Related papers: On Learned Operator Correction in Inverse Problems

We propose a new learning-based approach to solve ill-posed inverse problems in imaging. We address the case where ground truth training samples are rare and the problem is severely ill-posed - both because of the underlying physics and…

Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…

Data driven models of dynamical systems help planners and controllers to provide more precise and accurate motions. Most model learning algorithms will try to minimize a loss function between the observed data and the model's predictions.…

This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…

In recent years, there has been a growing interest in data-driven approaches in physics, such as extended dynamic mode decomposition (EDMD). The EDMD algorithm focuses on nonlinear time-evolution systems, and the constructed Koopman matrix…

We consider a class of inverse problems characterized by forward operators that are partially specified, non-smooth, and non-differentiable. Although generative inverse solvers have made significant progress, we find that these forward…

In this paper, we consider a deep learning approach to the limited aperture inverse obstacle scattering problem. It is well known that traditional deep learning relies solely on data, which may limit its performance for the inverse problem…

We consider the problem of learning optimal solutions of a partially known linear optimization problem and recovering its underlying cost function where a set of past decisions and the feasible set are known. We develop a new framework,…

Linear inverse problems are highly common in practical real-world applications from industry to medical imaging. The forward operator is often built on some approximations of the studied system. Handling inaccuracies in the forward operator…

Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results.…

Variational regularization techniques are dominant in the field of mathematical imaging. A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user. A by now common strategy to…

Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous…

In this work we deal with parametric inverse problems, which consist in recovering a finite number of parameters describing the structure of an unknown object, from indirect measurements. State-of-the-art methods for approximating a…

Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to…

Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…

Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…

A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…

Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of…

Retrieval systems rely on representations learned by increasingly powerful models. However, due to the high training cost and inconsistencies in learned representations, there is significant interest in facilitating communication between…

We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…