This repository contains code corresponding to the paper

Baumgärtner, Herzog, Schmidt, Weiß The Proximal Map of the Weighted Mean Absolute Error arxiv: 2209.13545

• The file prox_wmae.py contains a vectorized implementation of Algorithm 1 in the paper.
• The file demo_prox_wmae.py demonstrates a simple call of this algorithm.
• The file demo_cameraman.py generates the image denoising example of the noisy cameraman image, as presented in Section 4.
• The file demo_deflection.py computes the deflection energy minimization, as presented in Section 5. The results can be rendered using pvpython, which is done in paraview_render_results.py.

In order to resolve the dependencies, it is advised to run the code inside a Docker container, following the included Dockerfile:

docker build -t prox_wmae_code .
docker run -ti -v $(pwd):/home/fenics/shared prox_wmae_code 'python3 generate_all.py'