Related papers: Well-posedness and trivial solutions to inverse ei…

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…

Deep-learning-based methods for different applications have been shown vulnerable to adversarial examples. These examples make deployment of such models in safety-critical tasks questionable. Use of deep neural networks as inverse problem…

In this paper we extend a recent idea of formulating and regularizing inverse problems as minimization problems, so without using a forward operator, thus avoiding explicit evaluation of a parameter-to-state map. We do so by rephrasing…

A stabilized version of the fundamental solution method to catch ill-conditioning effects is investigated with focus on the computation of complex-valued elastic interior transmission eigenvalues in two dimensions for homogeneous and…

Vector tomography methods intend to reconstruct and visualize vector fields in restricted domains by measuring line integrals of projections of these vector fields. Here, we deal with the reconstruction of irrotational vector functions from…

Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of the major concerns in the medical imaging domain. Typical examples include undersampled magnetic resonance…

The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…

Learning based methods are now ubiquitous for solving inverse problems, but their deployment in real-world applications is often hindered by the lack of ground truth references for training. Recent self-supervised learning strategies offer…

This article is devoted to forward and inverse problems associated with time-independent semilinear nonlocal wave equations. We first establish comprehensive well-posedness results for some semilinear nonlocal wave equations. The main…

We consider and analyze applying a spectral inverse iteration algorithm and its subspace iteration variant for computing eigenpairs of an elliptic operator with random coefficients. With these iterative algorithms the solution is sought…

We consider solving ill-posed imaging inverse problems without access to an explicit image prior or ground-truth examples. An overarching challenge in inverse problems is that there are many undesired images that fit to the observed…

Self-organizing systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organization central to understanding natural complexity. A fundamental challenge…

We study an inverse problem for a coupled system of semilinear Helmholtz equations where we are interested in reconstructing multiple coefficients in the system from internal data measured in applications such as thermoacoustic imaging. We…

The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…

In the present paper we consider application of overcomplete dictionaries to solution of general ill-posed linear inverse problems. In the context of regression problems, there has been enormous amount of effort to recover an unknown…

In this paper, we study the inverse problem for a class of abstract ultraparabolic equations which is well-known to be ill-posed. We employ some elementary results of semi-group theory to present the formula of solution, then show the…

We consider a method for neutron residual strain/stress analysis combining features of transmission strain tomography (e.g. through Braggs edge imaging) and neutron diffraction techniques. Analogous to transmission strain tomography, our…

We consider Sturm-Liouville problems with a discontinuity in an interior point, which are motivated by the inverse problems for the torsional modes of the Earth. We assume that the potential on the right half-interval and the coefficient in…

The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…

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…