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

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.