Learning optimal orders of the underlying Euclidean norm in total variation image denoising

2019/03/28 by Liu, Pan, Schönlieb, Carola-Bibiane
#26B30 #47J20 #94A08 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.11953

Abstract

A novel class of semi-norms, generalising the notion of the isotropic total variation TV₂ and the an-isotropic total variation TV₁ is introduced. A supervised learning method via bilevel optimisation is proposed for the computation of optimal parameters for this class of regularizers. Existence of solutions to the bilevel optimisation approach is proven. Moreover, a finite-dimensional approximation scheme for the bilevel optimisation approach is introduced that can numerically compute a global optimizer to any given accuracy.

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