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arXiv · 2210.11958

Non-local $BV$ functions and a denoising model with $L^1$ fidelity

Konstantinos Bessas·Giorgio Stefani
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Abstract

We study a general total variation denoising model with weighted $L^1$ fidelity, where the regularizing term is a non-local variation induced by a suitable (non-integrable) kernel $K$, and the approximation term is given by the $L^1$ norm with respect to a non-singular measure with positively lower-bounded $L^\infty$ density. We provide a detailed analysis of the space of non-local $BV$ functions with finite total $K$-variation, with special emphasis on compactness, Lusin-type estimates, Sobolev embeddings and isoperimetric and monotonicity properties of the $K$-variation and the associated $K$-perimeter. Finally, we deal with the theory of Cheeger sets in this non-local setting and we apply it to the study of the fidelity in our model.

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BibTeXRIS

Konstantinos Bessas, Giorgio Stefani. 2022-10-21. Non-local $BV$ functions and a denoising model with $L^1$ fidelity. https://arxiv.org/abs/2210.11958

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