Related papers: Some comments on the inverse problem of pure point…
We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measurements is available. For a large class of inverse problems…
We prove for the first time that, if a linear inverse problem exhibits a group symmetry structure, gradient-based optimizers can be designed to exploit this structure for faster convergence rates. This theoretical finding demonstrates the…
We analyze convergence of the Levenberg-Marquardt method for solving nonlinear inverse problems in Hilbert spaces. Specifically, we establish local convergence and convergence rates for a class of inverse problems that satisfy H\"{o}lder…
A class of inverse problems for restoring the right-hand side of a parabolic equation for a large class of positive operators with discrete spectrum is considered. The results on existence and uniqueness of solutions of these problems as…
Spatially resolving two incoherent point sources whose separation is well below the diffraction limit dictated by classical optics has recently been shown possible using techniques that decompose the incoming radiation into orthogonal…
We study the well-posedness of a semilinear fractional diffusion equation and formulate an associated inverse problem. We determine fractional power type nonlinearities from the exterior partial measurements of the Dirichlet-to-Neumann map.…
The inverse problem of amplitude reconstruction on an inclined line based on the values of amplitude or its module as recorded on semi-infinite line orthogonal to the beam propagation direction is considered within the framework of 2D…
We consider the homogenization for time-fractional diffusion equations in a periodic structure and we derive the homogenized time-fractional diffusion equation. Then we discuss the determination of the constant diffusion coefficient by…
Three papers describing different methods to solve the inverse scattering problem of the reconstruction of the shape and/or impedance of an obstacle have been chosen for analysis. This literature review consists of an evaluation of these…
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…
In this article we study the retrospective inverse problem. The retrospective inverse problem consists of in the reconstruction of a priori unknown initial condition of the dynamic system from its known final condition. Existence and…
A review of some of the author's results in the area of inverse scattering is given. The following topics are discussed: 1) Property $C$ and applications, 2) Stable inversion of fixed-energy 3D scattering data and its error estimate, 3)…
Diffusion probabilistic models (DPMs) are a key component in modern generative models. DPM-solvers have achieved reduced latency and enhanced quality significantly, but have posed challenges to find the exact inverse (i.e., finding the…
We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…
We extend a modal theory of diffraction by a set of parallel fibers to deal with the case of a hard boundary: that is a structure made for instance of air-holes inside a dielectric matrix. Numerical examples are given concerning some…
This paper provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination…
In this paper, we propose an approach combining diffusion models and inverse problems for the reconstruction of circumstellar disk images. Our method builds upon the Rhapsodie framework for polarimetric imaging, substituting its classical…
We consider the numerical solution of scalar wave equations in domains which are the union of a bounded domain and a finite number of infinite cylindrical waveguides. The aim of this paper is to provide a new convergence analysis of both…
By suitable examples we illustrate an algorithm for composition of inverse problems.
We consider the following geometric optics problem: Construct a system of two reflectors which transforms a spherical wavefront generated by a point source into a beam of parallel rays. This beam has a prescribed intensity distribution. We…