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

2022/10/21 by Konstantinos Bessas, Giorgio Stefani, Bessas, Konstantinos +1 · 1 citation
Computer Science · Mathematics · #26B30 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Primary 49Q20. Secondary 94A08

paper · pdf · doi:10.48550/arxiv.2210.11958

openalex publication_date 2022/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a general total variation denoising model with weighted L¹ 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 L¹ 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.

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