank component can be described as the parts-based representation. Parts refer to the various ground objects in HSI. A new update rule of the low-rank component and sparse component is proposed. The proposed approach can be divided into three main steps: first, further refining the low-rank component in the LRaSMD model as the parts-based representation. Then, the HSI is decomposed as three parts: the product of the basis matrix and coefficient matrix, sparse matrix, and noise. Second, the basis vectors matrix, coefficient matrix, and sparse matrix are solved by the new update rules. Third, since the anomaly targets exist in the sparse matrix, the sparse matrix is thus employed to detect the anomaly targets. The experiments implemented for five data sets demonstrate that the proposed algorithm achieved a better performance than the traditional algorithms.

Low-Rank and Sparse Matrix Decomposition With Orthogonal Subspace Projection-Based Background Suppression for Hyperspectral Anomaly Detection

Although the low-rank and sparse matrix decomposition (LRaSMD)-based anomaly detectors can effectively extract the low-rank structure as the background component and the sparse structure as the anomaly component for anomaly detection (AD) while simultaneously considering the additive noise, the background interferences in the sparse component remain a serious problem that will increase the false alarm rate and influence the detection of real anomalies. To alleviate this issue, a novel LRaSMD with orthogonal subspace projection (OSP)-based background suppression and adaptive weighting for hyperspectral AD is proposed in this letter. Based on the fact that the background interferences in the sparse component are mainly some sparse objects with slight spectral differences from the main background, the OSP is employed to project the sparse component into the background orthogonal subspace that is estimated from the low-rank component to suppress the background interferences and highlight the anomalies. Furthermore, the low-rank component provides an effective estimation of the background statistics, which can be used to adaptively weigh the detection results. Experiments on both synthetic and real hyperspectral data sets demonstrate the effectiveness of the proposed algorithm.

Local hyperspectral anomaly detection method based on low-rank and sparse matrix decomposition

Anomaly detection (AD) is an important technique for hyperspectral image processing and analysis. Typically, it is accomplished by extracting knowledge from the background and distinguishing anomalies and background using the difference between them. However, it is almost impossible to obtain “pure” background to achieve an ideal detection because of anomaly contamination. The low-rank and sparse matrix decomposition (LRaSMD) technique has been proved to have the potential to solve the aforementioned problem. But the accuracy and time consumption need to be further improved. Thus we propose a local hyperspectral AD method based on LRaSMD with an optimization algorithm for better performance. The LRaSMD technique is first implemented with semisoft Go decomposition (GoDec) rather than GoDec to quickly and accurately set the background apart from the anomalies. Then the low-rank prior knowledge of the background is fully explored to compute the background statistics. After that, the local Mahalanobis distance of pixels is calculated with the sliding dual-window strategy to detect the probable anomalies. The proposed method is validated using four real hyperspectral data sets with ground-truth information. Our experimental results indicate that the proposed method achieves better detection performance as compared with the comparison algorithms.

Multi‐view registration based on weighted LRS matrix decomposition of motions

Recently, the low‐rank and sparse (LRS) matrix decomposition has been introduced as an effective mean to solve the multi‐view registration. It views each available relative motion as a block element to reconstruct one sparse matrix, which then is used to approximate the low‐rank matrix, where global motions can be recovered for multi‐view registration. However, this approach is sensitive to the sparsity of the reconstructed matrix and it treats all block elements equally in spite of their varied reliabilities. Therefore, this study proposes an effective approach for multi‐view registration by weighted LRS matrix decomposition. On the basis of the inverse symmetry property of relative motions, it first proposes a completion method to reduce the sparsity of the reconstructed matrix. The reduced sparsity of the reconstructed matrix can improve the robustness and efficiency of LRS matrix decomposition. Then, it proposes the weighted LRS matrix decomposition, where each block element is assigned with one estimated weight to denote its reliability. By introducing the weight, more accurate registration results can be efficiently recovered from the estimated low‐rank matrix. Experimental results tested on public datasets illustrate the superiority of the proposed approach over the state‐of‐the‐art approaches on robustness, accuracy and efficiency.

Low-rank and sparse matrix decomposition with background position estimation for hyperspectral anomaly detection

Hyperspectral anomaly detection (AD) has attracted much attention over the last 20 years. It distinguishes pixels with significant spectral differences from the background without any prior knowledge. The low-rank and sparse matrix decomposition (LRaSMD)-based detector has been applied to AD, where the anomaly value is measured by Euclidean distance based on the sparse component. However, the background interference in sparse component seriously increases the false alarm rate and influences the detection of real anomalies. In this paper, a novel AD method based on LRaSMD and background position estimation is proposed, which aims to suppress background interference in the sparse component for a better separation between background and anomalies. Firstly, the original sparse matrix is obtained using the traditional LRaSMD method. Secondly, the abundance maps are constructed by the sequential maximum angel convex cone (SMACC) endmember extraction model. Thirdly, considering that the anomalies occupy only a few pixels with a low probability, the coordinate positions of background pixels are estimated through these abundance maps. Finally, the spectra corresponding to these positions in the original sparse matrix are replaced with zero vectors, and the final anomaly value is calculated based on the improved sparse matrix. The proposed method achieves an outstanding performance by considering both the spectral and spatial characteristics of anomalies. Experimental results on synthetic and real-world hyperspectral datasets demonstrate the superiority of the proposed method compared with several state-of-the-art AD detectors.