Robust phase retrieval algorithm for noisy diffraction patterns using normalized convolution

Phase retrieval is an iterative method that has been developed to recover the lost phase information in coherent diffraction imaging. The most widely used algorithm is the hybrid input-output (HIO) algorithm because of its ability to avoid local minimum. Unfortunately the presence of noise in the images acquired disturbs the convergence of the algorithm. A few solutions have been proposed in order to improve the quality of the recovered images but they unfortunately still suffer from oscillations even though they are less susceptible to noise than the traditional method. In this paper, we propose a robust method to reconstruct diffraction patterns which are corrupted by Poisson noise. Our method relies on the HIO algorithm, combined with a Gaussian filter to avoid the oscillation and with normalized convolution (NC) to improve the quality of the filtered images. We describe the principle of our approach and present the results of simulations which have been made to evaluate its performance and to draw a comparison with the others existing algorithms that have been developed so far.