Many inverse problems involve two or more sets of variables that represent different physical quantities but are tightly coupled with each other. For example, image superresolution requires joint estimation of the image and motion parameters from noisy measurements. Exploiting this structure is key for efficiently solving these largescale optimization problems, which are often illconditioned. In this paper, we present a new method called Linearize And Project (LAP) that offers a flexible framework for solving inverse problems with coupled variables. LAP is most promising for cases when the subproblem corresponding to one of the variables is considerably easier to solve thanmore »
This content will become publicly available on November 1, 2022
A Krylov subspace type method for Electrical Impedance Tomography
Electrical Impedance Tomography (EIT) is a wellknown imaging technique for detecting the electrical properties of an object in order to detect anomalies, such as conductive or resistive targets. More specifically, EIT has many applications in medical imaging for the detection and location of bodily tumors since it is an affordable and noninvasive method, which aims to recover the internal conductivity of a body using voltage measurements resulting from applying low frequency current at electrodes placed at its surface. Mathematically, the reconstruction of the internal conductivity is a severely illposed inverse problem and yields a poor quality image reconstruction. To remedy this difficulty, at least in part, we regularize and solve the nonlinear minimization problem by the aid of a Krylov subspacetype method for the linear sub problem during each iteration. In EIT, a tumor or general anomaly can be modeled as a piecewise constant perturbation of a smooth background, hence, we solve the regularized problem on a subspace of relatively small dimension by the Flexible GolubKahan process that provides solutions that have sparse representation. For comparison, we use a wellknown modified Gauss–Newton algorithm as a benchmark. Using simulations, we demonstrate the effectiveness of the proposed method. The obtained reconstructions indicate more »
 Award ID(s):
 1633608
 Publication Date:
 NSFPAR ID:
 10341200
 Journal Name:
 ESAIM: Mathematical Modelling and Numerical Analysis
 Volume:
 55
 Issue:
 6
 Page Range or eLocationID:
 2827 to 2847
 ISSN:
 0764583X
 Sponsoring Org:
 National Science Foundation
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