Related papers: Dynamic inverse problems: Online regularisation th…
Diffuse Optical Tomography (DOT) is an emerging technology in medical imaging which employs light in the NIR spectrum to estimate the distribution of optical coefficients in biological tissues for diagnostic and monitoring purposes. DOT…
The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography (CT). As the (naive) solution does not depend…
We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward…
Variational regularisation is the primary method for solving inverse problems, and recently there has been considerable work leveraging deeply learned regularisation for enhanced performance. However, few results exist addressing the…
Learning-based and data-driven techniques have recently become a subject of primary interest in the field of reconstruction and regularization of inverse problems. Besides the development of novel methods, yielding excellent results in…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
In this paper we provide optimal bounds for fully discrete approximations to finite horizon problems via dynamic programming. We adapt the error analysis in \cite{nos} for the infinite horizon case to the finite horizon case. We prove an a…
Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Since inverse problems typically suffer from instability with respect to data perturbations, a variety of regularization…
Regularization by denoising (RED) is a powerful framework for solving imaging inverse problems. Most RED algorithms are iterative batch procedures, which limits their applicability to very large datasets. In this paper, we address this…
In this note we solve a general statistical inverse problem under absence of knowledge of both the noise level and the noise distribution via application of the (modified) heuristic discrepancy principle. Hereby the unbounded (non-Gaussian)…
This paper develops a discrete data-driven approach for solving the inverse source problem of the wave equation with final time measurements. Focusing on the $L^2$-Tikhonov regularization method, we analyze its convergence under two…
Recently, optimal time variable learning in deep neural networks (DNNs) was introduced in arXiv:2204.08528. In this manuscript we extend the concept by introducing a regularization term that directly relates to the time horizon in discrete…
Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their solutions may have significant intrinsic uncertainty. Analysing…
In this article, we propose a novel regularization method for a class of nonlinear inverse problems that is inspired by an application in quantitative magnetic resonance imaging (qMRI). The latter is a special instance of a general…
We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the…
Online mirror descent (OMD) is a fundamental algorithmic paradigm that underlies many algorithms in optimization, machine learning and sequential decision-making. The OMD iterates are defined as solutions to optimization subproblems which,…
We investigate online convex optimization in non-stationary environments and choose the dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible…
This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate…
In this paper, we present a practical algorithm based on sparsity regularization to effectively solve nonlinear dynamic inverse problems that are encountered in subsurface model calibration. We use an iteratively reweighted algorithm that…
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 yields useful insights into the convergence of the…