Phase Local Approximation (PhaseLa) Technique for Phase Unwrap From Noisy Data

摘要

The local polynomial approximation $({hbox {LPA}})$ is a nonparametric regression technique with pointwise estimation in a sliding window. We apply the ${hbox {LPA}}$ of the argument of $cos $ and $sin $ in order to estimate the absolute phase from noisy wrapped phase data. Using the intersection of confidence interval $({hbox {ICI}})$ algorithm, the window size is selected as adaptive pointwise varying. This adaptation gives the phase estimate with the accuracy close to optimal in the mean squared sense. For calculations, we use a Gauss–Newton recursive procedure initiated by the phase estimates obtained for the neighboring points. It enables tracking properties of the algorithm and its ability to go beyond the principal interval $[-pi,pi)$ and to reconstruct the absolute phase from wrapped phase observations even when the magnitude of the phase difference takes quite large values. The algorithm demonstrates a very good accuracy of the phase reconstruction which on many occasion overcomes the accuracy of the state-of-the-art algorithms developed for noisy phase unwrap. The theoretical analysis produced for the accuracy of the pointwise estimates is used for justification of the ${hbox {ICI}}$ adaptation algorithm.