Efficient algorithms for generating interpolated (zoomed) MR images.

Abstract

This paper discusses the two-dimensional implementation of a number of modified fast Fourier transform (FFT) algorithms that efficiently interpolate (zoom) magnetic resonance (MR) images. If the original image was sampled at a rate satisfying the Nyquist criterion, these algorithms would effectively increase the sampling rate, permitting image details to be more easily discerned. The Skinner interpolating fast Fourier transform (SIFFT) avoids many of the computationally unnecessary complex multiplications that occur when interpolating using the normal fast Fourier transform algorithm. The novel interpolating fast Fourier transform (NIFFT) offers further savings when a subimage is required. Theoretical and experimental timings that compare the use of the normal FFT, SIFFT, and NIFFT algorithms for interpolation are given using magnetic resonance image reconstruction examples. Time savings of a factor of 2 to 4 are possible in typical experimental situations. Time savings of factors of 5 to 20 are possible when zooming images using two-dimensional band selectable digital filtering (2D-BSDF) in combination with decimation and the SIFFT algorithm. In 2D-BSDF, the original MRI data set is reduced in size to retain only those frequency components corresponding to a desired subimage, thereby decreasing the computational load associated with further processing. A significant reduction in computation time is achieved when modeling is combined with 2D-BSDF and SIFFT as fewer points require modeling.