Approximation of a complex interferogram by a sum of complex exponentials: an application to phase unwrapping

摘要

Phase unwrapping (PU), i.e. the retrieval of absolute phases from wrapped, noisy phase measurements, is a tough problem which arises in various realms of signal processing. Generally, the adopted PU strategy consists in integrating the estimated phase gradients or instantaneous frequencies (IFs). The standard IF estimation technique used by most PU algorithms is the simple wrapping-of-the-wrapped-phase-gradient rule. However, this rule results in a strongly biased estimations as the noise level grows. The idea on which this paper relies consists in locally approximating the interferogram by a sum of complex exponentials. The algorithm described in this paper makes use of the Matrix Pencial (MP) method for estimating the parameters of these exponentials, i.e. their amplitude and frequency. The proposed algorithm is applied to the unwrapping of noisy synthetic interferograms. The results are compared with those obtained unwrapping the same interferograms by means of the classical wrapping-of-the-wrapped-phase-gradient rule.