Compressive Bayesian K-SVD

•A novel fully-automated compressive dictionary learning method is proposed.•All the parameters including the sparsity are estimated through Bayesian inference.•Our method achieves high performance at both signal recovery and classification.

Compressed Sensing (CS) is an established way to perform efficient dimensionality reduction during a signal's acquisition process. However, the common transform bases used in CS to represent a signal often lead to a compressible representation that is not optimal in terms of compactness. In this paper we present a novel dictionary learning algorithm designed to work with CS data. Following our approach, dictionaries learned directly from the signal's random projections are specifically suited to the signal class of interest, resulting in very sparse representations. Moreover, since the proposed method lays its foundation in a Bayesian dictionary learning algorithm, no prior information such as the signals' sparsity is needed because it is inferred directly from the data. We show the superiority of our approach by comparing it with a state-of-the-art CS dictionary learning algorithm.