相关论文: Stability of Current Density Impedance Imaging

We consider the imaging of anisotropic conductivity tensors $\gamma=(\gamma_{ij})_{1\leq i,j\leq 2}$ from knowledge of several internal current densities $\mathcal{J}=\gamma\nabla u$ where $u$ satisfies a second order elliptic equation…

The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to…

Deep learning, due to its unprecedented success in tasks such as image classification, has emerged as a new tool in image reconstruction with potential to change the field. In this paper we demonstrate a crucial phenomenon: deep learning…

In this paper, we present sharp stability results for various reverse isoperimetric problems in $\mathbb R^2$. Specifically, we prove the stability of the reverse isoperimetric inequality for $\lambda$-convex bodies -- convex bodies with…

We present a novel method for reconstructing the thermal conductivity coefficient in 1D and 2D heat equations using moving sensors that dynamically traverse the domain to record sparse and noisy temperature measurements. We significantly…

We consider the electrostatic inverse boundary value problem also known as electrical impedance tomography (EIT) for the case where the conductivity is a piecewise linear function on a domain $\Omega\subset\mathbb{R}^n$ and we show that a…

In this paper we prove several new stability results for the reconstruction of binary images from two projections. We consider an original image that is uniquely determined by its projections and possible reconstructions from slightly…

We consider the problem of recovering an isotropic conductivity outside some perfectly conducting or insulating inclusions from the interior measurement of the magnitude of one current density field $|J|$. We prove that the conductivity…

The problem of image reconstruction under multiple light scattering is usually formulated as a regularized non-convex optimization. A deep learning architecture, Scattering Decoder (ScaDec), was recently proposed to solve this problem in a…

We consider the inverse problem of estimating the shape profile of an unknown deposit from a set of eddy current impedance measurements. The measurements are acquired with an axial probe, which is modeled by a set of coils that generate a…

In Electrical Impedance Tomography (EIT) one wants to image the conductivity distribution of a body from current and voltage measurements carried out on its boundary. In this paper we consider the underlying mathematical model, the inverse…

Charge density waves (CDWs) are understood in great details in one dimension, but they remain largely enigmatic in two dimensional systems. In particular, numerous aspects of the associated energy gap and the formation mechanism are not…

In this paper we address the issue of output instability of deep neural networks: small perturbations in the visual input can significantly distort the feature embeddings and output of a neural network. Such instability affects many deep…

We provide a mathematical analysis and a numerical framework for Lorentz force electrical conductivity imaging. Ultrasonic vibration of a tissue in the presence of a static magnetic field induces an electrical current by the Lorentz force.…

Coherent diffractive imaging (CDI) has been widely applied in the physical and biological sciences using synchrotron radiation, XFELs, high harmonic generation, electrons and optical lasers. One of CDI's important applications is to probe…

This paper is concerned with the stability issue in determining absorption and diffusion coefficients in photoacoustic imaging. Assuming that the medium is layered and the acoustic wave speed is known we derive global H\"{o}lder stability…

We discuss a new approach to three-dimensional electrical impedance imaging based on a reduction of the information to be demanded from a reconstruction algorithm. Images are obtained from a single measurement by suitably simplifying the…

In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward…

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.…

We prove new global stability estimates for the Gel'fand-Calderon inverse problem in 3D. For sufficiently regular potentials this result of the present work is a principal improvement of the result of [G. Alessandrini, Stable determination…