Reconstruction of isotropic and anisotropic conductivities from power densities in three dimensions
This repository contains MATLAB code illustrating the reconstruction algorithms that recovers the isotropic and anisotropic conductivity from power density measurements, on a cube-shaped domain. This code was developed and tested in MATLAB version R2016b.
run/ directory contains two runfiles
runIsoimplements the isotropic reconstruction
runAnisoimplements the anisotropic reconstruction
Both of the runfiles
- computes the solutions and power densities using FDM (5-pt stencil) or FEM (quadratic, PDE Toolbox)
- computes the reconstruction using methods outlined in the referenced paper
plot/ directory contains plotting tools of the output. For example, all figures in the referenced paper
can be reproduced by running
- MATLAB PDE Toolbox for solving the anisotropic forward problem.
- Manifold-valued Image Restoration Toolbox (MVIRT) for plotting anisotropic coefficient.
A modified version of
helpers/plotSPD.mis used. [Github repo]
- Imaging of isotropic and anisotropic conductivities from power densities in three dimensions
F. Monard and D. Rim
Inverse Probl. (2018) 34 (7), 075005 [arXiv]
- MVIRT, A toolbox for manifold-valued image registration.
Bergmann, R (2017).
IEEE International Conference on Image Processing, IEEE ICIP 2017, Beijing, China, September 17–20, 2017 [Github repo]
- A second order non-smooth variational model for restoring manifold-valued images
M. Bačák, R. Bergmann, G. Steidl, A. Weinmann (2016).
SIAM Journal on Scientific Computing. 38, (1), A567–A597. [doi] [www]