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

Abstract

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.