Hierarchical Sparse Signal Recovery by Variational Bayesian Inference

This letter addresses the recovery of hierarchical sparse signals in a Bayesian framework. Hierarchical sparse signals exhibit two levels of sparsity, i.e., block-sparsity among different blocks and internal sparsity within each individual block. As in sparse Bayesian learning, each component of the coefficient vector is firstly modeled as a Gaussian distributed variable with zero mean. To enforce the two-level hierarchical sparsity, the variance is further modeled by two classes of hidden variables controlling the block-sparsity and the internal sparsity, respectively. Finally, variational Bayesian inference is used to recover the coefficient vector from the noise corrupted data. Numerical simulation and experimental results show that the proposed method outperforms those recently reported recovery methods.