Denoising of Sensory Data by Maximum Likelihood Estimation of Sparse Components

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.