Use Radon transform to remove diffraction spikes in a telescope image
For a full discussion, visit : https://erellaz.com/diffraction-spike-attenuation/
The linear Radon transform is a well established integral transform which maps the space (x, y) domain into a new domain, the radon domain (tau, p).
See Wikipedia: Radon transform, Hough transform, Sonogram, Tau p transform.
The Radon transform collapses (focuses) linear events into points.
After Radon transform:
- The linear events (diffraction patterns) and the signal are disjoint (map in different areas of the Radon plane)
- The linear events (diffraction patterns) are collapsed (concentrated in a small area of the Radon plane). So now the diffraction can be muted (masked) without damaging the data.
The code attached is written in python 2. I will futurize to python 3 at some point.
The module astropy.io handles fits format (works on both mono and RGB) for input and output. Skimage is used for the radon and inverse radon transform.
There is quite a bit happening under the hood. The data is split in overlapping window, each processed independently. This is a classical signal processing technique.
Bottom line: it works, as shown in the example attached. The diffraction is attenuated or even completely removed. The underlying data is revealed.