A unified algorithmic framework for dynamic compressive sensing

Abstract

We present a unified algorithmic framework, termed PLAY-CS, for dynamic tracking and reconstruction of signal sequences exhibiting intrinsic structured dynamic sparsity. By leveraging specific statistical assumptions on the dynamic filtering of these sequences, our framework integrates a variety of existing dynamic compressive sensing (DCS) algorithms. This is facilitated by the introduction of a novel Partial-Laplacian filtering sparsity model, which is designed to capture more complex dynamic sparsity patterns. Within this unified DCS framework, we derive a new algorithm, ${\text{PLAY}}^{+}$-CS. Notably, the ${\text{PLAY}}^{+}$-CS algorithm eliminates the need for a priori knowledge of dynamic signal parameters, as these are adaptively learned through an expectation–maximization framework. Moreover, we extend the ${\text{PLAY}}^{+}$-CS algorithm to tackle the dynamic joint sparse signal reconstruction problem involving multiple measurement vectors. The proposed framework demonstrates superior performance in practical applications, such as real-time massive multiple-input multiple-output (MIMO) communication for dynamic channel tracking and background subtraction from online compressive measurements, outperforming existing DCS algorithms.