Related papers: A sharp bound on RIC in generalized orthogonal mat…
In this paper, we present a novel yet simple homotopy proximal mapping algorithm for compressive sensing. The algorithm adopts a simple proximal mapping of the $\ell_1$ norm at each iteration and gradually reduces the regularization…
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…
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 study distributed schemes for high-dimensional sparse linear regression, based on orthogonal matching pursuit (OMP). Such schemes are particularly suited for settings where a central fusion center is connected to end machines, that have…
Compressed Sensing aims to capture attributes of $k$-sparse signals using very few measurements. In the standard Compressed Sensing paradigm, the $\m\times \n$ measurement matrix $\A$ is required to act as a near isometry on the set of all…
Direction of Arrival (DOA) estimation of multiple narrow-band coherent or partially coherent sources is a major challenge in array signal processing. Though many subspace- based algorithms are available in literature, none of them tackle…
In this paper, we address the sparse multiple measurement vector (MMV) problem where the objective is to recover a set of sparse nonzero row vectors or indices of a signal matrix from incomplete measurements. Ideally, regardless of the…
In Compressive Sensing, the Restricted Isometry Property (RIP) ensures that robust recovery of sparse vectors is possible from noisy, undersampled measurements via computationally tractable algorithms. It is by now well-known that Gaussian…
This paper studies the joint support recovery of similar sparse vectors on the basis of a limited number of noisy linear measurements, i.e., in a multiple measurement vector (MMV) model. The additive noise signals on each measurement vector…
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…
In this work, we analyze modulated sampling schemes, such as the Nyquist Folding Receiver, which are highly efficient, readily implementable, non-uniform sampling schemes that allows for the blind estimation of a narrow-band signal's…
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…
In this paper, we study a general low-rank matrix recovery problem with linear measurements corrupted by some noise. The objective is to understand under what conditions on the restricted isometry property (RIP) of the problem local search…
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…
This paper addresses the reconstruction of sparse signals from generalized linear measurements. Signal sparsity is assumed to be sublinear in the signal dimension while it was proportional to the signal dimension in conventional research.…
We study the problem of recovering the sparsity pattern of block-sparse signals from noise-corrupted measurements. A simple, efficient recovery method, namely, a block-version of the orthogonal matching pursuit (OMP) method, is considered…
Sparse signal recovery deals with finding the sparsest solution of an under-determined linear system $\vx = \mQ\vs$. In this paper, we propose a novel greedy approach to addressing the challenges from such a problem. Such an approach is…
A major enterprise in compressed sensing and sparse approximation is the design and analysis of computationally tractable algorithms for recovering sparse, exact or approximate, solutions of underdetermined linear systems of equations. Many…
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…
Greedy approaches in general, and orthogonal matching pursuit in particular, are the most commonly used sparse recovery techniques in a wide range of applications. The complexity of these approaches is highly dependent on the size of the…