Calibrationless parallel imaging reconstruction based on structured low-rank matrix completion

Purpose A calibrationless parallel imaging reconstruction method, termed simultaneous autocalibrating and k-space estimation (SAKE), is presented. It is a data-driven, coil-by-coil reconstruction method that does not require a separate calibration step for estimating coil sensitivity information. Methods In SAKE, an undersampled, multichannel dataset is structured into a single data matrix. The reconstruction is then formulated as a structured low-rank matrix completion problem. An iterative solution that implements a projection-onto-sets algorithm with singular value thresholding is described. Results Reconstruction results are demonstrated for retrospectively and prospectively undersampled, multichannel Cartesian data having no calibration signals. Additionally, non-Cartesian data reconstruction is presented. Finally, improved image quality is demonstrated by combining SAKE with wavelet-based compressed sensing. Conclusion Because estimation of coil sensitivity information is not needed, the proposed method could potentially benefit MR applications where acquiring accurate calibration data is limiting or not possible at all. Magn Reson Med 72:959–970, 2014. © 2013 Wiley Periodicals, Inc.