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The Capped Separable Difference of Two Norms for Signal Recovery

Author

Listed:
  • 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)

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.

Suggested Citation

  • Zhiyong Zhou & Gui Wang, 2024. "The Capped Separable Difference of Two Norms for Signal Recovery," Mathematics, MDPI, vol. 12(23), pages 1-10, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3717-:d:1530494
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    References listed on IDEAS

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    1. Ke-Lin Du & M. N. S. Swamy & Zhang-Quan Wang & Wai Ho Mow, 2023. "Matrix Factorization Techniques in Machine Learning, Signal Processing, and Statistics," Mathematics, MDPI, vol. 11(12), pages 1-50, June.
    2. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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