In this paper, we propose a Wirtinger flow algorithm with optimal stepsize for short-time Fourier transform (STFT) phase retrieval. Based on the Wirtinger flow algorithm, we utilizes a noise relaxation to acquire high signal-to-noise-ratio (SNR) reconstruction and an optimal stepsize strategy to accelerate the convergence. The proposed algorithm satisfies the regularity condition for constant modulus signals with noise-free STFT measurements, and has theoretical basin of attraction. Numerical results demonstrate the convergence for noise-free measurements, and the effectiveness in noise reduction.
In this paper, we propose an end-to-end neural network abbreviated as TCNN to solve the blind phase retrieval problem in multiple scattering imaging. TCNN is a kind of auto-encoder with a transform layer, which acts as a bridge between transforming domains. Compared to double phase retrieval method, TCNN can directly estimate the image from those phaseless measurements through the nonlinear network structure. During training, the parameters of TCNN are updated by the adaptive moment estimation algorithm Adam. Numerical experiments show that TCNN can recover images with comparable quality to that of state-of-the-art methods. Moreover, TCNN hugely reduces the time cost for recovering images once the training procedure is completed.
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