MR image reconstruction from generalized projections

Purpose: Currently, the time required for image reconstruction is prohibitively long if data are acquired using multidimensional imaging trajectories that make use of multichannel systems equipped with nonlinear gradients. Methods are presented that reduce the computational complexity of the iterative time-domain reconstruction algorithm down from O(N4 ) to O(N3 ). Theory: For generalized projections, a large class of multidimensional imaging trajectories, the encoding matrix can be focused to sparse bands by introducing an appropriate filter function along the frequency-encoding direction. The reconstruction can be speeded up by ignoring values below a predefined threshold level. Methods: Two methods are presented that differ in how the filter is incorporated into the reconstruction algorithm. The first method represents, without implementation of a threshold, a weighted version of the time-domain method, while the second method is equivalent to it. Results: Simulation and measurement results show that image reconstruction from high-resolution imaging data can be speeded up by up to two orders of magnitude. While the weighted reconstruction requires more iterations to reach an optimum than the second method, it is less sensitive to thresholding. Conclusion: For complex spatial encoding strategies that involve nonlinear gradient fields, fast and accurate image reconstruction methods are provided that are particularly efficient for high-resolution anatomical imaging