Low-rank And Sparse Decomposition Research Articles

Low-Rank and Sparse Decomposition for Low-Query Decision-Based Adversarial Attacks

Deep learning models are susceptible to contrived adversarial examples, even in the decision-based black-box setting where the attacker has access to the model’s decisions only. Developing more efficient and practical attacks help in better understanding the limitations of deep models. It is important that attacks are crafted with limited queries to avoid suspicion. Since the required number of queries increase with dimensions, low-dimensional embeddings are attractive. This low query budget constraint is a bottleneck for learning-based and data-driven attacks which rely heavily on querying the model. We propose LSDAT, an image-agnostic non-data-driven decision-based black-box attack that exploits low-rank and sparse decomposition (LSD) of images to dramatically reduce the queries and improve fooling rates compared to existing methods. LSDAT crafts perturbations in the low-dimensional subspace formed by the sparse component of the input image and that of a target adversarial image to obtain query-efficiency. A viable perturbation is obtained by traversing the path between the input and adversarial sparse components. Theoretical analyses are provided to justify the functionality of LSDAT. Unlike other competitors (e.g., FFT), LSD works directly in the image domain to guarantee that non-ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> constraints, such as sparsity, are satisfied. LSDAT offers better control over the number of queries and is computationally efficient as it performs sparse decomposition of the input and adversarial images only once to generate all queries. Four variants of LSDAT are presented for different scenarios including a pure black-box attack where no queries are allowed. We demonstrate ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> , ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> bounded attacks with LSDAT to evince its efficiency compared to baseline attacks in diverse low-query budget scenarios. LSDAT obtains 15 to 20% improvement in fooling ResNet-50 while using far fewer queries than competing methods in a similar setting.

A railway intrusion detection method based on decomposition and semi-supervised learning for accident protection

In recent years, video surveillance has become increasingly popular in railway intrusion detection. However, it is still quite challenging to detect the intruded objects efficiently and accurately because: (a) The backgrounds of video frames generated by the fixed cameras are similar and only few intrusive frames are available, resulting in a lack of diversity among video frames, and further leading to over fitting of the detection models during training; (b) The intrusion of small targets or targets far from the location of camera exhibits sparsity relative to the wide monitoring view of the camera, which challenges the detection of such targets in a complex background; (c) The extreme imbalance between non-intrusive frames and intrusive frames, as well as a large number of unlabeled frames, hinder the effective training of the detection model and weaken its capacity of generalization. To tackle the above issue, this article develops an effective intrusion detection method by combining low-rank and sparse decomposition (LRSD) and Semi-supervised Support Vector Domain Description (Semi-SVDD). Firstly, LRSD is used to decompose the monitored video into a background and a foreground. Then, based on the semantic segmentation method, we extract the mask of the track region in the decomposed background, which is used to mask the foreground. Next, by using both the labeled and unlabeled frames of the masked foreground, Semi-SVDD is established for the intrusion detection. Numerical results show that the removal of background interference and the combination of the labeled and unlabeled information help to improve the performance of the proposed method, and thus superior to benchmark methods.

Simultaneous spatial and temporal regularization in low-dose dynamic contrast-enhanced CT cerebral perfusion studies.

