Fourier Image Manipulation Tools¶
There are a few interesting Fourier-based image manipulation tools implemented in this package.
The Fourier shift theorem allows an image to be shifted in any directions by an arbitrary amount, including sub-pixel shifts. It is more computationally efficient than most interpolation techniques (or at least, so I think). It is described well in this lecture and in the NRAO interferometry course.
The shift code is in
The similarity theorem, or scale theorem, allows you to upsample timestreams. You cannot gain information below the image scale, but it is useful for getting sub-pixel information about gaussian peaks, for example. This NRAO lecture details the math.
I made use of a lot of not particularly easy to find documents when writing this code.
As stated elsewhere, though, the main inspiration for this work was Manuel Guizar’s DFT upsampling technique