Deblurring and Denoising of Images by Nonlocal Functionals

A Higher Order Model for Image Restoration: The One-Dimensional Case

“…The extension of our results to higher dimensions will be the subject of a subsequent paper. For completeness we conclude by mentioning that other approaches have been considered to avoid staircasing: The works by Geman and Reynolds [7] and Chambolle and Lions [3] contain a different use of higher order derivatives as regularizing terms; in [2], Blomgren, Chan, and Mulet propose a BV -H 1 interpolation approach, while Kindermann, Osher, and Jones avoid in [9] the use of second derivatives by considering a sort of nonlocal total variation.…”

An Improved Image Denoising Model Based on Nonlocal Means Filter

“…Motivated by the work of Kindermann, Osher, and Jones [28], Gilboa and Osher [20,29] wanted to combine the TV model and the nonlocal means filter into a nonlocal TV model, so that the corresponding 1 model is just a regularization of the nonlocal means filter. They realized this idea successfully, by introducing suitable nonlocal operators, which was motivated by the work of Zhou-schölkopf [30,31].…”

Nonlocal Similarity Image Filtering

“…There are several other methods based on the idea of nonlocal means filter [7]. For example, Kervrann, et al [21] improve it by using an adaptive window size; [22,23] formalize a variational nonlocal framework motivated from graph theory [24]; Chatterjee, et al [25] generalize nonlocal means to high-order kernel regression. Nonetheless, all the methods interpret the concept of "similarity" only up to translation, while we extend it to a more general similarity transformation, i.e., scaling and rotation.…”