Phase retrieval with a dual recursive scheme.

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Since optical sensors cannot detect the phase information of the light wave, recovering the missing phase from the intensity measurements, called phase retrieval (PR), is a natural and important problem in many imaging applications. In this paper, we propose a learning-based recursive dual alternating direction method of multipliers, called RD-ADMM, for phase retrieval with a dual and recursive scheme. This method tackles the PR problem by solving the primal and dual problems separately. We design a dual structure to take advantage of the information embedded in the dual problem that can help with solving the PR problem, and we show that it is feasible to use the same operator for both the primal and dual problems for regularization. To demonstrate the efficiency of this scheme, we propose a learning-based coded holographic coherent diffractive imaging system to generate the reference pattern automatically according to the intensity information of the latent complex-valued wavefront. Experiments on different kinds of images with a high noise level indicate that our method is effective and robust, and can provide higher-quality results than other commonly-used PR methods for this setup.