Derandomized compressed sensing with nonuniform guarantees for ℓ_1 recovery

12/27/2019
by   Charles Clum, et al.
0

We extend the techniques of Hügel, Rauhut and Strohmer (Found. Comput. Math., 2014) to show that for every δ∈(0,1], there exists an explicit random m× N partial Fourier matrix A with m=spolylog(N/ϵ) and entropy s^δpolylog(N/ϵ) such that for every s-sparse signal x∈C^N, there exists an event of probability at least 1-ϵ over which x is the unique minimizer of z_1 subject to Az=Ax. The bulk of our analysis uses tools from decoupling to estimate the extreme singular values of the submatrix of A whose columns correspond to the support of x.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/05/2016

Sparse Recovery Guarantees from Extreme Eigenvalues Small Deviations

This article provides a new toolbox to derive sparse recovery guarantees...
research
07/02/2020

Local recovery bounds for prior support constrained Compressed Sensing

Prior support constrained compressed sensing has of late become popular ...
research
07/19/2022

A coherence parameter characterizing generative compressed sensing with Fourier measurements

In Bora et al. (2017), a mathematical framework was developed for compre...
research
10/30/2014

Two New Approaches to Compressed Sensing Exhibiting Both Robust Sparse Recovery and the Grouping Effect

In this paper we introduce a new optimization formulation for sparse reg...
research
10/10/2016

Robust Bayesian Compressed sensing

We consider the problem of robust compressed sensing whose objective is ...
research
04/13/2020

Analysis of The Ratio of ℓ_1 and ℓ_2 Norms in Compressed Sensing

We first propose a novel criterion that guarantees that an s-sparse sign...
research
06/29/2016

Small coherence implies the weak Null Space Property

In the Compressed Sensing community, it is well known that given a matri...

Please sign up or login with your details

Forgot password? Click here to reset