Aapo Hyvärinen and Patrik Hoyer
A. Hyvärinen. Gaussian Moments for Noisy Independent Component Analysis.
IEEE Signal Processing Letters, 6(6):145--147, 1999.
Abstract
Postscript
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A second approach is to consider the joint likelihood of the mixing matrix and the independent components. See this paper:
A. Hyvärinen. Independent Component Analysis in the Presence
of Gaussian Noise by Maximizing Joint Likelihood. Neurocomputing,
22:49-67, 1998.
Abstract
Postscript
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We have developed a method we call sparse code shrinkage for denoising. It is based on using the ICA representation of the data, e.g. images, which is closely connected to so-called sparse coding. For information on what the ICA representation of images looks like, see this page. Using maximum likelihood estimation of the noise-free independent components, we obtain a method that is quite similar to wavelet shrinkage and coring methods.
Here is an example of the obtained results. Top-left: the original image (standard deviation of pixels is 1.0). Top-right: Gaussian noise of standard deviation 0.5 added. Bottom-left: classic wiener filter restoration. Bottom-right: Sparse Code Shrinkage.
For more details, see the articles available on the publication pages of
Aapo Hyvärinen
and Patrik Hoyer