Analysis-based sparse reconstruction with synthesis-based solvers

On the optimality of a L1/L1 solver for sparse signal recovery from sparsely corrupted compressive measurements

This short note proves the $\ell_2-\ell_1$ instance optimality of a $\ell_1/\ell_1$ solver, i.e a variant of \emph{basis pursuit denoising} with a $\ell_1$ fidelity constraint, when applied to the estimation of sparse (or compressible) signals observed by sparsely corrupted compressive measurements. The approach simply combines two known results due to Y. Plan, R. Vershynin and E. Candès.

Analysis and Synthesis Prior Greedy Algorithms for Non-linear Sparse Recovery

In this work we address the problem of recovering sparse solutions to non linear inverse problems. We look at two variants of the basic problem, the synthesis prior problem when the solution is sparse and the analysis prior problem where the solution is cosparse in some linear basis. For the first problem, we propose non linear variants of the Orthogonal Matching Pursuit (OMP) and CoSamp algorithms; for the second problem we propose a non linear variant of the Greedy Analysis Pursuit (GAP) algorithm. We empirically test the success rates of our algorithms on exponential and logarithmic functio…

Can we allow linear dependencies in the dictionary in the sparse synthesis framework?

Signal recovery from a given set of linear measurements using a sparsity prior has been a major subject of research in recent years. In this model, the signal is assumed to have a sparse representation under a given dictionary. Most of the work dealing with this subject has focused on the reconstruction of the signal's representation as the means for recovering the signal itself. This approach forced the dictionary to be of low coherence and with no linear dependencies between its columns. Recently, a series of contributions that focus on signal recovery using the analysis model find that line…

Analysis-by-Synthesis Quantization for Compressed Sensing Measurements

We consider a resource-limited scenario where a sensor that uses compressed sensing (CS) collects a low number of measurements in order to observe a sparse signal, and the measurements are subsequently quantized at a low bit-rate followed by transmission or storage. For such a scenario, we design new algorithms for source coding with the objective of achieving good reconstruction performance of the sparse signal. Our approach is based on an analysis-by-synthesis principle at the encoder, consisting of two main steps: (1) the synthesis step uses a sparse signal reconstruction technique for meas…

一种稀疏Kaczmarz求解器和线性化Bregman方法用于在线压缩感知

A sparse Kaczmarz solver and a linearized Bregman method for online compressed sensing

本文提出了一种计算稀疏或最小TV解的线性系统算法框架，包含Kaczmarz方法和线性化Bregman方法作为特例，并引入了稀疏Kaczmarz求解器等新方法，适用于测量缓慢且昂贵的在线压缩感知、TV断层成像和射电干涉测量等问题。

The Design of Sparse Antenna Array

The aim of antenna array synthesis is to achieve a desired radiation pattern with the minimum number of antenna elements. In this paper the antenna synthesis problem is studied from a totally new perspective. One of the key principles of compressive sensing is that the signal to be sensed should be sparse or compressible. This coincides with the requirement of minimum number of element in the antenna array synthesis problem. In this paper the antenna element of the array can be efficiently reduced via compressive sensing, which shows a great improvement to the existing antenna synthesis method…