An efficient non-iterative reconstruction algorithm for parallel MRI with arbitrary k-space trajectories

Parallel imaging using multiple receiver coils has emerged as an effective tool to reduce imaging time in various MRI applications. Although several different image reconstruction methods have been developed and demonstrated to be successful for Cartesian k-space trajectories, there is a lack of efficient reconstruction methods for arbitrary trajectories. In this paper, we formulate the reconstruction problem in k-space and propose a novel image reconstruction method that is fast and effective for arbitrary trajectories. To obtain the desired image, the method reconstructs the Nyquist-sampled k-space data of the image on a uniform Cartesian grid from the undersampled multichannel k-space data on an arbitrary grid, followed by inverse Fourier transform. We demonstrate the effectiveness of the proposed fast algorithm using simulations. In particular, we compare the proposed method with the existing iterative method and show that the former is able to achieve similar image quality to the latter but with reduced computational complexity.