Related papers: Stabilizing Inverse Problems by Internal Data
We show that the inference problem of constraining the dipole amplitude with inclusive deep inelastic scattering data can be written into a discrete linear inverse problem, in an analogous manner as can be done for computed tomography. To…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
We study the stability of an inverse problem for the fractional conductivity equation on bounded smooth domains. We obtain a logarithmic stability estimate for the inverse problem under suitable a priori bounds on the globally defined…
This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the…
We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements…
We consider the reconstruction of the diffusion and absorption coefficients of the diffusion equation from the internal information of the solution obtained from the first step of the inverse photoacoustic tomography (PAT). In practice, the…
It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…
We investigate a general elliptic problem given in a bounded Euclidean domain with boundary data in Nikolskii spaces of low, specifically, negative order. The right-hand side of the elliptic differential equation is supposed to be an…
In Electrical Impedance Tomography (EIT), the internal conductivity of a body is recovered via current and voltage measurements taken at its surface. The reconstruction task is a highly ill-posed nonlinear inverse problem, which is very…
This paper investigates the problem of data-driven modeling of port-Hamiltonian systems while preserving their intrinsic Hamiltonian structure and stability properties. We propose a novel neural-network-based port-Hamiltonian modeling…
In this paper, we design a stabilizing state-feedback control law for a system represented by a general class of integral delay equations subject to a pointwise and distributed input delay. The proposed controller is defined in terms of…
We introduce a mathematical model for ultrasound modulated optical tomography and present a simple reconstruction scheme for recovering the spatially varying optical absorption coefficient from scanning measurements with narrowly focused…
Data assisted reconstruction algorithms, incorporating trained neural networks, are a novel paradigm for solving inverse problems. One approach is to first apply a classical reconstruction method and then apply a neural network to improve…
This work considers using reduced basis techniques in connection to (smoothened) total variation regularization in electrical impedance tomography, but analogous ideas can also be used for other inverse elliptic boundary value problems. It…
In the past five years, deep learning methods have become state-of-the-art in solving various inverse problems. Before such approaches can find application in safety-critical fields, a verification of their reliability appears mandatory.…
Implicit inverse problems, in which noisy observations of a physical quantity are used to infer a nonlinear functional applied to an associated function, are inherently ill posed and often exhibit non uniqueness of solutions. Such problems…
The purpose of this paper is to propose a non-iterative method for the inverse conductivity problem of recovering multiple small anomalies from the boundary measurements. When small anomalies are buried in a conducting object, the electric…
In non-destructive imaging the information about the spatial pattern of a samples interior has to be transferred to the sample surface by certain waves, e.g. ultrasound or electromagnetic waves. At the sample surface these waves can be…
Regularization is a long-standing challenge for ill-posed linear inverse problems, and a prototype is the Fredholm integral equation of the first kind with additive Gaussian measurement noise. We introduce a new RKHS regularization adaptive…
In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…