22 citations · 84 across the 21 of their papers we have counts for
24 papers
Gradient Descent on Point Clouds and Applications in Learned Operator Correction
Andreas Hauptmann, Yury Korolev, Matthew Thorpe
We consider the problem of minimising an energy over an unknown manifold that is given implicitly by a point cloud. For a known manifold one can define a gradient descent scheme an…
Approximation of Maximally Monotone Operators : A Graph Convergence Perspective
Takashi Furuya, Yury Korolev, Takaharu Yaguchi
Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-includ…
Large Data Limits of Laplace Learning for Gaussian Measure Data in Infinite Dimensions
Zhengang Zhong, Yury Korolev, Matthew Thorpe
Laplace learning is a semi-supervised method, a solution for finding missing labels from a partially labeled dataset utilizing the geometry given by the unlabeled data points. The…
Introduction to Nonlinear Spectral Analysis
Leon Bungert, Yury Korolev
These notes are meant as an introduction to the theory of nonlinear spectral theory. We will discuss the variational form of nonlninear eigenvalue problems and the corresponding no…
Fast Inexact Bilevel Optimization for Analytical Deep Image Priors
Mohammad Sadegh Salehi, Tatiana A. Bubba, Yury Korolev
The analytical deep image prior (ADP) introduced by Dittmer et al. (2020) establishes a link between deep image priors and classical regularization theory via bilevel optimization.…
Analysis of mean-field models arising from self-attention dynamics in transformer architectures with layer normalization
Martin Burger, Samira Kabri, Yury Korolev +2
The aim of this paper is to provide a mathematical analysis of transformer architectures using a self-attention mechanism with layer normalization. In particular, observed patterns…
A Lipschitz spaces view of infinitely wide shallow neural networks
Francesca Bartolucci, Marcello Carioni, José A. Iglesias +3
We revisit the mean field parametrization of shallow neural networks, using signed measures on unbounded parameter spaces and duality pairings that take into account the regularity…
Inverse Problems with Learned Forward Operators
Simon Arridge, Andreas Hauptmann, Yury Korolev
Solving inverse problems requires the knowledge of the forward operator, but accurate models can be computationally expensive and hence cheaper variants that do not compromise the…
A sparse optimization approach to infinite infimal convolution regularization
Kristian Bredies, Marcello Carioni, Martin Holler +2
In this paper we introduce the class of infinite infimal convolution functionals and apply these functionals to the regularization of ill-posed inverse problems. The proposed regul…
Unsupervised Learning of the Total Variation Flow
Tamara G. Grossmann, Sören Dittmer, Yury Korolev +1
The total variation (TV) flow generates a scale-space representation of an image based on the TV functional. This gradient flow observes desirable features for images, such as shar…
Gaussian random fields on non-separable Banach spaces
Yury Korolev, Jonas Latz, Carola-Bibiane Schönlieb
We study Gaussian random fields on certain Banach spaces and investigate conditions for their existence. Our results apply inter alia to spaces of Radon measures and Hölder functio…
Image reconstruction in light-sheet microscopy: spatially varying deconvolution and mixed noise
Bogdan Toader, Jerome Boulanger, Yury Korolev +4
We study the problem of deconvolution for light-sheet microscopy, where the data is corrupted by spatially varying blur and a combination of Poisson and Gaussian noise. The spatial…
Eigenvalue Problems in : Optimality Conditions, Duality, and Relations with Optimal Transport
Leon Bungert, Yury Korolev
In this article we characterize the eigenvalue problem associated to the Rayleigh quotient $\left.{\|\nabla u\|_{\mathrm{L}^\infty}}\middle/{\|u\|_\infty}\right…
Two-layer neural networks with values in a Banach space
Yury Korolev
We study two-layer neural networks whose domain and range are Banach spaces with separable preduals. In addition, we assume that the image space is equipped with a partial order, i…
Data driven reconstruction using frames and Riesz bases
Andrea Aspri, Leon Frischauf, Yury Korolev +1
We study the problem of regularization of inverse problems adopting a purely data driven approach, by using the similarity to the method of regularization by projection. We provide…
Deeply Learned Spectral Total Variation Decomposition
Tamara G. Grossmann, Yury Korolev, Guy Gilboa +1
Non-linear spectral decompositions of images based on one-homogeneous functionals such as total variation have gained considerable attention in the last few years. Due to their abi…
Variational regularisation for inverse problems with imperfect forward operators and general noise models
Leon Bungert, Martin Burger, Yury Korolev +1
We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lat…
Structural analysis of an -infinity variational problem and relations to distance functions
Leon Bungert, Yury Korolev, Martin Burger
In this work we analyse the functional defined on Lipschitz functions with homogeneous Dirichlet boundary conditions. Our analysis is performed di…
Total Variation Regularisation with Spatially Variable Lipschitz Constraints
Martin Burger, Yury Korolev, Simone Parisotto +1
We introduce a first order Total Variation type regulariser that decomposes a function into a part with a given Lipschitz constant (which is also allowed to vary spatially) and a j…
Data driven regularization by projection
Andrea Aspri, Yury Korolev, Otmar Scherzer
We study linear inverse problems under the premise that the forward operator is not at hand but given indirectly through some input-output training pairs. We demonstrate that regul…
A total variation based regularizer promoting piecewise-Lipschitz reconstructions
Martin Burger, Yury Korolev, Carola-Bibiane Schönlieb +1
We introduce a new regularizer in the total variation family that promotes reconstructions with a given Lipschitz constant (which can also vary spatially). We prove regularizing pr…
Convergence rates and structure of solutions of inverse problems with imperfect forward models
Martin Burger, Yury Korolev, Julian Rasch
The goal of this paper is to further develop an approach to inverse problems with imperfect forward operators that is based on partially ordered spaces. Studying the dual problem y…
Image reconstruction with imperfect forward models and applications in deblurring
Yury Korolev, Jan Lellmann
We present and analyse an approach to image reconstruction problems with imperfect forward models based on partially ordered spaces - Banach lattices. In this approach, errors in t…
Diffusion tensor imaging with deterministic error bounds
Artur Gorokh, Yury Korolev, Tuomo Valkonen
Errors in the data and the forward operator of an inverse problem can be handily modelled using partial order in Banach lattices. We present some existing results of the theory of…