Stable and robust $\ell_p$-constrained compressive sensing recovery via robust width property

TL;DR

This paper extends the analysis of compressive sensing recovery to the p-constrained case using the robust width property, establishing measurement conditions for Gaussian matrices with high probability.

Contribution

It generalizes previous 2-constrained results to 1p-constrained compressive sensing, providing new theoretical insights and conditions for robust recovery.

Findings

Conditions on measurements for Gaussian matrices are established.

The robust width property is validated for 1p constraints.

Extension of recovery guarantees from 2 to 1p setting.

Abstract

We study the recovery results of $\ell_p$-constrained compressive sensing (CS) with $p\geq 1$ via robust width property and determine conditions on the number of measurements for standard Gaussian matrices under which the property holds with high probability. Our paper extends the existing results in Cahill and Mixon (2014) from $\ell_2$-constrained CS to $\ell_p$-constrained case with $p\geq 1$ and complements the recovery analysis for robust CS with $\ell_p$ loss function.