Support knowledge-aided sparse Bayesian learning for compressed sensing

In this paper, we study the problem of sparse signal recovery when partial but partly erroneous prior knowledge of the signal´s support is available. Based on the conventional sparse Bayesian learning framework, we propose an improved hierarchical prior model. The proposed modeling constitutes a three-layer hierarchical form. The first two layers, similar to the conventional sparse Bayesian learning, place a Gaussian-inverse-Gamma prior on the signal, while the third layer is newly added, with a prior placed on the parameters {b_i}, where {b_i} are parameters characterizing the sparsity-controlling hyperparameters {α_i}. Such a modeling enables to automatically learn the true support from partly erroneous information through learning the values of the parameters {b_i}. A variational Bayesian inference algorithm is developed based on the proposed prior model. Numerical results are provided to illustrate the performance of the proposed algorithm.