Related papers: Stability estimates for the regularized inversion …

We consider perturbed nonlinear ill-posed equations in Hilbert spaces, with operators that are monotone on a given closed convex subset. A simple stable approach is Lavrentiev regularization, but existence of solutions of the regularized…

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…

Consider linear ill-posed problems governed by the system $A_i x = y_i$ for $i =1, \cdots, p$, where each $A_i$ is a bounded linear operator from a Banach space $X$ to a Hilbert space $Y_i$. In case $p$ is huge, solving the problem by an…

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…

Limited-angle and sparse-view computed tomography (LACT and SVCT) are crucial for expanding the scope of X-ray CT applications. However, they face challenges due to incomplete data acquisition, resulting in diverse artifacts in the…

In this article, we show that the projection-free, snapshot-based, balanced truncation method can be applied directly to unstable systems. We prove that even for unstable systems, the unmodified balanced proper orthogonal decomposition…

Let $g$ be a Riemannian metric for $\mathbf{R}^d$ ($d\geq 3$) which differs from the Euclidean metric only in a smooth and strictly convex bounded domain $M$. The lens rigidity problem is concerned with recovering the metric $g$ inside $M$…

In this letter we show that although the application of standard Lyapunov analysis predicts that completely integrable Kepler motion is unstable, the geometrical analysis of Horwitz et al [1] predicts the observed stability. This seems to…

We derive and analyse a new variant of the iteratively regularized Landweber iteration, for solving linear and nonlinear ill-posed inverse problems. The method takes into account training data, which are used to estimate the interior of a…

We prove a stability theorem for finite-dimensional analytic inverse problems. Let \(U\subset\R^m\) be an open parameter set, let \(F(p)\) be a boundary measurement operator, and let \(R(p)\) be the finite-dimensional quantity to be…

We describe the minimax reconstruction rates in linear ill-posed equations in Hilbert space when smoothness is given in terms of general source sets. The underlying fundamental result, the minimax rate on ellipsoids, is proved similarly to…

In this article, we provide stability estimates for the finite element discretization of a class of inverse parameter problems of the form $-\nabla\cdot(\mu S) = \g f$ in a domain $\Omega$ of $\R^d$. Here $\mu$ is the unknown parameter to…

Stability and error analysis remain challenging for problems that lack regularity properties near solutions, are subject to large perturbations, and might be infinite dimensional. We consider nonconvex optimization and generalized equations…

We consider the inverse problem of determining the metric-measure structure of collapsing manifolds from local measurements of spectral data. In the part I of the paper, we proved the uniqueness of the inverse problem and a continuity…

A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from…

The high energy physics unfolding problem is an important statistical inverse problem in data analysis at the Large Hadron Collider (LHC) at CERN. The goal of unfolding is to make nonparametric inferences about a particle spectrum from…

We investigate the reconstruction problem of limited angle tomography. Such problems arise naturally in applications like digital breast tomosynthesis, dental tomography, electron microscopy etc. Since the acquired tomographic data is…

Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply-rates are employed here for…

Due to depth ambiguities and occlusions, lifting 2D poses to 3D is a highly ill-posed problem. Well-calibrated distributions of possible poses can make these ambiguities explicit and preserve the resulting uncertainty for downstream tasks.…

Single image inverse problem is a notoriously challenging ill-posed problem that aims to restore the original image from one of its corrupted versions. Recently, this field has been immensely influenced by the emergence of deep-learning…