Related papers: Imaging with Kantorovich-Rubinstein discrepancy
The Monge-Kantorovich problem is revisited by means of a variant of the saddle-point method without appealing to $c$-conjugates. A new abstract characterization of the optimal plans is obtained in the case where the cost function takes…
We propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including denoising, segmentation and motion estimation, which are…
This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to…
Data unfolding -- the removal of noise or artifacts from measurements -- is a fundamental task across the experimental sciences. Of particular interest are applications in physics, where the dominant approach is Richardson-Lucy (RL)…
One revisits the standard saddle-point method based on conjugate duality for solving convex minimization problems. Our aim is to reduce or remove unnecessary topological restrictions on the constraint set. Dual equalities and…
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…
In image processing, classical methods minimize a suitable functional that balances between computational feasibility (convexity of the functional is ideal) and suitable penalties reflecting the desired image decomposition. The fact that…
In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…
Conventional model-based image denoising optimizations employ convex regularization terms, such as total variation (TV) that convexifies the $\ell_0$-norm to promote sparse signal representation. Instead, we propose a new non-convex total…
This article presents a new class of distances between arbitrary nonnegative Radon measures inspired by optimal transport. These distances are defined by two equivalent alternative formulations: (i) a dynamic formulation defining the…
Suppose we are given two metric spaces and a family of continuous transformations from one to the other. Given a probability distribution on each of these two spaces - namely the source and the target measures - the Wasserstein alignment…
Many numerical and learning algorithms rely on the solution of the Monge-Kantorovich problem and Wasserstein distances, which provide appropriate distributional metrics. While the natural approach is to treat the problem as an…
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…
We consider composite linear inverse problems where the signal to recover is modeled as a sum of two functions. We study a variational framework formulated as an optimization problem over the pairs of components using two regularization…
We propose numerical algorithms for solving large deformation diffeomorphic image registration problems. We formulate the nonrigid image registration problem as a problem of optimal control. This leads to an infinite-dimensional partial…
The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in its solution. In particular, the OT problem defines a…
In this paper we present a spatially-adaptive method for image reconstruction that is based on the concept of statistical multiresolution estimation as introduced in [Frick K, Marnitz P, and Munk A. "Statistical multiresolution Dantzig…
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…
High-quality dehazing performance is highly dependent upon the accurate estimation of transmission map. In this work, the coarse estimation version is first obtained by weightedly fusing two different transmission maps, which are generated…
We consider the simultaneous optimal transportation of measures, where the target marginal is not necessarily fixed. For this problem, we prove the existence of a solution for completely regular spaces and investigate the structure of the…