Direct reconstruction of MR images from data acquired on a non-Cartesian grid using an equal-phase-line algorithm.

Abstract

The equal-phase line (EPL) algorithm is proposed as a means of allowing rapid Fourier transform (FT) reconstruction of MR image data acquired on a non-Cartesian grid. The pixels on the image are grouped according to their positions. The pixels in a group have the same phase in the complex exponential function -exp[j2pi(xu + yv)] and receive the same contribution from a data point. Each group is related to an EPL in the image space. The contribution of a data point can then be distributed to the pixels along the EPLs. The described EPL algorithm enables a decrease of the reconstruction time to about 40% of the direct FT (DrFT) for the non-Cartesian data. A numerical phantom and two sets of in vivo spiral data were used to investigate an optimal number of the EPLs and to measure the reconstruction time. The EPL algorithm runs nearly as fast as the look-up table (LUT) method (Dale et al. IEEE Trans Med Imaging 2001;20:207-217), but it does not require a large memory to store the coefficients in advance, as is required in the LUT method. Thus, the EPL algorithm can be used to reconstruct images up to 512 x 512 pixels in size in a PC of limited memory, and may be more conveniently applied to a multiprocessor system.