Compressed sensing

About: Compressed sensing is a research topic. Over the lifetime, 16412 publications have been published within this topic receiving 358493 citations. The topic is also known as: compressive sensing & compressive sampling.

Simultaneous fast joint sparse recovery for WSN and IoT applications

Abstract: Joint sparse recovery aims to recover a number of sparse signals having joint sparsity from multiple compressed measurements. Such a problem is finding increasing applications in wireless sensor networks (WSN) and Internet of Things (IoT) where multiple sensors collect measurements. However, existing algorithms lack both reconstruction accuracy and speed at the same time. In this study, the authors propose a joint sparse recovery algorithm, simultaneous fast matching pursuit (SFMP), which exploits some of the concepts developed for the fast matching pursuit (FMP) algorithm. SFMP achieves significant improvement in reconstruction time and speed compared to other related existing algorithms. In contrast to related algorithms, support selection is performed efficiently as the number of selected atoms is adapted from an iteration to another. Furthermore, signal estimation is performed avoiding large matrix inversion as in related algorithms. Moreover, simultaneously pruning the estimated signals, results in removing incorrectly selected ones. Due to the efficient selection strategy and the simultaneous pruning operation, the algorithm shows significant improvement in reconstruction accuracy from noisy measurements. SFMP achieves significant speed improvement over simultaneous orthogonal matching pursuit, and significant accuracy improvement over simultaneous compressive sampling matching pursuit, requiring a much smaller number of measurements.

Robust 1-bit compressed sensing via hinge loss minimization

Abstract: This work theoretically studies the problem of estimating a structured high-dimensional signal $x_0 \in \mathbb{R}^n$ from noisy $1$-bit Gaussian measurements. Our recovery approach is based on a simple convex program which uses the hinge loss function as data fidelity term. While such a risk minimization strategy is very natural to learn binary output models, such as in classification, its capacity to estimate a specific signal vector is largely unexplored. A major difficulty is that the hinge loss is just piecewise linear, so that its "curvature energy" is concentrated in a single point. This is substantially different from other popular loss functions considered in signal estimation, e.g., the square or logistic loss, which are at least locally strongly convex. It is therefore somewhat unexpected that we can still prove very similar types of recovery guarantees for the hinge loss estimator, even in the presence of strong noise. More specifically, our non-asymptotic error bounds show that stable and robust reconstruction of $x_0$ can be achieved with the optimal oversampling rate $O(m^{-1/2})$ in terms of the number of measurements $m$. Moreover, we permit a wide class of structural assumptions on the ground truth signal, in the sense that $x_0$ can belong to an arbitrary bounded convex set $K \subset \mathbb{R}^n$. The proofs of our main results rely on some recent advances in statistical learning theory due to Mendelson. In particular, we invoke an adapted version of Mendelson's small ball method that allows us to establish a quadratic lower bound on the error of the first order Taylor approximation of the empirical hinge loss function.

Stagewise regularized orthogonal matching pursuit algorithm

Abstract: A novel reconstruction algorithm(stagewise regularized orthogonal matching pursuit)was proposed to reconstruct signals without prior sparsity information.The method constructed the candidate set by designing threshold based on the residual from signal reconstruction.The extracted signal atoms from the candidate set were merged with the previous support set.When the candidate set was a null set,the atom with the greatest correlation was directly added to the support set.Finally,the refinement of signal approximation and residual updating were achieved by solving a least-square algorithm on the support set.The experimental results for Gaussian signal and binary signal with a length of 256show that the probability of exact reconstruction can be reached above 90%on the conditions of signal sparsity of 50and 40,and the reconstructing effects and reconstructing speeds are better thanthose of similar algorithms under the same condition of signal sparsity.This algorithm is proved to be higher processing speeds and more stabile.

Multistatic radar imaging via decentralized and collaborative subspace pursuit

Abstract: The task of multistatic radar imaging can be converted to the problem of jointly sparse signal recovery. In this paper, the algorithm named decentralized and collaborative subspace pursuit (DCSP) is utilized in multistatic radar systems to obtain a high-resolution image. By embedding collaboration among radar nodes and fusion strategy into each iteration of the standard subspace pursuit (SP) algorithm, DCSP is capable of providing satisfactory image even if some radar nodes suffer from relatively low signal-to-noise ratios (SNRs). Compared to the existing algorithms based on linear programming, DCSP has much lower computational complexity at the cost of increased communication overhead in the radar network. Keywords—Multistatic radar imaging; compressive sensing; subspace pursuit.

One-Bit Quantization Design and Adaptive Methods for Compressed Sensing

Abstract: There have been a number of studies on sparse sig- nal recovery from one-bit quantized measurements. Nevertheless, little attention has been paid to the choice of the quantization thresholds and its impact on the signal recovery performance. This paper examines the problem of one-bit quantizer design for sparse signal recovery. Our analysis shows that the magnitude ambiguity that ever plagues conventional one-bit compressed sensing methods can be resolved, and an arbitrarily small reconstruction error can be achieved by setting the quantization thresholds close enough to the original unquantized measure- ments. Note that the unquantized data are inaccessible by us. To overcome this difficulty, we propose an adaptive quantiza tion method that iteratively refines the quantization threshold s based on previous estimate of the sparse signal. Numerical results are provided to collaborate our theoretical results and to illu strate the effectiveness of the proposed algorithm.