Related papers: High SNR Consistent Compressive Sensing Without Si…
Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming…
A class of recovering algorithms for 1-bit compressive sensing (CS) named Soft Consistency Reconstructions (SCRs) are proposed. Recognizing that CS recovery is essentially an optimization problem, we endeavor to improve the characteristics…
In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
The theory of Compressed Sensing (CS) asserts that an unknown signal $x\in\mathbb{R}^p$ can be accurately recovered from an underdetermined set of $n$ linear measurements with $n\ll p$, provided that $x$ is sufficiently sparse. However, in…
Support estimation (SE) of a sparse signal refers to finding the location indices of the non-zero elements in a sparse representation. Most of the traditional approaches dealing with SE problem are iterative algorithms based on greedy…
Compressed sensing (sparse signal recovery) has been a popular and important research topic in recent years. By observing that natural signals are often nonnegative, we propose a new framework for nonnegative signal recovery using…
Matching pursuit, especially its orthogonal version (OMP) and variations, is a greedy algorithm widely used in signal processing, compressed sensing, and sparse modeling. Inspired by constrained sparse signal recovery, this paper proposes a…
We consider the high-dimensional sparse linear regression problem of accurately estimating a sparse vector using a small number of linear measurements that are contaminated by noise. It is well known that the standard cadre of…
In the theory of compressed sensing (CS), the sparsity $\|x\|_0$ of the unknown signal $\mathbf{x} \in \mathcal{R}^n$ is of prime importance and the focus of reconstruction algorithms has mainly been either $\|x\|_0$ or its convex…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
Compressive sensing (CS) has recently emerged as a powerful framework for acquiring sparse signals. The bulk of the CS literature has focused on the case where the acquired signal has a sparse or compressible representation in an…
Compressed Sensing (CS) is an effective approach to reduce the required number of samples for reconstructing a sparse signal in an a priori basis, but may suffer severely from the issue of basis mismatch. In this paper we study the problem…
Consider the compressed sensing setup where the support $s^*$ of an $m$-sparse $d$-dimensional signal $x$ is to be recovered from $n$ linear measurements with a given algorithm. Suppose that the measurements are such that the algorithm does…
Recently, many practical algorithms have been proposed to recover the sparse signal from fewer measurements. Orthogonal matching pursuit (OMP) is one of the most effective algorithm. In this paper, we use the restricted isometry property to…
In this paper we present a new coherence-based performance guarantee for the Orthogonal Matching Pursuit (OMP) algorithm. A lower bound for the probability of correctly identifying the support of a sparse signal with additive white Gaussian…
Several exact recovery criteria (ERC) ensuring that orthogonal matching pursuit (OMP) identifies the correct support of sparse signals have been developed in the last few years. These ERC rely on the restricted isometry property (RIP), the…
Orthogonal Matching Pursuit (OMP) has been a powerful method in sparse signal recovery and approximation. However, OMP suffers computational issues when the signal has a large number of non-zeros. This paper advances OMP and its extension…
We provide new recovery bounds for hierarchical compressed sensing (HCS) based on prior support information (PSI). A detailed PSI-enabled reconstruction model is formulated using various forms of PSI. The hierarchical block orthogonal…
Sparse subspace clustering (SSC) using greedy-based neighbor selection, such as matching pursuit (MP) and orthogonal matching pursuit (OMP), has been known as a popular computationally-efficient alternative to the conventional…