To apply total generalized variation (TGV) and its combination with low-rank and sparse decomposition (LRSD) (LTGV) to cerebral perfusion studies using low-dose dynamic contrast-enhanced (DCE) CT and to quantitatively evaluate their performances through comparisons with those without any regularizers and those of total variation (TV) and its combination with LRSD (LTV) using simulation and clinical data. The simulation study used a realistic digital brain phantom. Low-dose DCE-CT images were reconstructed using the regularizers and primal-dual algorithm. Subsequently, cerebral perfusion parameter (CPP) images were generated from them. Thereafter, their quality was evaluated based on the peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM). Further, the accuracy of CPP estimation was evaluated through a linear regression analysis between the CPP values obtained by the above regularizers and those obtained from the noise-free DCE-CT images. In addition, the mean and standard deviation of the CPP were calculated (region analysis). In the clinical study, low-dose DCE-CT images were generated using normal-dose images acquired from a patient, and CPP images were generated from them similar to that in the simulation study. When using LTV and LTGV, both PSNR and SSIM were higher than those of the other methods with increasing regularization parameter values. The results of the linear regression and region analyses demonstrated that TGV generally exhibited the best performance, followed by LTGV, and finally that of TV was significantly different from those of the other regularizers. Despite an overall consistency between the simulation and clinical results, certain inconsistencies appeared owing to the difference in generating low-dose DCE-CT images. The results implied that TGV and LTGV were useful in improving the accuracy of CPP estimation using low-dose DCE-CT. This study provides an improved understanding of the performance of regularizers and is expected to aid in the selection of a suitable regularizer for low-dose DCE-CT perfusion studies.

Weighted Schatten p-norm and Laplacian scale mixture-based low-rank and sparse decomposition for foreground–background separation

Low-rank and sparse decomposition (LRSD) plays a vital role in foreground–background separation. The existing LRSD methods have the drawback: imprecise surrogate functions of rank and sparsity. We propose the weighted Schatten p-norm (WSN) and Laplacian scale mixture (LSM) method based on LRSD for foreground–background separation, which introduces the WSN and LSM to improve this drawback. To demonstrate the performance of the proposed method, it is applied to foreground–background separation and gets the highest average F-measure score.

GPR Clutter Removal Based on Factor Group-Sparse Regularization

Clutter removal is of vital importance to underground detection via ground penetrating radar (GPR) since the target response is usually overwhelmed by strong clutter. The low-rank and sparse decomposition (LRSD) method, which decomposes the GPR data into a low-rank background matrix and a sparse target matrix, has been applied in GPR. However, the existing LRSD-based methods, such as robust principal component analysis (RPCA) and robust non-negative matrix factorization, are sensitive to the regularization parameter or have high computation complexity. In this letter, a novel clutter removal based on factor group-sparse regularization is proposed. It uses a nonconvex matrix factorization as a surrogate for the matrix rank rather than the nuclear norm as in the RPCA. It has good efficiency and robustness to the parameters. Simulation and experimental results demonstrate that the proposed method has higher performance in terms of the improvement factor values and lower computational complexity than the state-of-the-art methods.

A Novel Convolutional Autoencoder-Based Clutter Removal Method for Buried Threat Detection in Ground-Penetrating Radar

The clutter encountered in ground-penetrating radar (GPR) systems seriously affects the performance of the subsurface target detection methods. A new clutter removal method based on convolutional autoencoders (CAEs) is introduced. The raw GPR image is encoded via successive convolution and pooling layers and then decoded to provide the clutter-free GPR image. The loss function is defined in terms of the reference clutter-free target image and the decoder output is optimized to learn the weight coefficients from the raw data. The method is compared to the conventional subspace methods, recently proposed nonnegative matrix factorization, as well as low-rank and sparse decomposition (LRSD) methods and dictionary separation-based morphological component analysis. CAE and its deeper version deep CAE (DCAE) are trained by several scenarios generated by the electromagnetic simulation tool gprMax. Simulation results demonstrate the effectiveness of the proposed method for challenging scenarios. While for real GPR image, the simulated data trained networks remain slightly behind the LRSD methods for the dry case, nonetheless, they outperform the aforementioned processing techniques for the more challenging wet case.

Research on the Segmentation of Biomarker for Chronic Central Serous Chorioretinopathy Based on Multimodal Fundus Image.

