Sparse Bayesian learning with dictionary refinement for super-resolution through time

This work proposes an extension of a sparse Bayesian learning with dictionary refinement (SBL-DR) algorithm for a super-resolution estimation of time-varying sparse signals. Such signals are represented as a superposition of unknown but fixed number of Dirac measures with a time-varying support; as such the signal is sparse at each moment of time yet locations of Dirac measures are allowed to vary. To recover such signals an optimization framework is proposed that combines SBL-DR techniques and a penalty term that imposes smoothness constraints on the support variations in time. In contrast to state-of-the-art approaches, which typically combine parameter estimation schemes with some tracking filters, the proposed approach leads to a single objective function that permits a joint recovery of a sparse superposition of time-varying functions (trajectories). A numerical algorithm for efficient optimization of the corresponding cost function is proposed and analyzed; its performance is compared to a Kalman Enhanced Superresolution Tracking algorithm on an example of estimating parameters of time-varying multipath channels.