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

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.