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MMSE Denoising of Sparse and Non-Gaussian AR(1) Processes

P. Tohidi, E. Bostan, P. Pad, M. Unser

Proceedings of the Forty-First IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'16), Shanghai, People's Republic of China, March 20-25, 2016, pp. 4333-4337.



We propose two minimum-mean-square-error (MMSE) estimation methods for denoising non-Gaussian first-order autoregressive (AR(1)) processes. The first one is based on the message passing framework and gives the exact theoretic MMSE estimator. The second is an iterative algorithm that combines standard wavelet-based thresholding with an optimized non-linearity and cycle-spinning. This method is more computationally efficient than the former and appears to provide the same optimal denoising results in practice. We illustrate the superior performance of both methods through numerical simulations by comparing them with other well-known denoising schemes.


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