Related papers: A sharp recovery condition for block sparse signal…
We investigate the problem of reconstructing sparse multivariate trigonometric polynomials from few randomly taken samples by Basis Pursuit and greedy algorithms such as Orthogonal Matching Pursuit (OMP) and Thresholding. While recovery by…
Recovery algorithms play a key role in compressive sampling (CS). Most of current CS recovery algorithms are originally designed for one-dimensional (1D) signal, while many practical signals are two-dimensional (2D). By utilizing 2D…
In this letter, we first construct a counter example to show that for any given positive integer $K\geq 2$ and for any $\frac{1}{\sqrt{K+1}}\leq t<1$, there always exist a $K-$sparse $\x$ and a matrix $\A$ with the restricted isometry…
We establish sufficient conditions of exact and almost full recovery of the node partition in Bipartite Stochastic Block Model (BSBM) using polynomial time algorithms. First, we improve upon the known conditions of almost full recovery by…
A greedy algorithm called Bayesian multiple matching pursuit (BMMP) is proposed to estimate a sparse signal vector and its support given $m$ linear measurements. Unlike the maximum a posteriori (MAP) support detection, which was proposed by…
Direction of Arrival (DOA) estimation of mixed uncorrelated and coherent sources is a long existing challenge in array signal processing. Application of compressive sensing to array signal processing has opened up an exciting class of…
We consider the following k-sparse recovery problem: design an m x n matrix A, such that for any signal x, given Ax we can efficiently recover x' satisfying ||x-x'||_1 <= C min_{k-sparse} x"} ||x-x"||_1. It is known that there exist…
Over the past years, there are increasing interests in recovering the signals from undersampling data where such signals are sparse under some orthogonal dictionary or tight framework, which is referred to be sparse synthetic model. More…
This paper presents an average case denoising performance analysis for the Subspace Pursuit (SP), the CoSaMP and the IHT algorithms. This analysis considers the recovery of a noisy signal, with the assumptions that (i) it is corrupted by an…
Sparse Subspace Clustering (SSC) is one of the most popular methods for clustering data points into their underlying subspaces. However, SSC may suffer from heavy computational burden. Orthogonal Matching Pursuit applied on SSC accelerates…
We propose a convex and fast signal reconstruction method for block sparsity under arbitrary linear transform with unknown block structure. The proposed method is a generalization of the similar existing method and can reconstruct signals…
The paper discusses the recovery of signals in the case that signals are nearly sparse with respect to a tight frame $D$ by means of the $l_1$-analysis approach. We establish several new sufficient conditions regarding the $D$-restricted…
Greed is good. However, the tighter you squeeze, the less you have. In this paper, a less greedy algorithm for sparse signal reconstruction in compressive sensing, named orthogonal matching pursuit with thresholding is studied. Using the…
We study a sample complexity vs. conditioning tradeoff in modern signal recovery problems (including sparse recovery, low-rank matrix sensing, covariance estimation, and abstract phase retrieval), where convex optimization problems are…
In this paper, we consider the problem of collaboratively estimating the sparsity pattern of a sparse signal with multiple measurement data in distributed networks. We assume that each node makes Compressive Sensing (CS) based measurements…
Compressed sensing is a developing field aiming at reconstruction of sparse signals acquired in reduced dimensions, which make the recovery process under-determined. The required solution is the one with minimum $\ell_0$ norm due to…
Given an overcomplete dictionary $A$ and a signal $b$ that is a linear combination of a few linearly independent columns of $A$, classical sparse recovery theory deals with the problem of recovering the unique sparse representation $x$ such…
Many applications concern sparse signals, for example, detecting anomalies from the differences between consecutive images taken by surveillance cameras. This paper focuses on the problem of recovering a K-sparse signal x in N dimensions.…
Highly coherent sensing matrices arise in discretization of continuum imaging problems such as radar and medical imaging when the grid spacing is below the Rayleigh threshold. Algorithms based on techniques of band exclusion (BE) and local…
We study the stable recovery of complex $k$-sparse signals from as few phaseless measurements as possible. The main result is to show that one can employ $\ell_1$ minimization to stably recover complex $k$-sparse signals from $m\geq O(k\log…