Related papers: Coherence-Based Performance Guarantees of Orthogon…
Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a…
We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of…
We study quantum sparse recovery in non-orthogonal, overcomplete dictionaries: given coherent quantum access to a state and a dictionary of vectors, the goal is to reconstruct the state up to $\ell_2$ error using as few vectors as possible.…
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…
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…
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…
In this paper, we introduce a novel algorithm named JS-gOMP, which enhances the generalized Orthogonal Matching Pursuit (gOMP) algorithm for improved noise robustness in sparse signal processing. The JS-gOMP algorithm uniquely incorporates…
Greedy algorithms for minimizing L0-norm of sparse decomposition have profound application impact on many signal processing problems. In the sparse coding setup, given the observations $\mathrm{y}$ and the redundant dictionary…
This paper is concerned with the performance of Orthogonal Matching Pursuit (OMP) algorithms applied to a dictionary $\mathcal{D}$ in a Hilbert space $\mathcal{H}$. Given an element $f\in \mathcal{H}$, OMP generates a sequence of…
The exact recovery property of Basis pursuit (BP) and Orthogonal Matching Pursuit (OMP) has a relation with the coherence of the underlying frame. A frame with low coherence provides better guarantees for exact recovery. In particular,…
Orthogonal Matching Pursuit (OMP) plays an important role in data science and its applications such as sparse subspace clustering and image processing. However, the existing OMP-based approaches lack of data adaptiveness so that the data…
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…
The most frequently used condition for sampling matrices employed in compressive sampling is the restricted isometry (RIP) property of the matrix when restricted to sparse signals. At the same time, imposing this condition makes it…
We address the exact recovery of a k-sparse vector in the noiseless setting when some partial information on the support is available. This partial information takes the form of either a subset of the true support or an approximate subset…
Orthogonal Matching Pursuit and Basis Pursuit are popular reconstruction algorithms for recovery of sparse signals. The exact recovery property of both the methods has a relation with the coherence of the underlying redundant dictionary,…
We propose a fast sequential algorithm for the fundamental problem of estimating frequencies and amplitudes of a noisy mixture of sinusoids. The algorithm is a natural generalization of Orthogonal Matching Pursuit (OMP) to the continuum…
We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occurring in clusters. An uncertainty relation for block-sparse signals is derived, based on a block-coherence measure, which we…
Sign truncated matching pursuit (STrMP) algorithm is presented in this paper. STrMP is a new greedy algorithm for the recovery of sparse signals from the sign measurement, which combines the principle of consistent reconstruction with…
Recovering the support of sparse vectors in underdetermined linear regression models, \textit{aka}, compressive sensing is important in many signal processing applications. High SNR consistency (HSC), i.e., the ability of a support recovery…
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…