Diffusion sampling schemes: A generalized methodology with nongeometric criteria

Abstract

Purpose:The aim of this paper is to show that geometrical criteria for designingmultishellq-space sampling procedures do not necessarily translate into recon-struction matrices with high figures of merit commonly used in the compressedsensing theory. In addition, we show that a well-known method for visitingk-space in radial three-dimensional acquisitions, namely, the Spiral Phyllotaxis,is a competitive initialization for the optimization of our nonconvex objectivefunction.Theory and Methods:We propose the gradient design method WISH (WeIght-ing SHells) which uses an objective function that accounts for weighted dis-tances between gradients withinM-tuples of consecutive shells, withMrangingbetween 1 and the maximum number of shellsS. All theM-tuples share thesame weight𝜔�M. The objective function is optimized for a sample of theseweights, using Spiral Phyllotaxis as initialization. State-of-the-art General Elec-trostatic Energy Minimization (GEEM) and Spherical Codes (SC) were used forcomparison. For the three methods, reconstruction matrices of the attenuationsignal using MAP-MRI were tested using figures of merit borrowed from theCompressed Sensing theory (namely, Restricted Isometry Property —RIP— andCoherence); we also tested the gradient design using a geometric criterion basedon Voronoi cells.Results:For RIP and Coherence, WISH got better results in at least one com-bination of weights, whilst the criterion based on Voronoi cells showed anunrelated pattern.Conclusion:The versatility provided by WISH is supported by better results.Optimization in the weight parameter space is likely to provide additionalimprovements. For a practical design with an intermediate number of gradients,our results recommend to carry out the methodology here used to determine theappropriate gradient table.