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Computing one-bit compressive sensing via zero-norm regularized DC loss model and its surrogate

Author

Listed:
  • Kai Chen

    (Renmin University of China)

  • Ling Liang

    (Guangzhou College of Technology and Business)

  • Shaohua Pan

    (South China University of Technology)

Abstract

One-bit compressed sensing is very popular in signal processing and communications due to its low storage costs and hardware complexity, but it is challenging to recover the signal by the one-bit information. In this paper, we propose a zero-norm regularized smooth difference of convexity (DC) loss model and derive a family of equivalent nonconvex surrogates covering the MCP and SCAD ones. Compared with the existing models, the new model and its SCAD surrogate have better robustness. To apply the proximal gradient (PG) methods with extrapolation to compute their $$\tau $$ τ -critical points, we provide the expression of the proximal mapping of the zero-norm (resp. $$\ell _1$$ ℓ 1 -norm) plus the indicator of unit sphere. In particular, we prove that under a mild condition, the objective functions of the proposed model and its SCAD surrogate are the KL function of exponent 0, so that the PG methods with extrapolation applied to them possess a local R-linear convergence rate and the PG methods applied to them have a finite termination. Numerical comparisons with several state-of-art methods show that in terms of the quality of solution, the proposed models are remarkably superior to the $$\ell _p$$ ℓ p -norm regularized models, and are comparable even superior to those models with a sparsity constraint involving the true sparsity and the sign flip ratio as inputs.

Suggested Citation

  • Kai Chen & Ling Liang & Shaohua Pan, 2025. "Computing one-bit compressive sensing via zero-norm regularized DC loss model and its surrogate," Journal of Global Optimization, Springer, vol. 92(3), pages 775-807, July.
    • Handle: RePEc:spr:jglopt:v:92:y:2025:i:3:d:10.1007_s10898-025-01495-4
    DOI: 10.1007/s10898-025-01495-4
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    References listed on IDEAS

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    1. Dongdong Zhang & Shaohua Pan & Shujun Bi & Defeng Sun, 2023. "Zero-norm regularized problems: equivalent surrogates, proximal MM method and statistical error bound," Computational Optimization and Applications, Springer, vol. 86(2), pages 627-667, November.
    2. Hédy Attouch & Jérôme Bolte & Patrick Redont & Antoine Soubeyran, 2010. "Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 438-457, May.
    3. 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.
    4. Yuqia Wu & Shaohua Pan & Shujun Bi, 2021. "Kurdyka–Łojasiewicz Property of Zero-Norm Composite Functions," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 94-112, January.
    5. J. Paul Brooks, 2011. "Support Vector Machines with the Ramp Loss and the Hard Margin Loss," Operations Research, INFORMS, vol. 59(2), pages 467-479, April.
    6. Yulan Liu & Shujun Bi & Shaohua Pan, 2018. "Equivalent Lipschitz surrogates for zero-norm and rank optimization problems," Journal of Global Optimization, Springer, vol. 72(4), pages 679-704, December.
    7. Yitian Qian & Shaohua Pan & Yulan Liu, 2023. "Calmness of partial perturbation to composite rank constraint systems and its applications," Journal of Global Optimization, Springer, vol. 85(4), pages 867-889, April.
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