Extension of Signal Model for Super Resolution Phase Retrieval in Continuous Domain

Abstract

Phase retrieval refers to the use of phaseless Fourier intensity measurement samples to recover the original signal. Different from the discrete signals for which the traditional algorithms are oriented, a continuous domain phase retrieval framework is proposed for sparse signals in time domain to better apply to real scenes. Because of its theoretical infinite resolution, it is also called super-resolution phase retrieval. However, the present method is only suitable for Dirac pulse train and non-uniform spline signal models, which has a narrow range and is difficult to adapt to the complex and changeable practical applications. Aiming at this problem, this paper first summarizes characteristic of signals by analyzing the existing framework: they can achieve super resolution of auto-correlation function, which contains all the information of the original parameterized signals. Next, we successfully extend the signal models to differential Dirac and piecewise polynomials, and give theoretical guarantees. Finally, the correctness of the proposed signal models is verified by the combination of simulations and practical experiment.