Iterative Reconstruction Methods for Non-cartesian Mri

For magnetic resonance imaging (MRI) with Cartesian k-space sampling, a simple inverse FFT usually suffices for image reconstruction. More sophisticated image reconstruction methods are needed for non-Cartesian k-space acquisitions. Regularized least-squares methods for image reconstruction involve minimizing a cost function consisting of a least-squares data fit term plus a regularizing roughness penalty that controls noise in the image estimate. Iterative algorithms are usually used to minimize such cost functions. This paper summarizes the formulation of iterative methods for image reconstruction from non-Cartesian k-space samples, and describes some of the benefits of iterative methods. The primary disadvantage of iterative methods is the increased computation time, and methods for accelerating convergence are also discussed.