Related papers: Regularization of Nonlinear Inverse Problems -- Fr…
Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…
Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Data-driven approaches for inverse problems aim for learning model and regularization parameters from observed data samples, and…
Unsupervised deep learning approaches have recently become one of the crucial research areas in imaging owing to their ability to learn expressive and powerful reconstruction operators even when paired high-quality training data is scarcely…
In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal…
Regularization-based approaches for injecting constraints in Machine Learning (ML) were introduced to improve a predictive model via expert knowledge. We tackle the issue of finding the right balance between the loss (the accuracy of the…
The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…
Image registration is fundamental in medical imaging applications, such as disease progression analysis or radiation therapy planning. The primary objective of image registration is to precisely capture the deformation between two or more…
In this paper we investigate a variety of deep learning strategies for solving inverse problems. We classify existing deep learning solutions for inverse problems into three categories of Direct Mapping, Data Consistency Optimizer, and Deep…
We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
Extracting information from nonlinear measurements is a fundamental challenge in data analysis. In this work, we consider separable inverse problems, where the data are modeled as a linear combination of functions that depend nonlinearly on…
The present paper studies so-called deep image prior (DIP) techniques in the context of ill-posed inverse problems. DIP networks have been recently introduced for applications in image processing; also first experimental results for…
Inverse problems are central to a wide range of fields, including healthcare, climate science, and agriculture. They involve the estimation of inputs, typically via iterative optimization, to some known forward model so that it produces a…
In this paper we consider the solution of monotone inverse problems using the particular example of a parameter identification problem for a semilinear parabolic PDE. For the regularized solution of this problem, we introduce a total…
Optimization plays an important role in solving many inverse problems. Indeed, the task of inversion often either involves or is fully cast as a solution of an optimization problem. In this light, the mere non-linear, non-convex, and…
Reconstructing the structure of the soil using non-invasive techniques is a very relevant problem in many scientific fields, like geophysics and archaeology. This can be done, for instance, with the aid of Frequency Domain Electromagnetic…
Solving inverse problems \(Ax = y\) is central to a variety of practically important fields such as medical imaging, remote sensing, and non-destructive testing. The most successful and theoretically best-understood method is convex…
Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in…
Current deep learning-based solutions for image analysis tasks are commonly incapable of handling problems to which multiple different plausible solutions exist. In response, posterior-based methods such as conditional Diffusion Models and…
This manuscript is designed to introduce students in applied mathematics and data science to the concept of regularization for ill-posed inverse problems. Construct a mathematical model that describes how an image gets blurred. Convert a…