相关论文: Total variation regularization for manifold-valued…
Total Variation Denoising (TVD) is a fundamental denoising and smoothing method. In this article, we identify a new local minmax/maxmin formula producing two estimators which sandwich the univariate TVD estimator at every point.…
In this paper, a variational, multi-dimensional model for image reconstruction is proposed, in which the regularization term consists of the $r$-order (an)-isotropic total variation seminorms $TV^r$, with $r\in \mathbb R^+$, defined via the…
We introduce discretizations of infinite-dimensional optimization problems with total variation regularization and integrality constraints on the optimization variables. We advance the discretization of the dual formulation of the total…
In this thesis, we offer a thorough investigation of different regularisation terms used in variational imaging problems, together with detailed optimisation processes of these problems. We begin by studying smooth problems and partially…
Despite the popularity and practical success of total variation (TV) regularization for function estimation, surprisingly little is known about its theoretical performance in a statistical setting. While TV regularization has been known for…
Hyperspectral analysis has gained popularity over recent years as a way to infer what materials are displayed on a picture whose pixels consist of a mixture of spectral signatures. Computing both signatures and mixture coefficients is known…
Graph-based methods have been proposed as a unified framework for discrete calculus of local and nonlocal image processing methods in the recent years. In order to translate variational models and partial differential equations to a graph,…
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…
Lifting methods allow to transform hard variational problems such as segmentation and optical flow estimation into convex problems in a suitable higher-dimensional space. The lifted models can then be efficiently solved to a global optimum,…
The recovery of images from the observations that are degraded by a linear operator and further corrupted by Poisson noise is an important task in modern imaging applications such as astronomical and biomedical ones. Gradient-based…
Solving an optimization problem whose objective function is the sum of two convex functions has received considerable interests in the context of image processing recently. In particular, we are interested in the scenario when a…
Total variation flow, total variation regularization and the taut string algorithm are known to be equivalent filters for one-dimensional discrete signals. In addition, the filtered signal simultaneously minimizes a large number of convex…
Non-Local Total Variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the Structure Tensor…
We consider one-dimensional variants of the classical first order total variation denoising model introduced by Rudin, Osher and Fatemi. This study is based on our previous work on various denoising and inpainting problems in image…
The curvature regularities are well-known for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually non-convex,…
In this paper, we consider the sparse regularization of manifold-valued data with respect to an interpolatory wavelet/multiscale transform. We propose and study variational models for this task and provide results on their well-posedness.…
Total Generalized Variation (TGV) has recently been proven certainly successful in image processing for preserving sharp features as well as smooth transition variations. However, none of the existing works aims at numerically calculating…
In inverse problems, prior information and a priori-based regularization techniques play important roles. In this paper, we focus on image restoration problems, especially on restoring images whose texture mainly follow one direction. In…
We consider denoising and deblurring problems for tensors. While images can be discretized as matrices, the analogous procedure for color images or videos leads to a tensor formulation. We extend the classical ROF functional for variational…
Flash X-ray computed tomography (CT) is an important imaging modality for characterization of high-speed dynamic events, such as Kolsky bar impact experiments for the study of mechanical properties of materials subjected to impulsive…