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Complex Sparse Signal Recovery with Adaptive Laplace Priors

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Document pages: 13 pages

Abstract: Because of its self-regularizing nature and uncertainty estimation, theBayesian approach has achieved excellent recovery performance across a widerange of sparse signal recovery applications. However, most methods are basedon the real-value signal model, with the complex-value signal model rarelyconsidered. Typically, the complex signal model is adopted so that phaseinformation can be utilized. Therefore, it is non-trivial to develop Bayesianmodels for the complex-value signal model. Motivated by the adaptive leastabsolute shrinkage and selection operator (LASSO) and the sparse Bayesianlearning (SBL) framework, a hierarchical model with adaptive Laplace priors isproposed for applications of complex sparse signal recovery in this paper. Theproposed hierarchical Bayesian framework is easy to extend for the case ofmultiple measurement vectors. Moreover, the space alternating principle isintegrated into the algorithm to avoid using the matrix inverse operation. Inthe experimental section of this work, the proposed algorithm is concerned withboth complex Gaussian random dictionaries and directions of arrival (DOA)estimations. The experimental results show that the proposed algorithm offersbetter sparsity recovery performance than the state-of-the-art methods fordifferent types of complex signals.

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