相关论文: Optimal rates for total variation denoising
We study the theoretical properties of image denoising via total variation penalized least-squares. We define the total vatiation in terms of the two-dimensional total discrete derivative of the image and show that it gives rise to denoised…
This work combines three paradigms of image processing: i) the total variation approach to denoising, ii) the superior structure of hexagonal lattices, and iii) fast and exact graph cut optimization techniques. Although isotropic in theory,…
We consider the problem of estimating a function defined over $n$ locations on a $d$-dimensional grid (having all side lengths equal to $n^{1/d}$). When the function is constrained to have discrete total variation bounded by $C_n$, we…
A novel class of semi-norms, generalising the notion of the isotropic total variation $TV_{2}$ and the an-isotropic total variation $TV_{1}$ is introduced. A supervised learning method via bilevel optimisation is proposed for the…
We address the problem of optimal scale-dependent parameter learning in total variation image denoising. Such problems are formulated as bilevel optimization instances with total variation denoising problems as lower-level constraints. For…
The total variation-based image denoising model has been generalized and extended in numerous ways, improving its performance in different contexts. We propose a new penalty function motivated by the recent progress in the statistical…
We revisit total variation denoising and study an augmented model where we assume that an estimate of the image gradient is available. We show that this increases the image reconstruction quality and derive that the resulting model…
Denoising is of utmost importance for the visualization and processing of images featuring low signal-to-noise ratio. Total variation methods are among the most popular techniques to perform this task improving the signal-to-noise ratio…
2D Total Variation Denoising (TVD) is a widely used technique for image denoising. It is also an important nonparametric regression method for estimating functions with heterogenous smoothness. Recent results have shown the TVD estimator to…
Motivated by the image denoising problem and the undesirable stair-casing effect of the total variation method, we introduce bounded variation spaces with generalized Orlicz growth. Our setup covers earlier variable exponent and double…
Total variation (TV) denoising is a nonparametric smoothing method that has good properties for preserving sharp edges and contours in objects with spatial structures like natural images. The estimate is sparse in the sense that TV…
Based on a nonsmooth coherence condition, we construct and prove the convergence of a forward-backward splitting method that alternates between steps on a fine and a coarse grid. Our focus is a total variation regularised inverse imaging…
We consider variations of the Rudin-Osher-Fatemi functional which are particularly well-suited to denoising and deblurring of 2D bar codes. These functionals consist of an anisotropic total variation favoring rectangles and a fidelity term…
This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space satisfying integrability conditions on their first variation. Firstly, the study of pointwise power decay rates almost everywhere of the…
We focus on the maximum regularization parameter for anisotropic total-variation denoising. It corresponds to the minimum value of the regularization parameter above which the solution remains constant. While this value is well know for the…
We introduce a class of higher-order anisotropic total variation regularisers, which are defined for possibly inhomogeneous, smooth elliptic anisotropies, that extends the Total Generalized Variation (TGV) regulariser and its variants. We…
In this work we consider a generalized bilevel optimization framework for solving inverse problems. We introduce fractional Laplacian as a regularizer to improve the reconstruction quality, and compare it with the total variation…
We analyse a new notion of total anisotropic higher-order variation which, differently from the Total Generalized Variation by Bredies et al., quantifies for possibly non-symmetric tensor fields their variations at arbitrary order weighted…
We propose the use of the Kantorovich-Rubinstein norm from optimal transport in imaging problems. In particular, we discuss a variational regularisation model endowed with a Kantorovich-Rubinstein discrepancy term and total variation…
We consider the problem of minimizing the continuous valued total variation subject to different unary terms on trees and propose fast direct algorithms based on dynamic programming to solve these problems. We treat both the convex and the…