Multiple Hypothesis Testing for Dynamic Support Recovery

This paper considers the problem of dynamic support recovery for jointly sparse signals from underdetermined measurements. Unlike Multiple Measurement Vector (MMV) models that assume a fixed support for all time instances, we allow the support to vary temporally following a finite state Markov chain. Instead of using l(1) minimization based algorithms, we cast the problem of dynamic support recovery as a multiple-hypothesis testing problem and analyze its performance. We derive an upper bound on the probability of error for the optimal decision rule which explicitly highlights the role of the time-varying priors associated with the Markov Chain. The results are valid for any transition probability matrix and choice of initial priors, and can also be used to study the MMV model as a special case.