Estimation of Dynamically Varying Support of Sparse Signals via Sequential Monte-Carlo Method

Abstract

In this paper, we address the problem of tracking time-varying support of a sparse signal given a sequence of observation vectors. We model the dynamic variation of the support set using the discrete-state Markov process and employ the Rao-Blackwellized sequential Monte Carlo method, which allows for separate tracking of the support set and the amplitude of the unknown signals. Specifically, the samples for the support variables are drawn from their posteriori joint distributions using a Gibbs sampler while the continuous amplitude variables are separately estimated using the Kalman filter. Our numerical evaluation shows that the proposed method achieves significant performance gain over the existing sparse estimation methods.