Related papers: Bregman Distances in Inverse Problems and Partial …
We study the problem of calculating noncommutative distances on graphs, using techniques from linear algebra, specifically, Birkhoff-James orthogonality. A complete characterization of the solutions is obtained in the case when the…
Twenty years ago the anti-reflective numerical boundary conditions (BCs) were introduced in a context of signal processing and imaging, for increasing the quality of the reconstruction of a blurred signal/image contaminated by noise and for…
Optimal transport distances have become a classic tool to compare probability distributions and have found many applications in machine learning. Yet, despite recent algorithmic developments, their complexity prevents their direct use on…
Inverse problems are inherently ill-posed and therefore require regularization techniques to achieve a stable solution. While traditional variational methods have well-established theoretical foundations, recent advances in machine learning…
A class of distance measures on probabilities -- the integral probability metrics (IPMs) -- is addressed: these include the Wasserstein distance, Dudley metric, and Maximum Mean Discrepancy. IPMs have thus far mostly been used in more…
Fibre Bragg Gratings have become widespread measurement devices in engineering and other fields of application. In all but a few cases, the relation between cause and effect is simplified to a proportional model. However, at its…
Partial differential equations have a wide range of applications in modeling multiple physical, biological, or social phenomena. Therefore, we need to approximate the solutions of these equations in computationally feasible terms. Nowadays,…
The contributions of the paper span theoretical and implementational results. First, we prove that Kd-trees can be extended to spaces in which the distance is measured with an arbitrary Bregman divergence. Perhaps surprisingly, this shows…
In this paper, we explore a specific optimization problem that involves the combination of a differentiable nonconvex function and a nondifferentiable function. The differentiable component lacks a global Lipschitz continuous gradient,…
This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint…
Non-linear filtering approaches allow to obtain decompositions of images with respect to a non-classical notion of scale. The associated inverse scale space flow can be obtained using the classical Bregman iteration applied to a convex,…
In this work we study the method of Bregman projections for deterministic and stochastic convex feasibility problems with three types of control sequences for the selection of sets during the algorithmic procedure: greedy, random, and…
We first formulate an inverse problem for a linear fractional Lam\'e system. We determine the Lam\'e parameters from exterior partial measurements of the Dirichlet-to-Neumann map. We further study an inverse obstacle problem as well as an…
This paper suggests a framework for the learning of discretizations of expensive forward models in Bayesian inverse problems. The main idea is to incorporate the parameters governing the discretization as part of the unknown to be estimated…
We introduce and analyze a fast iterative method based on sequential Bregman projections for nonlinear inverse problems in Banach spaces. The key idea, in contrast to the standard Landweber method, is to use multiple search directions per…
In this paper, we analyze the local convergence rate of optimistic mirror descent methods in stochastic variational inequalities, a class of optimization problems with important applications to learning theory and machine learning. Our…
Gromov-Wasserstein distance has found many applications in machine learning due to its ability to compare measures across metric spaces and its invariance to isometric transformations. However, in certain applications, this invariance…
Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…
Understanding visual scenes relies more and more on dense pixel-wise classification obtained via deep fully convolutional neural networks. However, due to the nature of the networks, predictions often suffer from blurry boundaries and…
We propose a novel stochastic distributed method for both monotone and strongly monotone variational inequalities with Lipschitz operator and proper convex regularizers arising in various applications from game theory to adversarial…