Optical reconstruction of echo planar MRI data sets

High speed magnetic resonance imaging is frequently accomplished using one of a family of echo planar imaging (EPI) methods. Many of these methods move through k-space in a decidedly non-linear fashion. Typically, the non- rectilinear data sets are interpolated onto a rectilinear grid and then reconstructed using an inverse FFT. We present a method of reconstructing non-rectilinear EPI MRI data sets utilizing an optoelectronic implementation of the 2D discrete Fourier transform (DFT) bypassing the need for interpolation or regridding. Each point in k-space is represented as a fringe pattern and is written onto a charge coupled device photosensing array. The transforms of each point are initially summed on the photodetector and finally digitally summed to form the complex image. Up to 64K arbitrarily spaced complex points can be transformed into a 256 X 256 complex output matrix in as little as 50 msec. Reconstruction of blipped sinusoidal data using a DFT results in image quality similar to traditional methods whereas preliminary results of DFT reconstruction of spiral k-space trajectory data sets shows improved resolution. We also examine methods of determining the true k-space trajectory and the affect on reconstruction artifacts.