Unique phase retrieval with a bandlimited image and its Fourier transformed constraints

Phase retrieval is a long-standing issue in imaging science; however, it always faces the problems of uniqueness and algorithm stagnation. Current methods to solve such problems rely heavily on support from prior information of the imaged object. In this paper, we propose an imaging method that leverages a bandlimited image and its Fourier transformed constraints for unique phase retrieval. This method can remove both trivial and nontrivial ambiguities by using the inherent constraints of the imaging system itself—without relying on prior information of the object. Furthermore, the proposed method has also been shown to succeed in special cases, including symmetric and pure phase objects. Improvement of convergence achieved by our approach is supported by numerical simulations.