Related papers: Mixed Operators in Compressed Sensing
This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary, but in a truly redundant dictionary.…
This paper addresses the problem of simultaneous signal recovery and dictionary learning based on compressive measurements. Multiple signals are analyzed jointly, with multiple sensing matrices, under the assumption that the unknown signals…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this correspondence, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via additive…
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…
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…
Cost-efficient compressive sensing is challenging when facing large-scale data, {\em i.e.}, data with large sizes. Conventional compressive sensing methods for large-scale data will suffer from low computational efficiency and massive…
We demonstrate a simple greedy algorithm that can reliably recover a d-dimensional vector v from incomplete and inaccurate measurements x. Here our measurement matrix is an N by d matrix with N much smaller than d. Our algorithm,…
Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only "approximately sparse", i.e. even though the signal contains only a small fraction of relevant (large)…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
Modern compression algorithms exploit complex structures that are present in signals to describe them very efficiently. On the other hand, the field of compressed sensing is built upon the observation that "structured" signals can be…
Highly coherent sensing matrices arise in discretization of continuum imaging problems such as radar and medical imaging when the grid spacing is below the Rayleigh threshold. Algorithms based on techniques of band exclusion (BE) and local…
This paper investigates the problem of recovering the support of structured signals via adaptive compressive sensing. We examine several classes of structured support sets, and characterize the fundamental limits of accurately recovering…
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…
Compressive sensing is a novel approach that linearly samples sparse or compressible signals at a rate much below the Nyquist-Shannon sampling rate and outperforms traditional signal processing techniques in acquiring and reconstructing…
We propose robust and efficient algorithms for the joint sparse recovery problem in compressed sensing, which simultaneously recover the supports of jointly sparse signals from their multiple measurement vectors obtained through a common…
Recently, greedy algorithm has received much attention as a cost-effective means to reconstruct the sparse signals from compressed measurements. Much of previous work has focused on the investigation of a single candidate to identify the…
Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform…
We study compressed sensing (CS) signal reconstruction problems where an input signal is measured via matrix multiplication under additive white Gaussian noise. Our signals are assumed to be stationary and ergodic, but the input statistics…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
We give some new results on sparse signal recovery in the presence of noise, for weighted spaces. Traditionally, were used dictionaries that have the norm equal to 1, but, for random dictionaries this condition is rarely satisfied.…