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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…
In this paper, we present coherence-based performance guarantees of Orthogonal Matching Pursuit (OMP) for both support recovery and signal reconstruction of sparse signals when the measurements are corrupted by noise. In particular, two…
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 paper, we propose a new orthogonal matching pursuit algorithm called quasi-OMP algorithm which greatly enhances the performance of classical orthogonal matching pursuit (OMP) algorithm, at some cost of computational complexity. We…
The orthogonal multi-matching pursuit (OMMP) is a natural extension of orthogonal matching pursuit (OMP). We denote the OMMP with the parameter $M$ as OMMP(M) where $M\geq 1$ is an integer. The main difference between OMP and OMMP(M) is…
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…
Orthogonal matching pursuit (OMP) and orthogonal least squares (OLS) are widely used for sparse signal reconstruction in under-determined linear regression problems. The performance of these compressed sensing (CS) algorithms depends…
Support recovery of sparse signals from noisy measurements with orthogonal matching pursuit (OMP) has been extensively studied. In this paper, we show that for any $K$-sparse signal $\x$, if a sensing matrix $\A$ satisfies the restricted…
A well-known analysis of Tropp and Gilbert shows that orthogonal matching pursuit (OMP) can recover a k-sparse n-dimensional real vector from 4 k log(n) noise-free linear measurements obtained through a random Gaussian measurement matrix…
As an extension of orthogonal matching pursuit (OMP) improving the recovery performance of sparse signals, generalized OMP (gOMP) has recently been studied in the literature. In this paper, we present a new analysis of the gOMP algorithm…
In this work we address the problem of recovering sparse solutions to non linear inverse problems. We look at two variants of the basic problem, the synthesis prior problem when the solution is sparse and the analysis prior problem where…
This paper considers the exact recovery of $k$-sparse signals in the noiseless setting and support recovery in the noisy case when some prior information on the support of the signals is available. This prior support consists of two parts.…
We study sparse approximation by greedy algorithms. Our contribution is two-fold. First, we prove exact recovery with high probability of random $K$-sparse signals within $\lceil K(1+\e)\rceil$ iterations of the Orthogonal Matching Pursuit…
This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements -- L_1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized…
Greedy sparse recovery has become a popular tool in many applications, although its complexity is still prohibitive when large sparsifying dictionaries or sensing matrices have to be exploited. In this paper, we formulate first a new class…
In this paper, the joint support recovery of several sparse signals whose supports present similarities is examined. Each sparse signal is acquired using the same noisy linear measurement process, which returns fewer observations than the…
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…
This paper provides a simple proof of the mutual incoherence condition $\mu < \frac{1}{2K-1}$ under which K-sparse signal can be accurately reconstructed from a small number of linear measurements using the orthogonal matching pursuit (OMP)…
Current orthogonal matching pursuit (OMP) algorithms calculate the correlation between two vectors using the inner product operation and minimize the mean square error, which are both suboptimal when there are non-Gaussian noises or…
We propose a class of greedy algorithms for weighted sparse recovery by considering new loss function-based generalizations of Orthogonal Matching Pursuit (OMP). Given a (regularized) loss function, the proposed algorithms alternate the…