Pedestrian Detection Based on Sparse and Low-Rank Matrix Decomposition

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.

Handbook of Robust Low-Rank and Sparse Matrix Decomposition: Applications in Image and Video Processing shows you how robust subspace learning and tracking by decomposition into low-rank and sparse matrices provide a suitable framework for computer vision applications. Incorporating both existing and new ideas, the book conveniently gives you one-stop access to a number of different decompositions, algorithms, implementations, and benchmarking techniques. Divided into five parts, the book begins with an overall introduction to robust principal component analysis (PCA) via decomposition into low-rank and sparse matrices. The second part addresses robust matrix factorization/completion problems while the third part focuses on robust online subspace estimation, learning, and tracking. Covering applications in image and video processing, the fourth part discusses image analysis, image denoising, motion saliency detection, video coding, key frame extraction, and hyperspectral video processing. The final part presents resources and applications in background/foreground separation for video surveillance. With contributions from leading teams around the world, this handbook provides a complete overview of the concepts, theories, algorithms, and applications related to robust low-rank and sparse matrix decompositions. It is designed for researchers, developers, and graduate students in computer vision, image and video processing, real-time architecture, machine learning, and data mining.

Chronic liver disease is a major worldwide health problem. Diagnosis and staging of chronic liver diseases is an important issue. In this paper, we propose a quantitative method of analyzing local morphological changes for accurate and practical computer-aided diagnosis of cirrhosis. Our method is based on sparse and low-rank matrix decomposition, since the matrix of the liver shapes can be decomposed into two parts: a low-rank matrix, which can be considered similar to that of a normal liver, and a sparse error term that represents the local deformation. Compared with the previous global morphological analysis strategy based on the statistical shape model (SSM), our proposed method improves the accuracy of both normal and abnormal classifications. We also propose using the norm of the sparse error term as a simple measure for classification as normal or abnormal. The experimental results of the proposed method are better than those of the state-of-the-art SSM-based methods.

Ground penetrating radar (GPR) uses electromagnetic waves to image, locate, and identify changes in electric and magnetic properties in the ground. The received signal comprises not only the target echoes but also strong reflections from the rough, uneven ground surface, which impair subsurface inspections and visualization of buried objects. In this paper, a background clutter mitigation and target detection method using low-rank and sparse priors is proposed for GPR data. The radar signal is decomposed into the sum of a low-rank component and a sparse component, plus noise. The low-rank component captures the ground surface reflections and background clutter, whereas the sparse component contains the target reflections. The effectiveness of the proposed method is evaluated on real radar signals collected from buried landmines and improvised explosive devices. The experimental results show that the proposed method successfully removes the background clutter and estimates the target signals.

This paper proposes a robust matrix completion method to solve the localization problem in wireless sensor networks. A novel cost function is formulated which inherently copes with missing measures and corrupted data. In particular, the proposed algorithm robustly completes the range map between pairs of sensors by casting the problem as a low-rank and sparse matrix decomposition, while constraining the solution to be close to an Euclidean Distance Matrix. Numerical accuracy and computational efficiency are demonstrated by synthetic experiments. The empirical results also show that our method outperforms state-of-the art algorithms in several scenarios.

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.

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).

Due to the limited resolution of hyperspectral sensors, anomalous targets expressed with subpixels are often mixed with nonhomogeneous backgrounds. This fact makes anomalies difficult to be distinguished from the surrounding background. From this perspective, we propose a novel hyperspectral anomaly detection (AD) algorithm based on low-rank & sparse matrix decomposition (LRaSMD) and support vector machine (SVM). First, based on the LRaSMD technique, the Go decomposition (GoDec) model is utilized to decompose the original image into three components: background, anomalies and noise. In this way, the robust background can be obtained. Subsequently, a clustering algorithm is employed to pick some obvious anomalies. Accordingly, we use both samples of background and anomaly to train an SVM model. The original dataset is sent into the SVM model and both anomalous components and background components can be classified. Experiments on a synthetic hyperspectral image validate the performance of the proposed method.

X-ray computed tomography (CT) is widely used, both clinically and preclinically, for fast, high-resolution anatomic imaging; however, compelling opportunities exist to expand its use in functional imaging applications. For instance, spectral information combined with nanoparticle contrast agents enables quantification of tissue perfusion levels, while temporal information details cardiac and respiratory dynamics. The authors propose and demonstrate a projection acquisition and reconstruction strategy for 5D CT (3D+dual energy+time) which recovers spectral and temporal information without substantially increasing radiation dose or sampling time relative to anatomic imaging protocols. The authors approach the 5D reconstruction problem within the framework of low-rank and sparse matrix decomposition. Unlike previous work on rank-sparsity constrained CT reconstruction, the authors establish an explicit rank-sparse signal model to describe the spectral and temporal dimensions. The spectral dimension is represented as a well-sampled time and energy averaged image plus regularly undersampled principal components describing the spectral contrast. The temporal dimension is represented as the same time and energy averaged reconstruction plus contiguous, spatially sparse, and irregularly sampled temporal contrast images. Using a nonlinear, image domain filtration approach, the authors refer to as rank-sparse kernel regression, the authors transfer image structure from the well-sampled time and energy averaged reconstruction to the spectral and temporal contrast images. This regularization strategy strictly constrains the reconstruction problem while approximately separating the temporal and spectral dimensions. Separability results in a highly compressed representation for the 5D data in which projections are shared between the temporal and spectral reconstruction subproblems, enabling substantial undersampling. The authors solved the 5D reconstruction problem using the split Bregman method and GPU-based implementations of backprojection, reprojection, and kernel regression. Using a preclinical mouse model, the authors apply the proposed algorithm to study myocardial injury following radiation treatment of breast cancer. Quantitative 5D simulations are performed using the MOBY mouse phantom. Twenty data sets (ten cardiac phases, two energies) are reconstructed with 88 μm, isotropic voxels from 450 total projections acquired over a single 360° rotation. In vivo 5D myocardial injury data sets acquired in two mice injected with gold and iodine nanoparticles are also reconstructed with 20 data sets per mouse using the same acquisition parameters (dose: ∼60 mGy). For both the simulations and the in vivo data, the reconstruction quality is sufficient to perform material decomposition into gold and iodine maps to localize the extent of myocardial injury (gold accumulation) and to measure cardiac functional metrics (vascular iodine). Their 5D CT imaging protocol represents a 95% reduction in radiation dose per cardiac phase and energy and a 40-fold decrease in projection sampling time relative to their standard imaging protocol. Their 5D CT data acquisition and reconstruction protocol efficiently exploits the rank-sparse nature of spectral and temporal CT data to provide high-fidelity reconstruction results without increased radiation dose or sampling time.

