Related papers: A sharp recovery condition for block sparse signal…
In this paper, we investigate the theoretical guarantees of penalized $\lun$ minimization (also called Basis Pursuit Denoising or Lasso) in terms of sparsity pattern recovery (support and sign consistency) from noisy measurements with…
We consider the problem of exact support recovery of sparse signals via noisy measurements. The main focus is the sufficient and necessary conditions on the number of measurements for support recovery to be reliable. By drawing an analogy…
This paper is motivated by the reconstruction problem on the sparse stochastic block model. Mossel, et. al. proved that a reconstruction algorithm that recovers an optimal fraction of the communities in the symmetric, 2-community case. The…
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…
Highly coherent sensing matrices arise in discretization of continuum problems such as radar and medical imaging when the grid spacing is below the Rayleigh threshold as well as in using highly coherent, redundant dictionaries as…
We shall show that if the restricted isometry constant (RIC) $\delta_{s+1}(A)$ of the measurement matrix $A$ satisfies $$ \delta_{s+1}(A) < \frac{1}{\sqrt{s + 1}}, $$ then the greedy algorithm Orthogonal Matching Pursuit(OMP) will succeed.…
Block sparsity is an important parameter in many algorithms to successfully recover block sparse signals under the framework of compressive sensing. However, it is often unknown and needs to be estimated. Recently there emerges a few…
We consider the problem of recovering off-the-grid spikes from linear measurements. The state of the art Over-Parametrized Continuous Orthogonal Matching Pursuit (OP-COMP) with Projected Gradient Descent (PGD) successfully recovers those…
Compressive sampling (CoSa) is a new methodology which demonstrates that sparse signals can be recovered from a small number of linear measurements. Greedy algorithms like CoSaMP have been designed for this recovery, and variants of these…
In this paper, we introduce a weighted $\ell_2/\ell_1$ minimization to recover block sparse signals with arbitrary prior support information. When partial prior support information is available, a sufficient condition based on the high…
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…
In this paper, we propose first a mmWave channel tracking algorithm based on multidimensional orthogonal matching pursuit algorithm (MOMP) using reduced sparsifying dictionaries, which exploits information from channel estimates in previous…
Numerical experiments in literature on compressed sensing have indicated that the reweighted $l_1$ minimization performs exceptionally well in recovering sparse signal. In this paper, we develop exact recovery conditions and algorithm for…
In this paper we define a new coherence index, named the global 2-coherence, of a given dictionary and study its relationship with the traditional mutual coherence and the restricted isometry constant. By exploring this relationship, we…
The orthogonal matching pursuit (OMP) is one of the mainstream algorithms for sparse data reconstruction or approximation. It acts as a driving force for the development of several other greedy methods for sparse data reconstruction, and it…
In this paper, we propose an algorithm referred to as multipath matching pursuit that investigates multiple promising candidates to recover sparse signals from compressed measurements. Our method is inspired by the fact that the problem to…
We propose novel necessary and sufficient conditions for a sensing matrix to be "$s$-good" - to allow for exact $\ell_1$-recovery of sparse signals with $s$ nonzero entries when no measurement noise is present. Then we express the error…
This paper demonstrates theoretically that if the restricted isometry constant $\delta_K$ of the compressed sensing matrix satisfies $$ \delta_{K+1} < \frac{1}{\sqrt{K}+1}, $$ then a greedy algorithm called Orthogonal Matching Pursuit (OMP)…
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,…
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…