Frames for compressed sensing using coherence

TL;DR

This paper presents new theoretical results on sparse signal recovery in noisy environments using weighted spaces, improving upon existing estimations for random dictionaries with non-unit norms.

Contribution

It introduces novel bounds and results for compressed sensing with weighted spaces, extending traditional dictionary assumptions to more general cases.

Findings

Improved estimations for sparse recovery in noisy settings.

Results applicable to dictionaries with non-unit norms.

Enhanced theoretical bounds compared to previous work.

Abstract

We give some new results on sparse signal recovery in the presence of noise, for weighted spaces. Traditionally, were used dictionaries that have the norm equal to 1, but, for random dictionaries this condition is rarely satisfied. Moreover, we give better estimations then the ones given recently by Cai, Wang and Xu.