At present, laser surgery is one of the effective ways to treat the chronic central serous chorioretinopathy (CSCR), in which the location of the leakage area is of great importance. In order to alleviate the pressure on ophthalmologists to manually label the biomarkers as well as elevate the biomarker segmentation quality, a semiautomatic biomarker segmentation method is proposed in this paper, aiming to facilitate the accurate and rapid acquisition of biomarker location information. Firstly, the multimodal fundus images are introduced into the biomarker segmentation task, which can effectively weaken the interference of highlighted vessels in the angiography images to the location of biomarkers. Secondly, a semiautomatic localization technique is adopted to reduce the search range of biomarkers, thus enabling the improvement of segmentation efficiency. On the basis of the above, the low-rank and sparse decomposition (LRSD) theory is introduced to construct the baseline segmentation scheme for segmentation of the CSCR biomarkers. Moreover, a joint segmentation framework consisting of the above method and region growing (RG) method is further designed to improve the performance of the baseline scheme. On the one hand, the LRSD is applied to offer the initial location information of biomarkers for the RG method, so as to ensure that the RG method can capture effective biomarkers. On the other hand, the biomarkers obtained by RG are fused with those gained by LRSD to make up for the defect of undersegmentation of the baseline scheme. Finally, the quantitative and qualitative ablation experiments have been carried out to demonstrate that the joint segmentation framework performs well than the baseline scheme in most cases, especially in the sensitivity and F1-score indicators, which not only confirms the effectiveness of the framework in the CSCR biomarker segmentation scene but also implies its potential application value in CSCR laser surgery.

GPR clutter reduction by multi-resolution based tensor RPCA

ABSTRACT A new clutter reduction method which utilizes the multi-resolution and multi-directional information of the ground-penetrating radar (GPR) image is proposed. Sub-images obtained by stationary wavelet transform (SWT) or nonsubsampled counterlet transform (NSCT) are cast into a tensor structure presenting higher information compared to the spatial input data. A tensor-robust principal component analysis (TRPCA) algorithm is used for low-rank and sparse decomposition (LRSD) followed by inverse transform of the sparse tensor component to provide the clutter reduction results. The proposed methods TRPCA-SWT and TRPCA-NSCT are compared both visually and quantitatively to robust principal component analysis (RPCA) and TRPCA-bandpass filter (TRPCA-BPF), which employ the spatial raw GPR data and outputs of simple low-pass and high-pass filters respectively. Visual and quantitative results demonstrate that the clutter reduction performance increases when a higher number of scales and directions are used prior to the LRSD decomposition. Moreover, one of the proposed methods, TRPCA-NSCT, removes the background noise more efficiently due to its higher multi-resolution and multi-direction investigation capability, increasing the performance of the target detection algorithms.

GPR clutter suppression by online stochastic tensor decomposition

ABSTRACT The clutter suppression is an active research area for ground-penetrating radar (GPR) and the current trends use low rank and sparse decomposition (LRSD) based methods which provide an overwhelming advantage over classical low-rank methods. However, there are not many studies about tensor decomposition methods which actually provide powerful tools such as tensor robust principal component analysis (TRPCA) method for decomposing a matrix into its low rank and sparse components, namely, clutter and target parts. In addition to the success of TRPCA and motivated by tensor decomposition results in video background subtraction compared to LRSD, we propose a new GPR clutter suppression method based on online stochastic tensor decomposition (OSTD) by adding a simple pre-transformation step. The proposed method is tested on both simulated and real datasets. Obtained results prove its superiority over the state-of-the-art clutter suppression methods.

Video-SAR Imaging of Dynamic Scenes Using Low-Rank and Sparse Decomposition

With the goal of persistent surveillance over a scene of interest, this paper proposes an approach for joint imaging and trajectory extraction of multiple moving objects, using circular video-SAR (ViSAR) mode. Unlike stationary SAR imaging where the phase perturbation of the received signal arises from the platform motion, the moving targets impose additional phase errors, contributing to defocusing of the moving targets’ images. Here, for proper imaging of the moving targets, specifically in low-signal-to-clutter-ratio (SCR) scenarios, their signatures are decomposed from the stationary background clutter by low rank and sparse decomposition (LRSD), before refocusing to their original positions. However, the rotation of the scene, which emerges as a consequence of circular SAR geometry, leads to undesirable decomposition results via LRSD. To facilitate the applicability of LRSD for moving target extraction in our setting, considering this rotation in our model, the decomposition is accomplished while this undesirable effect is automatically compensated for. In addition, to further guarantee that LRSD yields satisfactory decomposition results, phase errors due to platform motion are also jointly corrected along with the clutter separation process. Then, having decomposed the sequential sparse images of moving targets’ signatures, the additional phase errors caused by moving targets are compensated to refocus them to their original positions. After that, these focused sparse images of moving targets are combined to construct a single image where the trajectories of moving targets can be observed. Using this image, a composite image is also constructed, including both the moving objects’ trajectories and the stationary background, which can be used for target tracking applications. Through extensive experimental results we show the effectiveness of the proposed method on both synthetic and real SAR images.

