Related papers: Greedy Sparse Signal Reconstruction Using Matching…
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…
Some consequences of the Restricted Isometry Property (RIP) of matrices have been applied to develop a greedy algorithm called "ROMP" (Regularized Orthogonal Matching Pursuit) to recover sparse signals and to approximate non-sparse ones.…
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…
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 discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
RNA secondary structures prediction is one of the main issues in bioinformatics. It seeks to elucidate structural conserved regions within a set of RNA sequences. Unfortunately, finding an accurate conserved structure is a very hard task to…
We present an information-theoretic framework for sequential adaptive compressed sensing, Info-Greedy Sensing, where measurements are chosen to maximize the extracted information conditioned on the previous measurements. We show that the…
In many data acquisition systems it is common to observe signals whose amplitudes have been clipped. We present two new algorithms for recovering a clipped signal by leveraging the model assumption that the underlying signal is sparse in…
Sparse phase retrieval aims to recover a $k$-sparse signal from $m$ phaseless measurements. While the theoretically optimal sample complexity for successful recovery is $\Omega(k \log n)$, existing algorithms can only achieve this bound for…
It is known that certain structures of the signal in addition to the standard notion of sparsity (called structured sparsity) can improve the sample complexity in several compressive sensing applications. Recently, Hegde et al. proposed a…
Sparse signal representations based on linear combinations of learned atoms have been used to obtain state-of-the-art results in several practical signal processing applications. Approximation methods are needed to process high-dimensional…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
This paper addresses compressive sensing for multi-channel ECG. Compared to the traditional sparse signal recovery approach which decomposes the signal into the product of a dictionary and a sparse vector, the recently developed cosparse…
In this paper we study the compressed sensing problem of recovering a sparse signal from a system of underdetermined linear equations when we have prior information about the probability of each entry of the unknown signal being nonzero. In…
Sparse recovery can recover sparse signals from a set of underdetermined linear measurements. Motivated by the need to monitor large-scale networks from a limited number of measurements, this paper addresses the problem of recovering sparse…
Compressive sampling (CoSa) has provided many methods for signal recovery of signals compressible with respect to an orthonormal basis. However, modern applications have sparked the emergence of approaches for signals not sparse in an…
In this paper, we propose a new sparse signal recovery algorithm, referred to as sparse Kalman tree search (sKTS), that provides a robust reconstruction of the sparse vector when the sequence of correlated observation vectors are available.…
As a greedy algorithm to recover sparse signals from compressed measurements, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we introduce an extension of the OMP for pursuing…
This paper presents a new analysis for the orthogonal matching pursuit (OMP) algorithm. It is shown that if the restricted isometry property (RIP) is satisfied at sparsity level $O(\bar{k})$, then OMP can recover a $\bar{k}$-sparse signal…