COMPARING MR IMAGING PROPERTIES OF SPIRAL TRAJECTORIES USING THE SINGULAR SPECTRUM OF THE ANALYTICAL FOURIER BASIS CROSS-CORRELATION MATRIX

We compare fixed and variable density and randomized spiral trajectories for MR imaging in terms of PSF resolution and stopband ripple and noise amplification, with the singular value spectrum of the cross-correlation Fourier basis matrix as an analysis tool. We explain the rationale behind using that matrix and why its singular spectrum is meaningful. We show that the relative number of singular values above an easily determined threshold is an indicator of resolution, and the shape of the rest of the spectrum an indicator of noise vs. reconstruction accuracy tradeoffs.