A Low-Rank and Sparse Decomposition-Based Method of Improving the Accuracy of Sub-Pixel Grayscale Centroid Extraction for Spot Images

In order to improve the accuracy of sub-pixel grayscale centroid extraction for noise-containing spot images, an image denoising method based on low-rank and sparse decomposition (LRSD) was proposed in this paper. Relative total variation (RTV) was introduced into the method on the basis of the weighted nuclear norm minimization (WNNM) model to construct a new RTV-WNNM model, so as to enhance the denoising accuracy and detail-preserving capability of LRSD method. Alternating direction multiplier method (ADMM) was used to solve this convex problem iteratively. Moreover, in view that the existing LRSD denoising method had insufficient detail-preserving capability, an adaptive selection method of LRSD singular value threshold based on the improved elitist clone selection algorithm (ECSA) was also raised in this paper. The constructed RTV-WNNM model taken as the objective function, the improved ECSA could realize equilibrium between search in depth and optimization in breadth through the adaptive chaotic mutation operator and antibody reselection strategy based on antibody concentration and antigen affinity moment. Furthermore, it could reach rapid self-adaption to acquire a low-rank threshold and then form an image denoising fusion algorithm, which had both denoising and detail-preserving capabilities. Simulation and experimental results show that the proposed method can reach better results in both quantity measure and visual quality than the state-of-the-art image denoising methods, and it has also remarkably improved the accuracy of sub-pixel grayscale centroid extraction for noise-containing spot images.

Generalized nuclear norm and Laplacian scale mixture based low-rank and sparse decomposition for video foreground-background separation

Low-rank and sparse decomposition (LRSD) poses a big challenge problem in video foreground-background separation and many other fields due to its difficulties in approximations of low-rank and sparse parts. The rank and sparsity may not be well approximated in practice since these conventional approaches suffer from the suboptimal issues in many cases. In this paper, we adopt the generalized nuclear norm (GNN) and the Laplacian scale mixture (LSM) modeling to approximate the low-rank and sparse matrices, respectively, and propose a generalized formulation which called GNNLSM for nonconvex low-rank and sparse decomposition based on the GNN and the LSM. And then, we adopt the alternating direction method of multipliers (ADMM) to solve our proposed problem. Simulation results and discussions on video foreground-background separation are given to validate the superiority and the effectiveness of our proposed method.

Foreground-Background Separation via Generalized Nuclear Norm and Structured Sparse Norm Based Low-Rank and Sparse Decomposition

Low-rank and sparse decomposition (LRSD) has attracted wide attention in video foreground-background separation and many other fields. However, the traditional LRSD methods have many tough problems, such as the problems of the low accuracy of the surrogate functions of rank and sparsity, ignoring the spatial information of the videos and sensitivity to noise, etc. To deal with these problems, this paper proposes the generalized nuclear norm and structured sparse norm (GNNSSN) method based LRSD for video foreground-background separation, which introduces the generalized nuclear norm (GNN) and the structured sparse norm (SSN) to approximate the rank function and the l 0 -norm of the LRSD method. In addition, we extend our proposed model to a robust model against noise for practical applications, and we called the extended method as the robust generalized nuclear norm and structured sparse norm (RGNNSSN) method. At last, we use the alternating direction method of multipliers (ADMM) to solve our proposed two methods. Experimental results and discussions on video foreground-background separation demonstrate that our proposed two methods have better performances than other LRSD based foreground-background separation methods.

