Non-local BV functions and a denoising model with L¹ fidelity.

Bessas, Konstantinos; Stefani, Giorgio

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 ∞ 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.

FUNCTIONS of bounded variation; LAPLACIAN operator; IMAGE denoising; SET theory; DENSITY; ISOPERIMETRIC inequalities

Advances in Calculus of Variations, 2025, Vol 18, Issue 1, p189

1864-8258

Academic Journal

10.1515/acv-2023-0082