Subspace Constrained Variational Bayesian Inference for Structured Compressive Sensing with a Dynamic Grid

TL;DR

This paper introduces a subspace constrained variational Bayesian inference method for structured compressive sensing, significantly improving convergence speed and computational efficiency in dynamic grid scenarios.

Contribution

The paper proposes a novel SC-VBI framework that replaces high-dimensional matrix inverses with low-dimensional ones, enhancing efficiency and convergence in structured compressive sensing.

Findings

SC-VBI achieves faster convergence than existing methods.

The algorithm offers a better tradeoff between complexity and accuracy.

Simulation results validate improved performance over state-of-the-art algorithms.

Abstract

We investigate the problem of recovering a structured sparse signal from a linear observation model with an uncertain dynamic grid in the sensing matrix. The state-of-the-art expectation maximization based compressed sensing (EM-CS) methods, such as turbo compressed sensing (Turbo-CS) and turbo variational Bayesian inference (Turbo-VBI), have a relatively slow convergence speed due to the double-loop iterations between the E-step and M-step. Moreover, each inner iteration in the E-step involves a high-dimensional matrix inverse in general, which is unacceptable for problems with large signal dimensions or real-time calculation requirements. Although there are some attempts to avoid the high-dimensional matrix inverse by majorization minimization, the convergence speed and accuracy are often sacrificed. To better address this problem, we propose an alternating estimation framework based on a novel subspace constrained VBI (SC-VBI) method, in which the high-dimensional matrix inverse is replaced by a low-dimensional subspace constrained matrix inverse (with the dimension equal to the sparsity level). We further prove the convergence of the SC-VBI to a stationary solution of the Kullback-Leibler divergence minimization problem. Simulations demonstrate that the proposed SC-VBI algorithm can achieve a much better tradeoff between complexity per iteration, convergence speed, and performance compared to the state-of-the-art algorithms.