Statistical Recovery of Simultaneously Sparse Time-Varying Signals from Multiple Measurement Vectors

TL;DR

This paper introduces the sparse Kalman tree search (sKTS), a new algorithm for robustly recovering time-varying sparse signals from multiple correlated measurements, combining EM, Kalman smoothing, and greedy support estimation.

Contribution

The paper presents a novel sKTS algorithm that integrates EM, Kalman smoothing, and greedy tree search for improved sparse signal recovery in time-varying scenarios.

Findings

sKTS performs close to oracle Kalman estimators.

Effective in recovering correlated sparse signals.

Demonstrated through numerical experiments.

Abstract

In this paper, we propose a new sparse signal recovery algorithm, referred to as sparse Kalman tree search (sKTS), that provides a robust reconstruction of the sparse vector when the sequence of correlated observation vectors are available. The proposed sKTS algorithm builds on expectation-maximization (EM) algorithm and consists of two main operations: 1) Kalman smoothing to obtain the a posteriori statistics of the source signal vectors and 2) greedy tree search to estimate the support of the signal vectors. Through numerical experiments, we demonstrate that the proposed sKTS algorithm is effective in recovering the sparse signals and performs close to the Oracle (genie-based) Kalman estimator.