Subsampling Diffusion Gradients via Poisson Sphere Elimination

Abstract

Subsampling from a set of diffusion gradient directions is useful for evaluation of image acquisition and reconstruction strategies. However, a challenge associated with gradient subsampling is the requirement to ensure uniform distribution of a predetermined number of subsampled directions. Here, we introduce a method for near-uniform subsampling for an arbitrary target number of gradient directions.

Gradient subsampling requires the outcome to be ideally uniformly distributed for a target number of directions. Few methods have been proposed to tackle this problem. One approach is to select the gradient directions for each shell based on a smaller set of reference directions that are uniformly distributed. Another approach is to split a set of directions into subsets that are approximately uniformly distributed via iterative permutations. However, it is not straightforward using this method to choose a target number of output directions. In this work, we introduce a method for fast subsampling with an arbitrary target number of gradient directions without the need for reference directions or iterative optimization.

Methods

We employ Poisson sphere sample elimination for gradient subsampling.

Single-Shell Subsampling: With a desired Poisson sphere radius, a dart-throwing mechanism is used to determine whether each sample, in the order of increasing index, should be accepted or eliminated based on its distance to previously accepted samples. When two samples are close together, dart-throwing eliminates the sample with the greater index. Hence, given a set of samples in a particular order, dart-throwing picks a subset with an arbitrary size. To avoid explicitly specifying the Poisson sphere radius, we employ a greedy sample elimination algorithm to compute a weight for each sample in a given set and then eliminate the samples with weights greater than a threshold.

Multi-Shell Subsampling: We extend the above method to multi-shell subsampling with an arbitrary target number of gradient directions for each shell. For each sample in a shell, we can compute an intra-shell distance between the sample and the other samples in the same shell, and an inter-shell distance between the sample and the other samples in all shells collapsed into a single shell. We use a weighted combination of the two distances to select samples via Poisson sphere sample elimination. The optimal weight for distance combination is determined based on the minimum error between the spherical mean images computed with the subsampled directions and the original directions.

References

  1. Wu, Y., Ahmad, S., Ma, L., Yang, E., P.-T. Yap, 2021. Subsampling Diffusion Gradients via Poisson Sphere Elimination, ISMRM, May 15-20, 2021.

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