Analysis of noise-reducing phase retrieval

Previous work described a phase retrieval algorithm that accepts highly noisy Fourier modulus data and uses the numerous constraints on the coherence data, the image, and their interrelations to obtain high-quality images. In the context of intensity correlation imaging, computational results have shown that the technique is able to reduce the necessary imaging time by many orders of magnitude. The present paper is a theoretical examination of the algorithm, including the issues of convergence, the properties of the convergent image, and the relation between invariance of the image to random initial conditions and the accuracy of the foreground specification.