GPR Clutter Reduction by Robust Orthonormal Subspace Learning

The clutter severely decreases the target visibility, thus the detection rates in ground penetrating radar (GPR) systems. Recently proposed robust principal component analysis (RPCA) based clutter removal method decomposes the GPR image into its low rank and sparse parts corresponding to clutter and target components. Motivated by its encouraging results, many lower complexity low rank and sparse decomposition (LRSD) methods such as go decomposition (GoDec) or robust non-negative matrix factorization (RNMF) have been applied to GPR. This paper proposes a new clutter reduction method using robust orthonormal subspace learning (ROSL). The raw GPR image is decomposed into its clutter and target parts via ROSL. The proposed method is faster than the popular RPCA. Although it has similar complexity, and similar performance with GoDec and RNMF for fine tuned parameters of these methods, the proposed method does not require any presetting of the algorithm parameters. Its performance remains independent for a broad range parameter value. Results demonstrate that the proposed method achieves 14 - 48% higher performance in terms of PSNR values than the state-of-the-art LRSD methods for an arbitrary parameter choice.

Generalized singular value thresholding operator based nonconvex low-rank and sparse decomposition for moving object detection

Moving object detection is one of the most challenging tasks in computer vision and many other fields, which is the basis for high-level processing. Low-rank and sparse decomposition (LRSD) is widely used in moving object detection. The existing methods primarily address the LRSD problem by exploiting the approximation of rank functions and sparse constraints. Conventional methods usually consider the nuclear norm as the approximation of the low-rank matrix. However, the actual results show that the nuclear norm is not the best approximation of the rank function since it simultaneously minimize all the singular values. In this paper, we exploit a novel nonconvex surrogate function to approximate the low-rank matrix and propose a generalized formulation for nonconvex low-rank and sparse decomposition based on the generalized singular value thresholding (GSVT) operator. And then, we solve the proposed nonconvex problem via the alternating direction method of multipliers (ADMM), and also analyze its convergence. Finally, we give numerical results to validate the proposed algorithm on both synthetic data and real-life image data. The results demonstrate that our model has superior performance. And we use the proposed nonconvex model for moving objects detection, and provide the experimental results. The results show that the proposed method is more effective than representative LRSD based moving objects detection algorithms.

Low-Rank Based Image Analyses for Pathological MR Image Segmentation and Recovery.

The presence of pathologies in magnetic resonance (MR) brain images causes challenges in various image analysis areas, such as registration, atlas construction and atlas-based segmentation. We propose a novel method for the simultaneous recovery and segmentation of pathological MR brain images. Low-rank and sparse decomposition (LSD) approaches have been widely used in this field, decomposing pathological images into (1) low-rank components as recovered images, and (2) sparse components as pathological segmentation. However, conventional LSD approaches often fail to produce recovered images reliably, due to the lack of constraint between low-rank and sparse components. To tackle this problem, we propose a transformed low-rank and structured sparse decomposition (TLS2D) method. The proposed TLS2D integrates the structured sparse constraint, LSD and image alignment into a unified scheme, which is robust for distinguishing pathological regions. Furthermore, the well recovered images can be obtained using TLS2D with the combined structured sparse and computed image saliency as the adaptive sparsity constraint. The efficacy of the proposed method is verified on synthetic and real MR brain tumor images. Experimental results demonstrate that our method can effectively provide satisfactory image recovery and tumor segmentation.

