Partially parallel magnetic resonance imaging using arbitrary k-space trajectories with image reconstruction based on successive convolution operations

Abstract

In a first step of image formation by MRI or the like, a gridding convolution is performed for each coil using a Kaiser-Bessel kernel, so that each coil channel now contains data on grid points. In the second step, another 2D convolution is performed on each of the gridded coil data sets in either k-space or image space, and all the convolutions are summed up to produce the composite k-space data set for the target coil. In the third step, the composite data set is then transformed to form an un-aliased image for that coil. In the fourth step, the un-aliased images for all the coils are combined using square-root-of-sum-of-squares to form the final reconstructed image.