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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 reconstruction quality are desired. This chapter reviews…

Imaging problems such as the one in nanoCT require the solution of an inverse problem, where it is often taken for granted that the forward operator, i.e., the underlying physical model, is properly known. In the present work we address the…

We discuss the possibility to learn a data-driven explicit model correction for inverse problems and whether such a model correction can be used within a variational framework to obtain regularised reconstructions. This paper discusses the…

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…

The recent development of scintillation crystals combined with $\gamma$-rays sources opens the way to an imaging concept based on Compton scattering, namely Compton scattering tomography (CST). The associated inverse problem rises many…

Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…

In Magnetic Particle Imaging (MPI), it is typically assumed that the studied specimen is stationary during the data acquisition. In practical applications however, the searched-for 3D distribution of the magnetic nanoparticles might show a…

Consistent improvement of image priors over the years has led to the development of better inverse problem solvers. Diffusion models are the newcomers to this arena, posing the strongest known prior to date. Recently, such models operating…

There are various inverse problems -- including reconstruction problems arising in medical imaging -- where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask…

Inverse problems in imaging are typically ill-posed and are usually solved by employing regularized optimization techniques. The usage of appropriate constraints can restrict the solution space, thus making it feasible for a reconstruction…

The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as…

Reconstructing a dynamic object with affine motion in computerized tomography (CT) leads to motion artifacts if the motion is not taken into account. In most cases, the actual motion is neither known nor can be determined easily. As a…

With the recent advances in machine learning, problems that traditionally would require accurate modeling to be solved analytically can now be successfully approached with data-driven strategies. Among these, computing the inverse…

Deep neural networks have been applied successfully to a wide variety of inverse problems arising in computational imaging. These networks are typically trained using a forward model that describes the measurement process to be inverted,…

Deep learning-based models have demonstrated remarkable success in solving illposed inverse problems; however, many fail to strictly adhere to the physical constraints imposed by the measurement process. In this work, we introduce a…

Inverse problems are pervasive mathematical methods in inferring knowledge from observational and experimental data by leveraging simulations and models. Unlike direct inference methods, inverse problem approaches typically require many…

We study the efficient numerical solution of linear inverse problems with operator valued data which arise, e.g., in seismic exploration, inverse scattering, or tomographic imaging. The high-dimensionality of the data space implies…

Fast convergence and high-quality image recovery are two essential features of algorithms for solving ill-posed imaging inverse problems. Existing methods, such as regularization by denoising (RED), often focus on designing sophisticated…

In the past few years, deep learning-based methods have demonstrated enormous success for solving inverse problems in medical imaging. In this work, we address the following question:\textit{Given a set of measurements obtained from real…

It is well-known that accelerated gradient first-order methods possess optimal complexity estimates for the class of convex smooth minimization problems. In many practical situations it makes sense to work with inexact gradient information.…