English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study a general total variation denoising model with weighted $L^1$fidelity, where the regularizing term is a non-local variation induced by asuitable (non-integrable) kernel $K$, and the approximation term is given bythe $L^1$ norm with respect to a non-singular measure with positivelylower-bounded $L^\infty$ density. We provide a detailed analysis of the spaceof non-local $BV$ functions with finite total $K$-variation, with specialemphasis on compactness, Lusin-type estimates, Sobolev embeddings andisoperimetric and monotonicity properties of the $K$-variation and theassociated $K$-perimeter. Finally, we deal with the theory of Cheeger sets inthis non-local setting and we apply it to the study of the fidelity in ourmodel.

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