Alpha root filtering: new feature suggestion.

[iliailmer]

Description

I would like to add a new feature: root filtering. The basic idea is to use the fast Fourier transform on the input image and then raise the magnitude of the result to the power of $alpha$ ($alpha$-root) which is a user-specified parameter. Then, the magnitude of the inverse transform is returned by the function.

The papers utilizing the feature are here, here, and here.

I listed the main reference in the description of the function:
A. K. Jain, Fundamentals of Digital Image Processing. Upper SaddleRiver, NJ: Prentice-Hall, 1989.

Checklist

• Docstrings for all functions
• Gallery example in ./doc/examples (new features only)
• Benchmark in ./benchmarks, if your changes aren't covered by an
  existing benchmark
• Unit tests
• Clean style in the spirit of PEP8

For reviewers

• Check that the PR title is short, concise, and will make sense 1 year
  later.
• Check that new functions are imported in corresponding __init__.py.
• Check that new features, API changes, and deprecations are mentioned in
  doc/release/release_dev.rst.
• Consider backporting the PR with @meeseeksdev backport to v0.14.x

[pep8speaks]

Hello @iliailmer! Thanks for updating this PR. We checked the lines you've touched for PEP 8 issues, and found:

There are currently no PEP 8 issues detected in this Pull Request. Cheers! 🍻

Comment last updated at 2022-03-22 14:44:45 UTC

[emmanuelle]

Hi @iliailmer thank you for contributing high-quality code, and sorry for the time it took to start reviewing (don't hesitate to ping devs another time :-)). I'm a bit hesitant here because the alpha-root filtering papers do not have a lot of citations. Could you please explain the advantage of the method compared to existing skimage filters (gaussian blurring, unsharp_mask function for sharpening)?

[iliailmer]

Hi @emmanuelle , thank you for the response. I think the algorithm has additional benefits: it can bring out details in greyscale images, for instance when I run it on cameraman from skimage.data.camera image it brightens the image and brings out coat buttons, etc. it's also pretty fast.