Towards dictionary learning from images with non Gaussian noise

We address the problem of image dictionary learning from noisy images with non Gaussian noise. This problem is difficult. As a first step, we consider the extreme sparse code given by vector quantization, i.e. each pixel is finally associated to 1 single atom. For Gaussian noise, the natural solution is K-means clustering using the sum of the squares of differences between gray levels as the dissimilarity measure between patches. For non Gaussian noises (Poisson, Gamma,...), a new measure of dissimilarity between noisy patches is necessary. We study the use of the generalized likelihood ratios (GLR) recently introduced by Deledalle et al. in [1] to compare non Gaussian noisy patches. We propose a K-medoids algorithm generalizing the usual Linde-Buzo-Gray K-means using the GLR based dissimilarity measure. We obtain a vector quantization which provides a dictionary that can be very large and redundant. We illustrate our approach by dictionaries learnt from images featuring non Gaussian noise, and present preliminary denoising results.