Efficient k‐space sampling by density‐weighted phase‐encoding

Acquisition‐weighting improves the localization of MRI experiments. An approach to acquisition‐weighting in a purely phase‐encoded experiment is presented that is based on a variation of the sampling density in k‐space. In contrast to conventional imaging or to accumulation‐weighting, where k‐space is sampled with uniform increments, density‐weighting varies the distance between neighboring sampling points Δk to approximate a given radial weighting function. A fast, noniterative algorithm has been developed to calculate the sampling matrix in one, two, and three dimensions from a radial weighting function w(k), the desired number of scans NAtot and the nominal spatial resolution Δxnom. Density‐weighted phase‐encoding combines the improved shape of the spatial response function and the high SNR of acquisition‐weighting with an extended field of view. The artifact energy that results from aliasing due to a small field of view is substantially reduced. The properties of density‐weighting are compared to uniform and to accumulation‐weighted phase‐encoding in simulations and experiments. Density‐weighted 31P 3D chemical shift imaging of the human heart is shown which demonstrates the superior performance of density‐weighted metabolic imaging. Magn Reson Med 50:1266–1275, 2003. © 2003 Wiley‐Liss, Inc.