Related papers: RIP constants for deterministic compressed sensing…
Can compression algorithms be employed for recovering signals from their underdetermined set of linear measurements? Addressing this question is the first step towards applying compression algorithms for compressed sensing (CS). In this…
Compressive sensing (CS) is a new technology which allows the acquisition of signals directly in compressed form, using far fewer measurements than traditional theory dictates. Recently, many so-called signal space methods have been…
In this paper, we prove that the Paley graph conjecture implies that the Paley matrix has restricted isometry property (RIP) beating the square-root bottleneck for the sparsity level. Moreover, we show that the RIP of the Paley matrix…
In this paper, we study the restricted isometry property of partial random circulant matrices. For a bounded subgaussian generator with independent entries, we prove that the partial random circulant matrices satisfy $s$-order RIP with high…
In Compressed Sensing the matrices that satisfy the Restricted Isometry Property (RIP) play an important role. But to date, very few results for designing such matrices are available. For applications such as multiplier-less data…
A sufficient condition reported very recently for perfect recovery of a K-sparse vector via orthogonal matching pursuit (OMP) in K iterations is that the restricted isometry constant of the sensing matrix satisfies…
Millimeter wave beam alignment (BA) is a challenging problem especially for large number of antennas. Compressed sensing (CS) tools have been exploited due to the sparse nature of such channels. This paper presents a novel deterministic CS…
We consider designing a robust structured sparse sensing matrix consisting of a sparse matrix with a few non-zero entries per row and a dense base matrix for capturing signals efficiently We design the robust structured sparse sensing…
Recently, the 1-bit compressive sensing (1-bit CS) has been studied in the field of sparse signal recovery. Since the amplitude information of sparse signals in 1-bit CS is not available, it is often the support or the sign of a signal that…
The recovery of structured signals from a few linear measurements is a central point in both compressed sensing (CS) and discrete tomography. In CS the signal structure is described by means of a low complexity model e.g. co-/sparsity. The…
The paper introduces a framework for the recoverability analysis in compressive sensing for imaging applications such as CI cameras, rapid MRI and coded apertures. This is done using the fact that the Spherical Section Property (SSP) of a…
The goal of compressed sensing is to estimate a vector from an underdetermined system of noisy linear measurements, by making use of prior knowledge on the structure of vectors in the relevant domain. For almost all results in this…
Hierarchically sparse signals and Kronecker product structured measurements arise naturally in a variety of applications. The simplest example of a hierarchical sparsity structure is two-level $(s,\sigma)$-hierarchical sparsity which…
Closed-loop architecture is widely utilized in automatic control systems and attain distinguished performance. However, classical compressive sensing systems employ open-loop architecture with separated sampling and reconstruction units.…
Compressed sensing (CS) is a sampling paradigm that allows to simultaneously measure and compress signals that are sparse or compressible in some domain. The choice of a sensing matrix that carries out the measurement has a defining impact…
Compressive sensing (CS) allows for acquisition of sparse signals at sampling rates significantly lower than the Nyquist rate required for bandlimited signals. Recovery guarantees for CS are generally derived based on the assumption that…
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…
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…
Compressed sensing is the art of reconstructing structured $n$-dimensional vectors from substantially fewer measurements than naively anticipated. A plethora of analytic reconstruction guarantees support this credo. The strongest among them…
The restricted isometry constants (RICs) play an important role in exact recovery theory of sparse signals via l_q(0<q<=1) relaxations in compressed sensing. Recently, Cai and Zhang[6] have achieved a sharp bound \delta_tk<\sqrt{1-1/t} for…