Analytic Estimation of Subsample Spatial Shift Using the Phases of Multidimensional Analytic Signals

In this correspondence, a method of analytic subsample spatial shift estimation based on an
a

priori

n
-D signal model is proposed. The estimation uses the linear phases of
n
analytic signals defined with the multidimensional Hilbert transform. This estimation proposes: i) an analytic solution to the
n
-D shift estimation and ii) an estimation without processing complex cross-correlation function or cross-spectra between signals contrary to most phase shift estimators. The method provides better performance in estimating subsample shifts than two classical estimators, one using the maximum of cross-correlation function and the other seeking the zero of the complex correlation function phase. Two delay estimators using the in-phase and quadrature-phase components of signals are also compared to our estimator. Like most estimators using the complex signal phases, the estimator proposed herein presents the advantage of unaltered accuracy when low sampled signals are used. Moreover, we show that this method can be applied to motion tracking with ultrasound images. Thus, included in a block-based motion estimation method and tested with ultrasound data, this estimator provides an analytical solution to the translation estimation problem.