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## The Nonuniform FFT and Magnetic Resonance Image Reconstruction

### Leslie Greengard

Courant Institute, NYU

###
Thursday, April 5, 2007

007 Kemeny Hall, 4 pm

Tea 3:30 pm, 300 Kemeny Hall

**Abstract: ** The nonuniform FFT arises in a variety of
applications, from medical imaging to radio astronomy to the numerical
solution of partial differential equations. In a typical problem, one
is given an irregular sampling of *N* data points in the frequency
domain with the goal of reconstructing the corresponding function at
*N* points in the physical domain. When the sampling is uniform, the
fast Fourier transform (FFT) allows this calculation to be carried out
in *O(N\log N)* operations. Unfortunately, when the data is
nonuniform, the FFT does notapply. In the last few years, a number of
algorithms have been developed which overcome this limitation and are
often referred to as nonuniform FFTs. In this talk, we describe the
basic algorithm and its application to magnetic resonance imaging.

This talk will be accessible to graduate students.