MMSE Denoising of Sparse Lévy Processes via Message Passing

U. Kamilov, A. Amini, M. Unser

Proceedings of the Thirty-Seventh IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'12), 京都市 (Kyoto), Japan, March 25-30, 2012, pp. 3637–3640.

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Many recent algorithms for sparse signal recovery can be interpreted as maximum-a-posteriori (MAP) estimators relying on some specific priors. From this Bayesian perspective, state-of-the-art methods based on discrete-gradient regularizers, such as total-variation (TV) minimization, implicitly assume the signals to be sampled instances of Lévy processes with independent Laplace-distributed increments. By extending the concept to more general Lévy processes, we propose an efficient minimum-mean-squared error (MMSE) estimation method based on message-passing algorithms on factor graphs. The resulting algorithm can be used to benchmark the performance of the existing or design new algorithms for the recovery of sparse signals.

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DOI: 10.1109/ICASSP.2012.6288704