Codes for "Multigrid methods for total variation"

These codes implement the experiments for the article “Multigrid methods for total variation” (arXiv:2502.18659) by Felipe Guerra and Tuomo Valkonen.

Prerequisites

These codes were written for Julia 1.11. You may get Julia from julialang.org.

Usage

Navigate your unix (or other) shell to the directory containing this README.md and then run:

$ julia --project=.

The first time doing this, to ensure all the dependencies are installed, run

$ ]instantiate

Afterwards in the Julia shell, type:

> using MultigridCodes

This may take a while as Julia precompiles the code.

Then, to generate all the experiments for the article

> batchrun_article()

The results will be saved on disk.

Data sources

The Blue Marble image is in the public domain. It is loaded via the Julia TestImages package.

The file phantom_slice.mat is extracted, as described in phantom_slice.md, from

• Belzunce, M. A. (2018). High-Resolution Heterogeneous Digital PET [18F]FDG Brain Phantom based on the BigBrain Atlas (1.0) [Data set]. Zenodo. https://doi.org/10.5281/zenodo.1190598