Abstract #2432
A Theory for Sampling in k-Space - Parallel Imaging as Approximation in a Reproducing Kernel Hilbert Space
Vivek Athalye 1 , Michael Lustig 1 , and Martin Uecker 1
1
Electrical Engineering and Computer
Sciences, University of California, Berkeley, Berkeley,
CA, United States
We show that parallel imaging can be formulated as an
approximation of vector-valued functions in a
Reproducing Kernel Hilbert Space (RKHS). This
formulation provides new theoretical insights into
sampling and reconstruction in k-space. In particular,
we derive local bounds for the approximation error and
noise amplification maps in k-space. These new metrics
complement the existing g-factor maps and explain the
effect of different sampling schemes on reconstruction
quality. This is demonstrated for several sampling
patterns using numerical experiments.
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