Denoising of Nongaussian Data by Independent Component Analysis and Sparse Coding

Sparse coding is a method for nding a representation of data in which each of the components of the representation is only rarely signiicantly active. Such a representation is closely related to redundancy reduction and independent component analysis, and has some neurophysiological plausibility. In this paper, we show how sparse coding can be used for denoising. Using maximum likelihood estimation of nongaussian variables corrupted by gaussian noise, we show how to apply a shrinkage nonlinearity on the components of sparse coding so as to reduce noise. A theoretical analysis of the denoising capability of the method is given, and it is shown how to choose the optimal basis for sparse coding. Our method is closely related to the method of wavelet shrinkage, but has the the important beneet over wavelet methods that both the features and the shrinkage parameters are estimated directly from the data.