The Fourier Transform (FT) of a vector of N=N1⋅N2 elements is decomposable into N1 FTs of N2-sized vectors followed by N2 FTs of N1-sized vectors, a fact utilized iteratively to produce the Fast FT algorithm. Put in MRI terminology, reconstructing N=k⋅M slices from k-undersampled kz-stacked trajectory can be achieved by FT, followed by solution of the M SMS problems of k slices. This can be used to reduce such 3D reconstruction problems into SMS problems, reducing memory and computational demands. The observation extends to CAIPI patterns. We term this approach kCAIPI.
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