Radio Tomographic Imaging Based on Low-Rank and Sparse Decomposition

Imaging artifacts induced by the multipath interference in Radio-Frequency sensing network usually significantly degrade the performance of Radio Tomographic Imaging (RTI) and thereby has become a major challenge in the Device-Free Localization (DFL). The multipath in the environment often invalidates the commonly used sparsity-regularized methods for RTI reconstruction because the sparse multipath-induced imaging artifacts may be misestimated as the sparse target-induced attenuation. To enhance the sensing ability of the target's effect in RTI, for the first time, this paper utilized the Low-Rank and Sparse Decomposition (LRSD) to cope with the multipath-induced imaging artifacts and infer the sparse target-induced attenuation accurately. The experimental results demonstrated the significant advantages of the proposed LRSD method in the reconstructed RTI quality, DFL accuracy, and time complexity in comparison to the presenting commonly used methods, including Tikhonov Regularization and Bayesian Compressive Sensing (BCS). The above advantages make the proposed LRSD method highly expected to improve the RTI performance and also make it applicable for real-time DFL applications.

TV Regularized Low-Rank Framework for Localizing Premature Ventricular Contraction Origin

Premature ventricular contraction (PVC) can cause great harm to human health. Both invasive and non-invasive techniques for detecting electrical activity of PVC or locating ectopic pacemakers are used in clinical diagnosis. Among them, the electrocardiographic imaging is a popular method for non-invasive reconstruction of cardiac electrophysiology through body-surface potential (BSP). In this paper, we propose a novel framework based on low-rank and sparse decomposition (LSD) + total variation (TV) to solve the ill-posedness of the spatiotemporal ECG-inverse problem to reconstruct the cardiac electrical activity of PVC. The proposed framework considers the spatiotemporal distribution of multi-frame cardiac potential as a whole. The TV is used to filter out relatively smooth candidates from countless inverse solutions. In addition, LSD utilizes the low-rank characteristic of the potential background and the sparseness of the potential outliers to avoid the loss of potential details and improve the accuracy of potential reconstruction. This improves the quality of electrical activity retrieval and the accuracy of locating the PVC origin. The simulation experiments of ventricular pacing reconstruction and diagnostic experiments of real PVC patients prove that the proposed framework is superior to the conventional quadratic methods (Tikhonov-0 and Tikhonov-2) and the non-quadratic method TV.

Robust background subtraction method via low-rank and structured sparse decomposition

Background subtraction is a challenging problem in surveillance scenes. Although the low-rank and sparse decomposition (LRSD) methods offer an appropriate framework for background modeling, they fail to account for image's local structure, which is favorable for this problem. Based on this, we propose a background subtraction method via low-rank and SILTP-based structured sparse decomposition, named LRSSD. In this method, a novel SILTP-inducing sparsity norm is introduced to enhance the structured presentation of the foreground region. As an assistance, saliency detection is employed to render a rough shape and location of foreground. The final refined foreground is decided jointly by sparse component and attention map. Experimental results on different datasets show its superiority over the competing methods, especially under noise and changing illumination scenarios.

Spectrally-Spatially Regularized Low-Rank and Sparse Decomposition: A Novel Method for Change Detection in Multitemporal Hyperspectral Images

Change detection (CD) for multitemporal hyperspectral images (HSI) can be approached as classification consisting of two steps, change feature extraction and change identification. This paper is focused on binary classification of the changed and the unchanged samples, which is the essential case of change detection. Meanwhile, it is challenging to extract clean change features from heavily corrupted spectral change vectors (SCV) of multitemporal HSI. The corruptions can be characterized as gross sample-specific errors, i.e., outliers, and small entry-wise noise following Gaussian distribution. To address the issue, this paper proposes a novel Spectrally-Spatially (SS) Regularized Low-Rank and Sparse Decomposition (LRSD) model, denoted by LRSD_SS. It decomposes the SCV into three components, a locally smoothed low-rank matrix for the clean change features, a sparse matrix for the outliers and an error matrix for the small Gaussian noise. The proposed method is effective in change feature extraction and robust to noise corruptions as it exploits the underlying data structures of the SCV, especially local spectral-spatial smoothness. It is also efficient since there is a closed-form solution for the feature component in the optimization problem of LRSD_SS. The experimental results in the paper show that the proposed method outperforms several classic methods which only deal with the spectral domain of image samples, as well as some state-of-the-art methods which use both spectral and spatial information