fourier rotation problem: rotating an image in the fourier domain does produce rotations in the spatial domain, but there is some rotation of the phases as well. What is going on? How can we rotate an image in the frequency domain?
We are convolving two images. One is large (~ 2000x2000) while the other is rather small (~ 120x120). Is it really worthwhile to go to the fourier domain to do the convolution (as elementwise multiplication)?
We take the 120x120 pixel reference image and pad it to be the same size as the search image (say, 2000x2000) before taking the fourier transform. What is the effect in the fourier domain of padding-with-zeros in the spatial domain? Could we do the fourier transform on the small image and then do something equivalent to padding in the space domain, to save time?
detection response problem: We know that the "filter response" of a direct correlation match is the same as the autocorrelation function of the reference. Does it make sense to try to deconvolve this response pattern from the correlation map?
Through the process of particle picking by cross-correlation we find "anchor points" on the helix. We use these to form a line segment along the heiix, and then we choose boxes along this path with 90% overlap, which is fed into the particle reconstruction process which begins by determining the particle orientation of each box. It seems to me that this process is wasteful. Collectively, the boxes picked at each anchor point contain all the information about the helix. Reboxing with overlap seems like a hackish kludge to "spread the information around," enforcing symmetry incidentally and incompletely (the overlap is discrete), in the spatial domain. There must be a better way. This does, however, assume the existence of a reasonably good model; namely, one that gets the helical pitch right.