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L_p-Spherically Symmetric and L_p-nested Distributions for Patches of Natural Images

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Abstract: In this talk I will present our recent work on modelling patches of natural images with the class of Lp-sherically symmetric distributions and extension thereof. This class of distributions has many favorable properties like efficient maximum likelihood estimators and an easy sampling scheme. It not only contains the factorial Laplacian or the spherically symmetric model which are frequently used in image processing, but also a whole variety of intermediate models. I will demonstrate how this class gives rise to a simple non-linear mechanism severly reducing the higher order dependencies between linear filter responses on natural images. Finally, I will present a generalization of that class by replacing a single Lp-norm by an arbitrary cascade of Lp-norms. This class—-called Lp-nested symmetric distributions—-offers more flexibility while preserving the nice properties of Lp-spherically symmetric distributions. Additionally, it contains the probability models corresponding to mixed-norm regularizers which have recently gained increasing attention.

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