How does wavelet sharpening actually work, eg. in RegiStax?

Question

I recently came across some demonstrations on how to use RegiStax6 and its Wavelet filters to sharpen images, especially planetary shots.

The instructions I found and read/watched all had in common that there was a lot of playing with the different sliders, but no satisfying explanation of what the different values actually meant. Possibly partly because of that I have never been able to recreate the kind of sharpening that does seem to be possible with this tool!

So, for better usage of the wavelet tool (in registax oder some other software you might recommend) I would like to know: How do the different parameters ('denoise', 'sharpen', the unlabeled slider) in the different layers affect the image; how does the 'step increment' section affect the layers; an what could be a good approach to use all this in sharpening images?

(I do have some basic knowledge about filtering, had to code grayscale gaussian filtering by hand in university, but until now I have no clue how this wavelet sharpening works.)

Answer 1

The math is pretty simple.

1. Take an image, Lets call it LPF (Low Pass Filter) of Scale 0.
2. Blur it with LPF Filter (For example, Gaussian Blur). Call this result LPF of Scale 1.
3. Do LPF Scale n - LPF Scale n + 1 => HPF (High Pass Filter) Scale n + 1.

Do this over and over.
Now process the HPF images to taste and reverse the operation.

Wavelets are just a family of filters which can be used for that with special properties (One of them being the Gaussian Kernel).

You can read about it in Wikipedia - Pyramid (Image Processing) which is the proto type of Wavelets.

There is a tool for that in Photoshop called Know-How Transfer Wow! (Multi) Frequency Equalizer.