Approximate Message Passing with Built-in Parameter Estimation for Sparse Signal Recovery

The approximate message passing (AMP) algorithm shows advantage over conventional convex optimization methods in recovering under-sampled sparse signals. AMP is analytically tractable and has a much lower complexity. However, it requires that the true parameters of the input and output channels are known. In this paper, we propose an AMP algorithm with built-in parameter estimation that jointly estimates the sparse signals along with the parameters by treating them as unknown random variables with simple priors. Specifically, the maximum a posterior (MAP) parameter estimation is presented and shown to produce estimations that converge to the true parameter values. Experiments on sparse signal recovery show that the performance of the proposed approach matches that of the oracle AMP algorithm where the true parameter values are known.

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