Consistency of l1 recovery from noisy deterministic measurements

TL;DR

This paper proves that l1 minimization can reliably recover sparse and compressible vectors from noisy deterministic measurements with high probability, extending previous results to more general models.

Contribution

It introduces a new theoretical result demonstrating the consistency of l1 minimization for noisy deterministic measurements, including extensions to compressible vectors.

Findings

High-probability recovery guarantees for sparse vectors

Extension of results to compressible vectors

Theoretical validation of l1 minimization robustness

Abstract

In this paper a new result of recovery of sparse vectors from deterministic and noisy measurements by l1 minimization is given. The sparse vector is randomly chosen and follows a generic p-sparse model introduced by Candes and al. The main theorem ensures consistency of l1 minimization with high probability. This first result is secondly extended to compressible vectors.