Related papers: Comparison of threshold-based algorithms for spars…
This manuscript goes through the fundamental connections between statistical mechanics and estimation theory by focusing on the particular problem of compressive sensing. We first show that the asymptotic analysis of a sparse recovery…
Compressed sensing has been a very successful high-dimensional signal acquisition and recovery technique that relies on linear operations. However, the actual measurements of signals have to be quantized before storing or processing.…
Compressed Sensing aims to capture attributes of a sparse signal using very few measurements. Cand\`{e}s and Tao showed that sparse reconstruction is possible if the sensing matrix acts as a near isometry on all $\boldsymbol{k}$-sparse…
Compressed sensing is a developing field aiming at reconstruction of sparse signals acquired in reduced dimensions, which make the recovery process under-determined. The required solution is the one with minimum $\ell_0$ norm due to…
An important receiver operation is to detect the presence specific preamble signals with unknown delays in the presence of scattering, Doppler effects and carrier offsets. This task, referred to as "link acquisition", is typically a…
We consider linear sparse recovery problems where additional structure regarding the support of the solution is known. The form of the structure considered is non-overlapping sets of indices that each contain part of the support. An…
In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a {\rho}0-sparse signal of length N in a time linear in N and (ii) to perfectly recover the…
Compressive sensing (CS) is a signal processing technique that enables sub-Nyquist sampling and near lossless reconstruction of a sparse signal. The technique is particularly appealing for neural signal processing since it avoids the issues…
Compressed Sensing (CS) is an effective approach to reduce the required number of samples for reconstructing a sparse signal in an a priori basis, but may suffer severely from the issue of basis mismatch. In this paper we study the problem…
Compressive sensing (CS) is a new signal acquisition paradigm which shows that far fewer samples are required to reconstruct sparse signals than previously thought. Although most of the literature focuses on signals sparse in a fixed…
Compressive sensing claims that the sparse signals can be reconstructed exactly from many fewer measurements than traditionally believed necessary. One of issues ensuring the successful compressive sensing is to deal with the…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
There is a recent surge of interest in developing algorithms for finding sparse solutions of underdetermined systems of linear equations $y = \Phi x$. In many applications, extremely large problem sizes are envisioned, with at least tens of…
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…
In this paper, the joint support recovery of several sparse signals whose supports present similarities is examined. Each sparse signal is acquired using the same noisy linear measurement process, which returns fewer observations than the…
We study here sparse recovery problems in the presence of additive noise. We analyze a thresholding version of the CoSaMP algorithm, named Thresholding Greedy Pursuit (TGP). We demonstrate that an appropriate choice of thresholding…
The realisation of sensing modalities based on the principles of compressed sensing is often hindered by discrepancies between the mathematical model of its sensing operator, which is necessary during signal recovery, and its actual…
In a recent paper, the authors proposed a new class of low-complexity iterative thresholding algorithms for reconstructing sparse signals from a small set of linear measurements \cite{DMM}. The new algorithms are broadly referred to as AMP,…
We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we…
Compressive Sensing (CS) exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive, often random linear measurements of that signal. Strong theoretical guarantees have…