How to Use the Walsh Hadamard Transform to Filter 24 bit RGB Color Values in a Localized Spatial Region?
The JPEG-XR Standard is using the Walsh Hadamard transform (Instead of DCT / Wavelets).

It has pretty good results (Unfortunately, it didn't get enough traction, yet it is supported on Windows).

You can follow the standard and have idea how to use it for image compression.
You'll be able to even get some source code.