Streaming signal recovery using sparse Bayesian learning

We consider the progressive reconstruction of a streaming signal from compressive measurements. We reconstruct the streaming signal over shifting intervals using an algorithm based on sparse Bayesian learning (SBL). Although computationally expensive, compared to other recovery algorithms, SBL provide the full posterior distribution of the sparse coefficients rather than computing only a point estimate. We propose a modified SBL algorithm, which utilizes the previous estimates as well as their reconstruction errors to improve the performance of the algorithm. A warm-start procedure and fast update equations are proposed to reduce the computational cost and improve the speed of the SBL algorithm.