Improved Sufficient Condition for ℓ₁-ℓ₂-Minimization on Cumulative Coherence

Abstract

The cumulative coherence condition serves as a valuable tool within the realm of Compressed Sensing. However, its application to the $\ell _{1}-\ell _{2}$ -minimization model lacks thorough discussion. This paper aims to address this gap by introducing a sufficient condition for stable recovery of sparse vectors under the $\ell _{1}-\ell _{2}$ -minimization model, building upon the cumulative coherence condition. Moreover, employing graphical analysis, this study contrasts our proposed sufficient condition with existing criteria for stable recovery using both $\ell _{1}-\ell _{2}$ -minimization and $\ell _{1}$ -minimization models. Experimental data illustrate that our proposed sufficiency conditions exhibit less stringent requirements compared to established conclusions.

Keywords

• ℓ₁-ℓ₂-minimization
• cumulative coherence
• sparse signal
• compressed sensing