Iterative Bayesian Reconstruction of Non-IID Block-Sparse Signals
This addresses signal reconstruction in practical applications where block structures are non-i.i.d., offering an incremental improvement over existing methods.
This paper tackles the problem of reconstructing block-sparse signals with unknown block structures by proposing a Block Iterative Bayesian Algorithm (Block-IBA) that uses a Bernoulli-Gaussian hidden Markov model to handle non-i.i.d. signals, achieving effectiveness as demonstrated through numerical experiments and simulations.
This paper presents a novel Block Iterative Bayesian Algorithm (Block-IBA) for reconstructing block-sparse signals with unknown block structures. Unlike the existing algorithms for block sparse signal recovery which assume the cluster structure of the nonzero elements of the unknown signal to be independent and identically distributed (i.i.d.), we use a more realistic Bernoulli-Gaussian hidden Markov model (BGHMM) to characterize the non-i.i.d. block-sparse signals commonly encountered in practice. The Block-IBA iteratively estimates the amplitudes and positions of the block-sparse signal using the steepest-ascent based Expectation-Maximization (EM), and optimally selects the nonzero elements of the block-sparse signal by adaptive thresholding. The global convergence of Block-IBA is analyzed and proved, and the effectiveness of Block-IBA is demonstrated by numerical experiments and simulations on synthetic and real-life data.