Fourier-domain image optimization and deconvolution

This repository contains the implementation of the technical report on How to Solve Convex Image Optimization and Deconvolution Efficiently in the Fourier Domain, available online on arXiv.

Authors

• Majed El Helou
• Frederike Dümbgen (frederike.duembgen@epfl.ch)
• Radhakrishna Achanta
• Sabine Süsstrunk

Overview

This repository contains the following scripts:

• python/Convolution.ipynb
• matlab/Convolution.m

Scripts for visualizing the convolution in space and Fourier domains.

• python/Optimization.ipynb
• matlab/Optimization.m

Script for solving the image debluring example in Fourier domain.

• python/tools.py
• python/psf2otf.py
• matlab/sh_computation.m
• matlab/vec2mat.m

Tools for plotting and other basic operations.

Contribute

We are happy about contributions of any form (implementation in different programming language, improvement of existing code, etc.). Please submit a pull request if you have something to be added to the code, or send us an e-mail.

Acknowledgments

We would like to thank Dr. Zahra Sadeghipoor, Dr. Nikolaos Arvanitopoulos and Dr. Radhakrishna Achanta for valuable discussions and advice. The authors also thank Alexandre Boucaud for providing a python implementation of psf2otf.

License

This source code is provided under the MIT license.

If you are using this code or parts of it in your own implementation, please cite it as follows:

@article{el2018fourier,
  title={Fourier-domain optimization for image processing},
  author={El Helou, Majed and D{\"u}mbgen, Frederike and Achanta, Radhakrishna and S{\"u}sstrunk, Sabine},
  journal={arXiv preprint arXiv:1809.04187},
  year={2018}
}