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Recovery analysis for the ℓ p /ℓ1 minimization problem

  • Zhiyong Zhou ORCID logo EMAIL logo
Published/Copyright: November 15, 2024

Abstract

In this paper, we present a theoretical analysis of the p / 1 minimization method with 0 < p < 1 for sparse signal recovery. We provide a verifiable sufficient condition for the exact noiseless sparse recovery and establish reconstruction error bounds using q-ratio constrained minimal singular values (CMSV) and restricted isometry property (RIP) tools. Additionally, we adopt an efficient algorithm to solve the optimization problem and conduct numerical experiments to demonstrate its superior performance.

MSC 2020: 94A12; 94A20

Award Identifier / Grant number: 12201556

Award Identifier / Grant number: 12361054

Funding statement: This work was supported by the National Natural Science Foundation of China (Grants No. 12201556 and No. 12361054), and the Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ21A010003).

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Received: 2024-07-10
Revised: 2024-10-12
Accepted: 2024-10-28
Published Online: 2024-11-15
Published in Print: 2025-02-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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