@Article{JCM-43-43,
author = {Huang , JianwenZhang , FengLiu , XinlingWang , JianjunJia , Jinping and Wang , Runke},
title = {Stable Recovery of Sparse Signals with Non-Convex Weighted $r$-Norm Minus 1-Norm},
journal = {Journal of Computational Mathematics},
year = {2024},
volume = {43},
number = {1},
pages = {43--62},
abstract = {<p style="text-align: justify;">Given the measurement matrix $A$ and the observation signal $y,$ the central purpose
of compressed sensing is to find the most sparse solution of the underdetermined linear
system $y = Ax+z,$ where $x$ is the $s$-sparse signal to be recovered and $z$ is the noise vector.
Zhou and Yu [Front. Appl. Math. Stat., 5 (2019), Article 14] recently proposed a novel
non-convex weighted $ℓ_r−ℓ_1$ minimization method for effective sparse recovery. In this
paper, under newly coherence-based conditions, we study the non-convex weighted $ℓ_r −ℓ_1$ minimization in reconstructing sparse signals that are contaminated by different noises.
Concretely, the results reveal that if the coherence $\mu$ of measurement matrix $A$ fulfills $$\mu &lt; \kappa (s; r, α, N), s &gt; 1, α^{\frac{1}{r}} N^{\frac{1}{2}} &lt; 1,$$ then any $s$-sparse signals in the noisy scenarios could be ensured to be reconstructed
robustly by solving weighted $ℓ_r − ℓ_1$ minimization non-convex optimization problem. Furthermore, some central remarks are presented to clear that the reconstruction assurance is
much weaker than the existing ones. To the best of our knowledge, this is the first mutual
coherence-based sufficient condition for such approach.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2307-m2022-0225},
url = {http://global-sci.org/intro/article_detail/jcm/23529.html}
}