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.