  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.
