How to determine the scaling?

[dangallichan]

I've been very impressed overall with the power of the gpuNUFFT tool, but have a question for a particular use case: is there an easy way to determine the scaling that is applied between the image space and the frequency space, such that it could match using an FFT instead? What I mean by this is that if I have k-space data and reconstruct an image, the scaling is quite different to if I do an inverse FFT - and from the permutations I've tried it is not off by an obvious scaling (nxnynz for example). I wonder if there is a fixed scaling factor that is applied internally somewhere?

[FlorianKnoll]

Hi Dan,

what you are observing is that the NUFFT is a non-orthogonal transformation, in contrast to the FFT. So this is an inherent property of the NUFFT that the scaling before and after the transformation does not match. You can determine this by estimating the spectral radius of the operator (the eigenvalue with the largest magnitude), and one method to do this is the power iteration: https://en.wikipedia.org/wiki/Power_iteration.

Best wishes, Florian