The Capped Separable Difference of Two Norms for Signal Recovery

Zhiyong Zhou and Gui Wang ()
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Zhiyong Zhou: Department of Statistics and Data Science, Hangzhou City University, Hangzhou 310015, China
Gui Wang: Department of Statistics and Data Science, Hangzhou City University, Hangzhou 310015, China

Mathematics, 2024, vol. 12, issue 23, 1-10

Abstract: This paper introduces a novel capped separable difference of two norms (CSDTN) method for sparse signal recovery, which generalizes the well-known minimax concave penalty (MCP) method. The CSDTN method incorporates two shape parameters and one scale parameter, with their appropriate selection being crucial for ensuring robustness and achieving superior reconstruction performance. We provide a detailed theoretical analysis of the method and propose an efficient iteratively reweighted ℓ 1 (IRL1)-based algorithm for solving the corresponding optimization problem. Extensive numerical experiments, including electrocardiogram (ECG) and synthetic signal recovery tasks, demonstrate the effectiveness of the proposed CSDTN method. Our method outperforms existing methods in terms of recovery accuracy and robustness. These results highlight the potential of CSDTN in various signal-processing applications.

Keywords: sparse signal recovery; concave regularization; separable difference of two norms; null-space property; iteratively reweighted ?1 algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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