Robust Localization in Wireless Sensor Networks via Low-rank and 'Sparse Matrix Decomposition

This article puts forward a novel system for pedestrian detection tasks, which proposing a model with sparse and low-rank matrix decomposition, jointly alternating direction method to solve the convex relaxation problem. We present an efficient pedestrian detection system using mixing features with sparse and low-rank matrix decomposition to combine into a Kernel classifier. Results presented on our data set show competitive accuracy and robust performance of our system outperforms current state-of-the-art work. DOI : http://dx.doi.org/10.11591/telkomnika.v12i2.3859

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.

We propose a novel approach to the source localization and tracking problem in wireless sensor networks. By applying minimax approximation and semidefinite relaxation, we transform the traditionally nonlinear and nonconvex problem into convex optimization problems for two different source localization models involving measured distance and received signal strength. Based on the problem transformation, we develop a fast low-complexity semidefinite programming (SDP) algorithm for two different source localization models. Our algorithm can either be used to estimate the source location or be used to initialize the original nonconvex maximum likelihood algorithm.

Wireless sensor networks (WSNs) are emerging as an efficient way to sense the physical phenomenon without the need of wired links and spending huge money on sensor devices. In WSNs, finding the accurate locations of sensor nodes is essential since the location inaccuracy makes the collected data fruitless. In this paper, we propose a two-objective memetic approach called the Three Phase Memetic Approach that finds the locations of sensor nodes with high accuracy. The proposed algorithm is composed of three operators (phases). The first phase, which is a combination of three node-estimating approaches, is used to provide good starting locations for sensor nodes. The second and third phases are then utilized for mitigating the localization errors in the first operator. To test the proposed algorithm, we compare it with the simulated annealing-based localization algorithm, genetic algorithm-based localization, Particle Swarm Optimization-based Localization algorithm, trilateration-based simulated annealing algorithm, imperialist competitive algorithm and Pareto Archived Evolution Strategy on ten randomly created and four specific network topologies with four different values of transmission ranges. The comparisons indicate that the proposed algorithm outperforms the other algorithms in terms of the coordinate estimations of sensor nodes.

With the proliferation of the Internet of Things (IoT), employing Received Signal Strength (RSS) as a metric to determine the location of a target (e.g., person or mobile device) is of great interest in terms of cost and ease of implementation. Indeed, RSS measurements can be easily obtained for most off-the-shelf devices, such as WiFi- or ZigBee compatible devices or sensors. This paper deals with the indoor localization problem in wireless sensor networks (WSNs) and proposes a new approach for radio signal propagation modelling and localization estimation, that accounts for the imperfection of RSS measurements and the reliability of RSS sources by using the Dempster-Shafer Theory (DST). In the signal propagation modelling, key information regarding the geometry of indoor environment that is divided into zones separated by walls (zoning), are considered. Based on the number of walls, the RSS irregularities are estimated using different distance intervals, which are weighted by a probability density determined experimentally. To estimate the location of a target node, the PCR6 rule is used to combine the belief masses of the positions obtained from the probability density. In order to evaluate the performance of the proposed approach, an experimental WSN has been deployed in a living apartment. The obtained results demonstrate that the proposed approach improves the localization accuracy compared to the case without zoning. Moreover, the obtained localization mean error proves the feasibility of a precise localization of humans in indoor environments in the case of Ambient Assisted Living and Social Robotics applications.

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.

In this letter, we propose a new approach to the localization problem in wireless sensor networks using received-signal-strength (RSS) measurements. The problem is reformulated under the equivalent exponential transformation of the conventional path loss measurement model and the unscented transformation (UT), and is approximately approached by the maximum likelihood (ML) parameter estimation, which we refer to as the weighted least squares (WLS) approach. This formulation is used for sensor node localization in both noncooperative and cooperative scenarios. Simulation results confirm the effectiveness of the approach for both outdoor and indoor environments.

Graph invariants for unique localizability in cooperative localization of wireless sensor networks: Rigidity index and redundancy index

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.

The sensor network localization (SNL) problem in embedding dimension r consists of locating the positions of wireless sensors, given only the distances between sensors that are within radio range and the positions of a subset of the sensors (called anchors). Current solution techniques relax this problem to a weighted, nearest, (positive) semidefinite programming (SDP) completion problem by using the linear mapping between Euclidean distance matrices (EDM) and semidefinite matrices. The resulting SDP is solved using primal-dual interior point solvers, yielding an expensive and inexact solution. This relaxation is highly degenerate in the sense that the feasible set is restricted to a low dimensional face of the SDP cone, implying that the Slater constraint qualification fails. Cliques in the graph of the SNL problem give rise to this degeneracy in the SDP relaxation. In this paper, we take advantage of the absence of the Slater constraint qualification and derive a technique for the SNL problem, with exact data, that explicitly solves the corresponding rank restricted SDP problem. No SDP solvers are used. For randomly generated instances, we are able to efficiently solve many huge instances of this NP-hard problem to high accuracy by finding a representation of the minimal face of the SDP cone that contains the SDP matrix representation of the EDM. The main work of our algorithm consists in repeatedly finding the intersection of subspaces that represent the faces of the SDP cone that correspond to cliques of the SNL problem.