Minimum Complexity Pursuit: Stability Analysis

TL;DR

This paper extends the analysis of a universal recovery algorithm for structured signals, like sparse signals and low-rank matrices, from noise-free to noisy measurement scenarios, ensuring stability.

Contribution

It provides a stability analysis for the Minimum Complexity Pursuit algorithm in noisy environments, broadening its applicability to real-world scenarios.

Findings

The algorithm remains stable under noisy conditions.

Recovery guarantees extend from noise-free to noisy measurements.

Universal recovery is feasible for various structured signals.

Abstract

A host of problems involve the recovery of structured signals from a dimensionality reduced representation such as a random projection; examples include sparse signals (compressive sensing) and low-rank matrices (matrix completion). Given the wide range of different recovery algorithms developed to date, it is natural to ask whether there exist "universal" algorithms for recovering "structured" signals from their linear projections. We recently answered this question in the affirmative in the noise-free setting. In this paper, we extend our results to the case of noisy measurements.