A multiresolution approach to improve phase unwrapping

A method is presented for robust phase unwrapping based on instantaneous frequency estimation at multiple resolutions. Estimation is done of the frequency difference between resolution levels, resulting in asymptotically zero bias in the aliasing error. The frequency for the highest resolution level is found by the sum of difference frequencies, and the final frequency estimates are input to a least squares phase reconstruction algorithm. A hierarchical algorithm for frequency estimation at all resolution levels, based on the correlation Doppler centroid estimator, is derived. Also, an adaptive multiresolution approach is presented, in which the highest resolution level required for a frequency estimate without aliasing and thus a smooth phase reconstruction, is determined at each point. The method is investigated by simulations, and results show successful phase unwrapping without slope bias, even in the presence of undersampling and low coherence