New Accumulative Score Function Based Bound For Sparsity Level of L1 Minimization

TL;DR

This paper introduces a new accumulative score function (ASF) that provides a computationally efficient and sharper lower bound for the sparsity level recoverable by L1 minimization in compressed sensing, outperforming traditional coherence bounds.

Contribution

The paper proposes a novel ASF method to estimate the recoverable sparsity level with improved accuracy and lower computational complexity compared to existing bounds.

Findings

ASF offers a sharper lower bound for sparsity level than coherence.

ASF relates to RIC, enabling RIC-based bounds for SL.

ASF maintains low computational complexity.

Abstract

This paper discusses a fundamental problem in compressed sensing: the sparse recoverability of L1 minimization with an arbitrary sensing matrix. We develop an new accumulative score function (ASF) to provide a lower bound for the recoverable sparsity level (SL) of a sensing matrix while preserving a low computational complexity. We first define a score function for each row of a matrix, and then ASF sums up large scores until the total score reaches 0.5. Interestingly, the number of involved rows in the summation is a reliable lower bound of SL. It is further proved that ASF provides a sharper bound for SL than coherence We also investigate the underlying relationship between the new ASF and the classical RIC and achieve a RIC-based bound for SL.