Related papers: Modern Regularization Methods for Inverse Problems

Inverse Reinforcement Learning (IRL) aims to facilitate a learner's ability to imitate expert behavior by acquiring reward functions that explain the expert's decisions. Regularized IRL applies strongly convex regularizers to the learner's…

This paper aims to solve numerically the two-dimensional inverse medium scattering problem with far-field data. This is a challenging task due to the severe ill-posedness and strong nonlinearity of the inverse problem. As already known, it…

Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems. The original method, however, requires the inversion of the predictors covariance matrix. In case of collinearity…

This paper proposes a new way of regularizing an inverse problem in imaging (e.g., deblurring or inpainting) by means of a deep generative neural network. Compared to end-to-end models, such approaches seem particularly interesting since…

Image restoration refers to the process of reconstructing noisy, destroyed, or missing parts of an image, which is an ill-posed inverse problem. A specific regularization term and image degradation are typically assumed to achieve…

This paper focuses on the regularization of backward time-fractional diffusion problem on unbounded domain. This problem is well-known to be ill-posed, whence the need of a regularization method in order to recover stable approximate…

Mitigating shortcuts, where models exploit spurious correlations in training data, remains a significant challenge for improving generalization. Regularization methods have been proposed to address this issue by enhancing model…

In this paper, we consider optimal low-rank regularized inverse matrix approximations and their applications to inverse problems. We give an explicit solution to a generalized rank-constrained regularized inverse approximation problem,…

Regularization is commonly used for alleviating overfitting in machine learning. For convolutional neural networks (CNNs), regularization methods, such as DropBlock and Shake-Shake, have illustrated the improvement in the generalization…

Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…

Regularization is one of the crucial ingredients of deep learning, yet the term regularization has various definitions, and regularization methods are often studied separately from each other. In our work we present a systematic, unifying…

We study the inverse conductivity problem with discontinuous conductivities. We consider, simultaneously, a regularisation and a discretisation for a variational approach to solve the inverse problem. We show that, under suitable choices of…

Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…

Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP…

Subspace recycling techniques have been used quite successfully for the acceleration of iterative methods for solving large-scale linear systems. These methods often work by augmenting a solution subspace generated iteratively by a known…

Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…

This paper is concerned with the development, analysis and numerical realization of a novel variational model for the regularization of inverse problems in imaging. The proposed model is inspired by the architecture of generative…

Modelling real world systems frequently requires the solution of systems of nonlinear equations. A number of approaches have been suggested and developed for this computational problem. However, it is also possible to attempt solutions…

Testing of hypotheses is a well studied topic in mathematical statistics. Recently, this issue has also been addressed in the context of Inverse Problems, where the quantity of interest is not directly accessible but only after the…

During the past few years, inverse problem formulations of ultrasound beamforming have attracted a growing interest. They usually pose beamforming as a minimization problem of a fidelity term resulting from the measurement model plus a…