Phase-unwrapping algorithm for translation extraction from spherical navigator echoes.

Spherical navigator echoes have been shown to determine rigid-body rotation and translation simultaneously. Following the determination of rotation, translations are determined from the phase change between the baseline and transformed spherical navigator echoes. Because the measured phase change is limited in the interval (-pi, pi), a phase-unwrapping algorithm is required to recover the true phase change in absolute values. The unwrapping algorithm presented in this article is based on a priori information about the true translation-induced phase-change function. The algorithm is verified using simulation and in vivo experiments, and the accuracy and precision of translation determination are evaluated. Specifically, the effects of background and off-resonance-induced phase noise are explored. When the proposed phase-unwrapping algorithm was used, translations up to 15 mm were measured, with accuracy better than 5%; for translations up to 40 mm, an error of approximately 10% was observed.