Hybrid message passing for total variation regularized linear regression

Abstract

Total variation regularized linear regression has emerged as a dynamic research area in signal processing. Classical algorithms often struggle with high correlation in the unknown signal, which can impair their performance. This paper introduces a novel algorithm that addresses this challenge by integrating elements of traditional scalar-form message passing with recent innovations in vector-form message passing. The proposed approach not only captures the intricate structure within the signal but also efficiently handles high-dimensional inference tasks. When the prior of the target signal contains unknown parameters, the hybrid message-passing algorithm can be incorporated into a broader Expectation-Maximization framework, enabling iterative refinement of the parameter estimates. Furthermore, a set of state evolution (SE) equations is provided to describe the behavior of the proposed algorithm. Although derived heuristically, the SE equations empirically align with the algorithm’s mean squared error (MSE) performance with remarkable accuracy.