Pattern coupled sparse Bayesian learning for recovery of time varying sparse signals

In this paper, we consider the problem of recovering time-varying sparse signals whose sparsity patterns change slowly over time. We develop a new sparse Bayesian learning method for recovery of time-varying sparse signals. A pattern-coupled hierarchical Gaussian prior model is introduced to capture the correlation of the temporal support of time-varying sparse signals. Like the conventional sparse Bayesian learning framework, a set of hyperparameters are introduced to control the sparsity of the signal coefficients. The notable difference is that, for our model, the prior for each coefficient not only involves its own hyperparameter, but also the hyperparameters associated with the coefficients of neighboring temporal observations. In doing this way, sparsity patterns of adjacent (in time) coefficients are coupled through their shared hyperparameters. Hence the prior has the potential to encourage temporally correlated sparsity patterns, while without imposing any pre-defined structures on the recovered signals. Simulation results are provided to illustrate the effectiveness of the proposed algorithm.