Multidimensional phase unwrapping for consistent APF estimation

The instantaneous amplitude, phase, and frequency (APF) characterize a nonstationary signal on a fundamental level. In this paper, we seek to obtain a consistent multidimensional APF where the estimated phase and frequency agree and where the frequency can be obtained as the gradient of an analytical phase model. Currently existing multidimensional phase unwrapping algorithms are incapable of providing this because they erroneously assume bandlimits on the trajectory of the instantaneous frequency and thus suffer from the "phase aliasing" phenomenon. We present a new multidimensional phase unwrapping algorithm based on tensor product splines that does not make this assumption and thereby largely eliminates the deleterious effects of phase aliasing.