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Open AccessArticle
Data-Driven Method for Robust Recovery in 1-Bit Compressive Sensing with the Minimax Concave Penalty
by
Cui Jia
Cui Jia 1,2
and
Li Zhu
Li Zhu 1,*
1
School of Statistics and Data Science, Ningbo University of Technology, No. 201, Fenghua Road, Jiangbei District, Ningbo 315211, China
2
School of mathematics and Statistics, Wuhan University, Wuhan 430072, China
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(14), 2168; https://doi.org/10.3390/math12142168 (registering DOI)
Submission received: 12 June 2024
/
Revised: 6 July 2024
/
Accepted: 8 July 2024
/
Published: 10 July 2024
Abstract
With the advent of large-scale data, the demand for information is increasing, which makes signal sampling technology and digital processing methods particularly important. The utilization of 1-bit compressive sensing in sparse recovery has garnered significant attention due to its cost-effectiveness in hardware implementation and storage. In this paper, we first leverage the minimax concave penalty equipped with the least squares to recover a high-dimensional true signal with k-sparse from n-dimensional 1-bit measurements and discuss the regularization by combing the nonconvex sparsity-inducing penalties. Moreover, we give an analysis of the complexity of the method with minimax concave penalty in certain conditions and derive the general theory for the model equipped with the family of sparsity-inducing nonconvex functions. Then, our approach employs a data-driven Newton-type method with stagewise steps to solve the proposed method. Numerical experiments on the synthesized and real data verify the competitiveness of the proposed method.
Share and Cite
MDPI and ACS Style
Jia, C.; Zhu, L.
Data-Driven Method for Robust Recovery in 1-Bit Compressive Sensing with the Minimax Concave Penalty. Mathematics 2024, 12, 2168.
https://doi.org/10.3390/math12142168
AMA Style
Jia C, Zhu L.
Data-Driven Method for Robust Recovery in 1-Bit Compressive Sensing with the Minimax Concave Penalty. Mathematics. 2024; 12(14):2168.
https://doi.org/10.3390/math12142168
Chicago/Turabian Style
Jia, Cui, and Li Zhu.
2024. "Data-Driven Method for Robust Recovery in 1-Bit Compressive Sensing with the Minimax Concave Penalty" Mathematics 12, no. 14: 2168.
https://doi.org/10.3390/math12142168
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