The nonuniform of polarization information of backscattered light has always been a neglected characteristic in polarization underwater imaging, but its accurate estimation plays an important role in the quality of imaging results. Traditional polarization imaging methods assume that the degree of polarization and angle of polarization of backscattered light are constant. In fact, the polarization information of backscattering light is gradual, this assumption makes traditional methods work only in a small area of the camera's field of view, in which the change of the polarization information of backscattered light can be ignored. In this paper, by analyzing the distribution of backscattered light, it is concluded that its polarization information has the characteristics of low-rank. Then, the degree of polarization and angle of polarization of backscattered light were estimated by low-rank and sparse matrix decomposition, and the clear scene was reconstructed. Experimental results show that the proposed method breaks through the limitation of the assumption of backscattered light in traditional polarization imaging method, and expands the detection field under the same conditions, which makes it possible to develop polarization underwater imaging method to the direction of large field of view detection.

In this letter, we propose an unsupervised framework for speech noise reduction based on the recent development of low-rank and sparse matrix decomposition. The proposed framework directly separates the speech signal from noisy speech by decomposing the noisy speech spectrogram into three submatrices: the noise structure matrix, the clean speech structure matrix, and the residual noise matrix. Evaluations on the Noisex-92 dataset show that the proposed method achieves a signal-to-distortion ratio approximately 2.48 dB and 3.23 dB higher than that of the robust principal component analysis method and the non-negative matrix factorization method, respectively, when the input SNR is -5 dB.

Sparse and low rank matrix decomposition is a method that has recently been developed for estimating different components of hyperspectral data. The rank component is capable of preserving global data structures of data, while a sparse component can select the discriminative information by preserving details. In order to take advantage of both, we present a novel decision fusion based on joint low rank and sparse component (DFJLRS) method for hyperspectral imagery in this paper. First, we analyzed the effects of different components on classification results. Then a novel method adopts a decision fusion strategy which combines a SVM classifier with the information provided by joint sparse and low rank components. With combination of the advantages, the proposed method is both representative and discriminative. The proposed algorithm is evaluated using several hyperspectral images when compared with traditional counterparts.

针对多聚焦图像融合过程中存在聚焦边缘模糊、伪影和块效应的问题，提出一种基于低秩稀疏矩阵分解（LRSMD）和离散余弦变换（DCT）实现多聚焦图像融合的算法。首先，利用LRSMD将源图像分解为低秩和稀疏矩阵两部分；然后，设计DCT方法检测低秩矩阵部分聚焦区域，构建初始焦点决策图，并利用重复一致性验证方法验证决策图，同时设计基于形态滤波的融合策略，得到稀疏矩阵部分融合结果；最后，采用加权重构方法对两部分进行融合。实验结果表明，相较于其他5种主流算法，所提算法在主观评价上具有高清晰度和全聚焦的优势，在客观评价上，边缘信息保持度、峰值信噪比、结构相似性及相关系数4个指标最高分别提高了62.3%、6.3%、2.2%及6.3%，证明所提算法有效提升了对源图像聚焦信息的提取能力，增强了聚焦边缘细节信息，同时对伪影和块效应的减少起到了重要作用。

In this work we consider the problem of extraction and classification of moving targets in wide area imagery. We use the Air Force Research Laboratory's (AFRL) airborne multi-sensor dataset, MAMI-1, for testing, wherein moving targets mostly consist of people and vehicles. The movers are extracted using a novel sparse and low-rank matrix decomposition technique. We further compare the classification performance based on SIFT, Dense SIFT, and a superpixel based feature extraction. The results show the superpixel approach as the most advantageous.

An important stage in speech enhancement is to estimate noise signal which is a difficult task in non-stationary and low signal-to-noise conditions. This paper presents an iterative speech enhancement approach which requires no prior knowledge of noise and is based on low-rank sparse matrix decomposition using Gammatone filterbank and convex distortion measure. To estimate noise and speech, the noisy speech is decomposed into low-rank noise and sparse-speech parts by enforcing sparsity regularization. The exact distribution of noise signals and noise estimator is not required in this approach. The experimental results demonstrate that our approach outperforms competing methods and yields better overall speech quality and intelligibility. Moreover, composite objective measure reinforced a better performance in terms of residual noise and speech distortion in adverse noisy conditions. The time-varying spectral analysis validates significant reduction of the background noise.