Phase difference-based multichannel phase unwrapping

This work addresses the derivation of the phase difference-based maximum likelihood (ML) phase unwrapping algorithm. To this end, we derive the joint statistics of the phase differences on a two-dimensional grid for the multichannel case, where several scaled wrapped phase values are available. Subsequently, we determine and study the structure of the phase difference-based ML estimator and compare it to known phase unwrapping techniques. This work allows us to frame single and multichannel algorithms in a common formulation. Moreover, among the known single-channel phase difference-based procedures, we identify those attaining an ML solution. We also show that multichannel phase difference-based and, recently proposed, phase-based ML algorithms achieve equivalent solutions.