Related papers: A convergent algorithm for the hybrid problem of r…
In this paper, we consider the problem of phase retrieval, which consists of recovering an $n$-dimensional real vector from the magnitude of its $m$ linear measurements. We propose a mirror descent (or Bregman gradient descent) algorithm…
We study the inverse boundary value problem of detecting a non-uniform conductivity motivated by pacing-guided ablation in cardiac electrophysiology. At the stationary level, the transmembrane potential $u$ in a region…
Conductivity reconstruction in an inverse eddy current problem is considered in the present paper. With the electric field measurement on part of domain boundary, we formulate the reconstruction problem to a constrained optimization problem…
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 H(div)-conforming approach for the Brinkman equation is studied numerically, verifying the theoretical a priori and a posteriori analysis in previous work of the authors. Furthermore, the results are extended to cover a non-constant…
The phase retrieval problem is a fundamental problem in many fields, which is appealing for investigation. It is to recover the signal vector $\tilde{x}\in\mathbb{C}^d$ from a set of $N$ measurements $b_n=|f^*_n\tilde{x}|^2,\ n=1,\cdots,…
This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal $f \in \C^N$ and a randomly chosen set of frequencies $\Omega$ of mean size $\tau N$. Is it possible 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 inverse conductivity problem of how to reconstruct an isotropic electrical conductivity distribution $\gamma$ in an object from static electrical measurements on the boundary of the object. We give an exact reconstruction…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
Magnetic resonance electrical impedance tomography (MREIT) aims to recover the electrical conductivity distribution of an object using partial information of magnetic flux densities inside the tissue which can be measured using an MRI…
This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric…
In this paper we develop a convergence analysis in an infinite dimensional setting of the Levenberg-Marquardt iteration for the solution of a hybrid conductivity imaging problem. The problem consists in determining the spatially varying…
This article is concerned with the reconstruction of obstacle $\O$ immersed in a fluid flowing in a bounded domain $\Omega$ in the two dimensional case. We assume that the fluid motion is governed by the Stokes-Brinkmann equations. We make…
In this paper we address the problem of recovering a matrix, with inherent low rank structure, from its lower dimensional projections. This problem is frequently encountered in wide range of areas including pattern recognition, wireless…
In this paper we propose a new fast splitting algorithm to solve the Weighted Split Bregman minimization problem in the backward step of an accelerated Forward-Backward algorithm. Beside proving the convergence of the method, numerical…
We study existence of minimizers of the least gradient problem \[\inf_{v \in BV_g} \int_{\Omega}\varphi(x, Dv),\] where $BV_g=\{v \in BV(\Omega): \int_{\partial \Omega}gv=1\}$, $\varphi(x,p): \Omega\times \R^n \rightarrow \R$ is a convex,…
There are several hybrid inverse problems for equations of the form $\nabla \cdot D \nabla u - \sigma u = 0$ in which we want to obtain the coefficients $D$ and $\sigma$ on a domain $\Omega$ when the solutions $u$ are known. One approach is…
In Acousto-Electric tomography, the objective is to extract information about the interior electrical conductivity in a physical body from knowledge of the interior power density data generated from prescribed boundary conditions for the…
Ultrasound modulated bioluminescence tomography (UMBLT) is an imaging method which can be formulated as a hybrid inverse source problem. In the regime where light propagation is modeled by a radiative transfer equation, previous approaches…