Image Denoising by Sparse Code Shrinkage

Sparse coding is a method for finding a representation of data in which each of the components of the representation is only rarely significantlyactive. Such a representation isclosely related to independent component analysis (ICA) and has some neurophysiological plausibility. In this chapter, we show how sparse coding can be used for image denoising. We model the noise-free image data by independent component analysis and denoise a noisy image by maximum likelihood estimation of the noisy version of the ICA model. This leads to the application of a soft-thresholding (shrinkage) operator on the components of sparse coding. Our method is closely related to the method of wavelet shrinkage and coring methods, but it has the important benefit that the representation is determined solely by the statistical properties of the data. In fact, our method can be seen as a simple rederivation of the wavelet shrinkage method for image data, using just the basic principle of maximum likelihood estimation. On the other hand, it allows the method to adapt to different kinds of data sets.