MMSE denoising of sparse and non-Gaussian AR(1) processes

Pouria Tohidi; Emrah Bostan; Pedram Pad; Michael Unser

ICASSP 2016accepted0 citations

MMSE denoising of sparse and non-Gaussian AR(1) processes

Pouria Tohidi, Emrah Bostan, Pedram Pad, Michael Unser

Abstract

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.

BibTeX

@inproceedings{icassp2016_mmsedenoisingofs,
  title = {MMSE denoising of sparse and non-Gaussian AR(1) processes},
  author = {Pouria Tohidi and Emrah Bostan and Pedram Pad and Michael Unser},
  booktitle = {ICASSP 2016},
  year = {2016}
}