相关论文: Stability of Current Density Impedance Imaging
We consider the stability issue of the inverse conductivity problem for a conformal class of anisotropic conductivities in terms of the local Dirichlet-to-Neumann map. We extend here the stability result obtained by Alessandrini and…
In this work we consider stability of recovery of the conductivity and attenuation coefficients of the stationary Maxwell and Schr\"odinger equations from a complete set of (Cauchy) boundary data. By using complex geometrical optics…
X-ray computed tomographic infrastructures are medical imaging modalities that rely on the acquisition of rays crossing examined objects while measuring their intensity decrease. Physical measurements are post-processed by mathematical…
Image registration aims to establish spatial correspondence across pairs, or groups of images, and is a cornerstone of medical image computing and computer-assisted-interventions. Currently, most deep learning-based registration methods…
The high inertia of classical fluid coating processes severely limits the possibility of controlling the deposited film thickness through the entrainment velocity. We describe and characterize a new experimental device where the inertia is…
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…
In this work we propose and analyze a numerical method for electrical impedance tomography of recovering a piecewise constant conductivity from boundary voltage measurements. It is based on standard Tikhonov regularization with a…
The electric current conservation in a two-dimensional quantum wire under a time dependent field is investigated. Such a conservation is obtained as the global density of states contribution to the emittance is balanced by the contribution…
In this paper we study the inverse conductivity problem with partial data in dimension $n\geq 3$. We derive stability estimates for this inverse problem if the conductivity has $C^{1,\sigma}(\bar\Omega)\cap H^{3/2+\sigma}(\Omega)$…
Under a convexity assumption on the boundary we solve a local inverse problem, namely we show that the geodesic X-ray transform can be inverted locally in a stable manner; one even has a reconstruction formula. We also show that under an…
Recovering a high-quality image from noisy indirect measurements is an important problem with many applications. For such inverse problems, supervised deep convolutional neural network (CNN)-based denoising methods have shown strong…
This work presents a new constructive uniqueness proof for Calder\'on's inverse problem of electrical impedance tomography, subject to local Cauchy data, for a large class of piecewise constant conductivities that we call "piecewise…
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 $M$…
This article adapts the framework of metamorphosis to solve inverse problems in imaging that includes joint reconstruction and image registration. The deformations in question have two components, one that is a geometric deformation moving…
Recent advancements in Blind Image Restoration (BIR) methods, based on Generative Adversarial Networks and Diffusion Models, have significantly improved visual quality. However, they present significant challenges for Image Quality…
Ptychography, a special case of the phase retrieval problem, is a popular method in modern imaging. Its measurements are based on the shifts of a locally supported window function. In general, direct recovery of an object from such…
The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it…
We review recent stability and separation results in volume comparison problems and use them to prove several hyper- plane inequalities for intersection and projection bodies.
We lay the foundations for a new fast method to reconstruct the electron density in x-ray scanning applications using measurements in the dark field. This approach is applied to a type of machine configuration with fixed energy sensitive…
We prove an optimal stability estimate for Electrical Impedance Tomography with local data, in the case when the conductivity is precisely known on a neighborhood of the boundary. The main novelty here is that we provide a rather general…