A predictor–corrector phase unwrapping algorithm for temporally undersampled gradient-echo MRI
Deepu Kurian, Gisela E. Hagberg, Klaus Scheffler, Joseph Suresh Paul
Abstract
Purpose
To develop a method for unwrapping temporally undersampled and nonlinear gradient recalled echo (GRE) phase.
Theory and Methods
Temporal unwrapping is performed as a sequential one step prediction of the echo phase, followed by a correction to the nearest integer wrap-count. A spatio-temporal extension of the 1D predictor corrector unwrapping (PCU) algorithm improves the prediction accuracy, and thereby maintains spatial continuity. The proposed method is evaluated using numerical phantom, physical phantom, and in vivo brain data at both 3 T and 9.4 T. The unwrapping performance is compared with the state-of-the-art temporal and spatial unwrapping algorithms, and the spatio-temporal iterative virtual-echo based Nyquist sampled (iVENyS) algorithm.
Results
Simulation results showed significant reduction in unwrapping errors at higher echoes compared with the state-of-the-art algorithms. Similar to the iVENyS algorithm, the PCU algorithm was able to generate spatially smooth phase images for in vivo data acquired at 3 T and 9.4 T, bypassing the use of additional spatial unwrapping step. A key advantage over iVENyS algorithm is the superior performance of PCU algorithm at higher echoes.
Conclusion
PCU algorithm serves as a robust phase unwrapping method for temporally undersampled and nonlinear GRE phase, particularly in the presence of high field gradients.