A general framework for denoising phaseless diffraction measurements

We propose a general framework to recover underlying images from noisy phaseless diffraction measurements based on the alternating directional method of multipliers and the plug-and-play technique. The algorithm consists of three-step iterations: (i) Solving a generalized least square problem with the maximum a posteriori (MAP) estimate of the noise, (ii) Gaussian denoising and (iii) updating the multipliers. The denoising step utilizes higher order filters such as total generalized variation and nonlocal sparsity based filters including nonlocal mean (NLM) and Block-matching and 3D filtering (BM3D) filters. The multipliers are updated by a symmetric technique to increase convergence speed. The proposed method with low computational complexity is provided with theoretical convergence guarantee, and it enables recovering images with sharp edges, clean background and repetitive features from noisy phaseless measurements. Numerous numerical experiments for Fourier phase retrieval (PR) as coded diffraction and ptychographic patterns are performed to verify the convergence and efficiency, showing that our proposed method outperforms the state-of-art PR algorithms without any regularization and those with total variational regularization.