Smallest Singular Value: a metric for assessing k-space sampling patterns

A new metric for assessing k-space sampling patterns is presented, which analyzes the smallest singular values (SSV) of the image reconstruction linear operator. The SSV is described along with an efficient means of calculation. It is compared to the gold-standard g-factor, and ranks candidate sampling patterns very similarly. SSV can assess patterns in seconds to minutes, allowing for several interesting applications. We describe one application: assessing random sampling distributions for incoherent aliasing statistics on uniform and poisson-disk sampling patterns are easily computed over thousands of random patterns, and interesting trends arise!

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