Unsupervised Phase Retrieval Using Deep Approximate MMSE Estimation

Phase retrieval (PR) is about reconstructing a signal from the magnitude of a number of its complex-valued linear measurements. Recent rapid progress has been made on the development of neural network (NN) based methods for PR. Most of these methods employ pre-trained NNs for modeling target signals, and they require collecting large-scale datasets with ground-truth signals for pre-training, which can be very challenging in many scenarios. There are a few unsupervised learning methods employing untrained NN priors for PR which avoid using external datasets; however, their performance is unsatisfactory compared to pre-trained-NN-based methods. This paper proposes an unsupervised learning method for PR which does not rely on pre-trained NNs while providing state-of-the-art performance. The proposed method trains a randomly-initialized generative NN for signal reconstruction directly on the magnitude measurements of a target signal, which approximates the minimum mean squared error estimator via dropout-based model averaging. Such a model-averaging-based approach provides a better internal prior for the target signal than existing untrained-NN-based methods. The experiments on image reconstruction demonstrate both the advantage of our method over existing unsupervised methods and its competitive performance to pre-trained-NN-based methods.