Partial fourier reconstruction through data fitting and convolution in k‐space

A partial Fourier acquisition scheme has been widely adopted for fast imaging. There are two problems associated with the existing techniques. First, the majority of the existing techniques demodulate the phase information and cannot provide improved phase information over zero‐padding. Second, serious artifacts can be observed in reconstruction when the phase changes rapidly because the low‐resolution phase estimate in the image space is prone to error. To tackle these two problems, a novel and robust method is introduced for partial Fourier reconstruction, using k‐space convolution. In this method, the phase information is implicitly estimated in k‐space through data fitting; the approximated phase information is applied to recover the unacquired k‐space data through Hermitian operation and convolution in k‐space. In both spin echo and gradient echo imaging experiments, the proposed method consistently produced images with the lowest error level when compared to Cuppen's algorithm, projection onto convex sets–based iterative algorithm, and Homodyne algorithm. Significant improvements are observed in images with rapid phase change. Besides the improvement on magnitude, the phase map of the images reconstructed by the proposed method also has significantly lower error level than conventional methods. Magn Reson Med, 2009. © 2009 Wiley‐Liss, Inc.