PJSR can do FFTs on images so it must be available in PCL as well
Indeed it is. You can perform Fourier transforms of one-dimensional and two-dimensional data. FFTs are being extensively used in several modules, mainly for convolution. One of them is Deconvolution, where an FFT-based convolution routine (available in PCL as the FFTConvolution class) is used when the PSF kernel size is larger than 15x15 by default (for smaller kernels, a direct convolution in the spatial domain is more efficient). The same for UnsharpMask. FFTs are also being used in StarMask and a few other modules, such as RestorationFilter, and in the FFTRegistration script.
I have planned a DynamicFourierTransform tool. It will be, as it name suggests, an interactive tool that will allow you to explore and change (with standard painting tools) the frequency component of the Fourier transform of an image. Then the tool will perform the inverse transform (a la ATWT). It's actually quite easy, and funny.
Nevertheless, wavelet transforms are much more suitable than Fourier transforms for most of the image processing tasks carried out in astronomy. One reason is that the FT is not
localized, while the WT (with the à trous algorithm) is. Localized here means that you can differentiate on the transform the components that correspond to a particular location in spatial coordinates. In addition, the à trous transform is
redundant, which means that each scale is an image of the same dimensions as the original. The FT only works —and works extremely well for that— to isolate image structures as a function of their frequency. In contrast, the WT lets you isolate structures as a function of their scale, or relative size. The latter is much more useful for the majority of tasks that we perform.
For a star detector, the WT is much better than the FT. This is because the stars are not, in general, distributed uniformly on the image, or distributed following a patterned distribution. What characterizes stars is basically their sizes. For this reason I have implemented a wavelet-based star detector in StarAlignment, which works remarkably well (although it has its own drawbacks, as everything). The StarMask tool is also based on a multiscale transform, although in this case it is a morphological multiscale transform.
It's too bad Kevin's talk ended before he got to the part where he explained what to do next after you've discovered there are non-random patterns in your files. I'm still mulling on that.
This is indeed one task for which the FT is obviously an ideal tool: find regular patterns. Once you've find a feature characterized in frequency, you can alter the FT (only the frequency component, never touch the phase component) to remove that feature. The classical example is removing printing patterns on scanned images. You will be able to do this with the DynamicFourierTransform (or a similar tool written by somebody —someone dares? it is actually very easy). I strongly recommend you a thorough reading of Digital Image Processing by González et al.
