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Sparse Signal Recovery for Multiple Measurement Vectors with Temporally Correlated Entries: A Bayesian Perspective

Bayesian Sparse Signal Recovery (SSR) for Multiple Measurement Vectors, when elements of each row of solution matrix are correlated, is addressed in the paper. We propose a standard linear Gaussian observation model and a three-level hierarchical estimation framework, based on Gaussian Scale Mixture (GSM) model with some random and deterministic parameters, to model each row of the unknown solution matrix. This hierarchical model induces heavy-tailed marginal distribution over each row which encompasses several choices of distributions viz. Laplace distribution, Student's t distribution and Jeffery prior. Automatic Relevance Determination (ARD) phenomenon introduces sparsity in the model. It is interesting to see that Block Sparse Bayesian Learning framework is a special case of the proposed framework when induced marginal is Jeffrey prior. Experimental results for synthetic signals are provided to demonstrate its effectiveness. We also explore the possibility of using Multiple Measurement Vectors to model Dynamic Hand Posture Database which consists of sequence of temporally correlated hand posture sequence. It can be seen that by exploiting temporal correlation information present in the successive image samples, the proposed framework can reconstruct the data with less linear random measurements with high fidelity.