Abstract
AbstractIn this paper we study the(BV,Lp){(\mathrm{BV},L^{p})}-decomposition,p=1,2{p=1,2}, of functions in metric random walk spaces, a general workspace that includes weighted graphs and nonlocal models used in image processing. We obtain the Euler-Lagrange equations of the corresponding variational problems and their gradient flows. In the casep=1{p=1}we also study the associated geometric problem and the thresholding parameters describing the behavior of its solutions.
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