[gnuastro-devel] [task #14775] Convolution with varying PSF/Kernel over the image

[Mohammad Akhlaghi]

Follow-up Comment #1, task #14775 (project gnuastro):

This is just a brainstorm which only works in the spatial domain
<https://www.gnu.org/software/gnuastro/manual/html_node/Spatial-domain-convolution.html>.


Convolve can take a labeled image (the same size as the input) which will tell
it that we want a varying PSF. It will also take multiple kernels (through
multiple calls to `--kernel'). 

The label on each pixel can be used to identify which kernel should be used to
convolve that pixel (in the order that the user input the kernels). 

So for example Convolve can be called with a command like this:


$ astconvolve image.fits --labels=labels.fits --kernel=kernel1.fits \
              --kernel=kernel2.fits --kernel=kernel3.fits


For a simple example, if the image is 5x5, the following labeled image will
tell Convolve which kernel to use for which pixel. If the pixel has a label of
1, then `kernel1.fits' will be used to convolve it. Similarly, if it has a
label of 2 or 3, then `kernel2.fits' and `kernel3.fits' will be used
respectively.


3 3 2 3 3
3 2 1 2 3
3 1 1 1 3
3 2 1 2 3
3 3 2 3 3


If the kernels are all the same size, this is very easy to implement in the
spatial domain. We can later do some work to allow various sizes.

The great thing with this method is that it is completely non-parametric: the
kernels can be completely independent and can have any shape and the their
positioning is also completely free over the image. 

MakeProfiles (though its cercumference profile) can be used to make such a
labeled image in a circular/elliptical shape over an image.

I currently can't think how such a varying PSF can be implemented in the
frequency domain
<https://www.gnu.org/software/gnuastro/manual/html_node/Frequency-domain-and-Fourier-operations.html>.
I must confess I still haven't had the chance to go over the two references of
the previous post. I just thought of putting this here before I forget (I
don't have the time to implement it anyway now).

If you see any issues in this strategy, or have a better proposal, please
share your thoughts here so we can discuss it until a good solution is found.

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