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A Bayesian Approach to Total Least‐Squares in Perturbed Compressive Sensing

Year: 2025

Type: article

Abstract: ABSTRACT This paper introduces a Bayesian total least‐squares (B‐TLS) formulation to address the perturbed compressive sensing problem. Due to the presence of a nonconvex nonseparable penalty, applying the traditional alternating minimization method to this formulation poses mathematical and computational challenges. To mitigate this problem, we propose a Bayesian proximal alternating linearized minimization (BPALM) algorithm. In this algorithm, each subproblem is characterized by convexity and yields solutions that are explicit and analytical. We further demonstrate the convergence of the proposed algorithm towards a stationary point of the objective function. Numerical experiments in sparse signal recovery are conducted to exhibit the proposed algorithm's effectiveness and superiority, focusing on its computational efficiency and estimation accuracy.

Source: International Journal of Adaptive Control and Signal Processing

DOI: 10.1002/acs.70006

Authors: Junlin Li, Weiwei Sun, Feng Ding, Renzhi Lu

Institutions: Fuyang Normal University, Jiangnan University, Huazhong University of Science and Technology

Language: English

Topic: Sparse and Compressive Sensing Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, University Natural Science Research Project of Anhui Province

OpenAlex ID: W4416613893

FWCI:

Cites: 35

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