Anti-measurement Matrix Uncertainty Sparse Signal Recovery for Compressive Sensing

TL;DR

This paper introduces an anti-uncertainty sparse signal recovery method for compressive sensing that effectively handles measurement matrix uncertainty, improving reconstruction performance over traditional techniques.

Contribution

It proposes a novel anti-uncertainty constraint combining L2 and L1 norms to enhance sparse signal recovery under measurement matrix uncertainty.

Findings

Improved reconstruction accuracy with measurement matrix uncertainty.

The proposed method outperforms traditional recovery techniques.

Numerical simulations validate the effectiveness of the approach.

Abstract

Compressive sensing (CS) is a technique for estimating a sparse signal from the random measurements and the measurement matrix. Traditional sparse signal recovery methods have seriously degeneration with the measurement matrix uncertainty (MMU). Here the MMU is modeled as a bounded additive error. An anti-uncertainty constraint in the form of a mixed L2 and L1 norm is deduced from the sparse signal model with MMU. Then we combine the sparse constraint with the anti-uncertainty constraint to get an anti-uncertainty sparse signal recovery operator. Numerical simulations demonstrate that the proposed operator has a better reconstructing performance with the MMU than traditional methods.