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A sufficient condition for restoring sparse vectors from ℓ1−ℓ2 $\\ell _1-\\ell _2$ ‐minimization with cumulative coherence
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A sufficient condition for restoring sparse vectors from ℓ1−ℓ2 $\\ell _1-\\ell _2$ ‐minimization with cumulative coherence
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Journal Article
A sufficient condition for restoring sparse vectors from ℓ1−ℓ2 $\\ell _1-\\ell _2$ ‐minimization with cumulative coherence
2023
Overview
This paper focuses on the compressed sensing ℓ1−ℓ2 $\\ell _1-\\ell _2$ ‐minimization model and develops new bounds on cumulative coherence μ1(s) $\\mu _1(s)$ . It is pointed out that if cumulative coherence μ1(s) $\\mu _1(s)$satisfies Equation (2) or (11), then the sparse signal can stably recover in noise model and exactly recover in free noise by ℓ1−ℓ2 $\\ell _1-\\ell _2$ ‐minimization model. From this paper, it is found that based on some condition of cumulative coherence, the ℓ1−ℓ2 $\\ell _1-\\ell _2$ ‐minimization model can exactly recover s‐sparse signals in noiseless cases and stably recover s‐sparse signals in the noise cases.
Publisher
John Wiley & Sons, Inc
