Partial Regularity for Degenerate Variational Problems and Image Restoration Models in Bv
نویسنده
چکیده
We establish partial and local C1,α-regularity results for vectorial almost-minimizers of convex variational integrals in BV. In particular, we investigate cases with a degenerate or singular behavior of p-Laplace type, and we cover (local) minimizers of the exemplary integrals ∫
منابع مشابه
Existence and almost everywhere regularity of generalized minimizers for a class of variational problems with linear growth related to image inpainting
We continue the analysis of some modifications of the total variation image inpainting method formulated on the space BV (Ω) in the sense that we generalize the main results of [32] to the case that a more general data fitting term is involved. As in [32] we deal with vector-valued images, we do not impose any structure condition on our density F and the dimension of the domain Ω is arbitrary. ...
متن کاملInterior gradient regularity for BV minimizers of singular variational problems
We consider a class of vectorial integrals with linear growth, where, as a key feature, some degenerate/singular behavior is allowed. For generalized minimizers of these integrals in BV, we establish interior gradient regularity and — as a consequence — uniqueness up to constants. In particular, these results apply, for 1 < p < 2, to the singular model integrals ∫ Ω (1 + |∇w(x)|) 1 p dx . MSC (...
متن کاملAdaptive Image Reconstruction Using Information Measures
We present a class of nonlinear adaptive image restoration filters which may be steered to preserve sharp edges and contrasts in the restorations. From a theoretical point of view we discuss the associated variational problems and prove existence of solutions in certain Sobolev spaces W 1,p or in a BV -space. The degree of regularity of the solution may be understood as a mathematical explanati...
متن کاملPartial Regularity for a Selective Smoothing Functional for Image Restoration in BV Space
In this paper we study the partial regularity of a functional on BV space proposed by Chambolle and Lions [3] for the purposes of image restoration. The functional is designed to smooth corrupted images using isotropic diffusion via the Laplacian where the gradients of the image are below a certain threshold and retain edges where gradients are above the threshold using the total variation. Her...
متن کاملVariational image restoration by means of wavelets: simultaneous decomposition, deblurring and denoising
Inspired by papers of Vese–Osher [OV02] and Osher–Solé–Vese [OSV02] we present a wavelet–based treatment of variational problems arising in the field of image processing. In particular, we follow their approach and discuss a special class of variational functionals that induce a decomposition of images into oscillating and cartoon components and possibly an appropriate ‘noise’ component. In the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014