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Compressive parameter estimation via approximate message passing

The literature on compressive parameter estimation has been mostly focused on the use of sparsity dictionaries that encode a sampling of the parameter space; these dictionaries, however, suffer from coherence issues that must be controlled for successful estimation. We propose the use of statistical parameter estimation methods within the approximate message passing (AMP) algorithm for signal recovery. Our proposed work leverages the recently highlighted connection between statistical denoising methods and the thresholding step commonly used during recovery. As an example, we consider line spectral estimation by leveraging the well-known Root MUSIC algorithm. Numerical experiments show significant improvements in estimation performance.