Phase retrieval for block sparsity based on adaptive coupled variational Bayesian learning

Phase retrieval (PR) of block-sparse signals is a new branch of sparse PR that causes rising research, which focusses with methods owing a high successful rate. However, the recovery performances of existing methods for block sparsity are usually unfit for large-scale problems with unacceptable compute complexity. We derive an algorithm for PR of block sparsity via variational Bayesian learning with expectation maximisation to mitigate this drawback. In the proposed algorithm, the block-sparse structure is modelled by the hierarchical constructional priors with a novel adaptive coupled pattern, which provides a strong relationship between the neighbour blocks. Simulations indicate that the proposed algorithm outperforms the existing methods in success rate, noise-robustness, and signal detection rate in large-scale cases with acceptable computation complexity.