Untrained neural network embedded Fourier phase retrieval from few
  measurements
Liyuan Ma Hongxia Wang Ningyi Leng Ziyang Yuan
Fourier phase retrieval (FPR) is a challenging task widely used in various
applications. It involves recovering an unknown signal from its Fourier
phaseless measurements. FPR with few measurements is important for reducing
time and hardware costs, but it suffers from serious ill-posedness. Recently,
untrained neural networks have offered new approaches by introducing learned
priors to alleviate the ill-posedness without requiring any external data.
However, they may not be ideal for reconstructing fine details in images and
can be computationally expensive. This paper proposes an untrained neural
network (NN) embedded algorithm based on the alternating direction method of
multipliers (ADMM) framework to solve FPR with few measurements. Specifically,
we use a generative network to represent the image to be recovered, which
confines the image to the space defined by the network structure. To improve
the ability to represent high-frequency information, total variation (TV)
regularization is imposed to facilitate the recovery of local structures in the
image. Furthermore, to reduce the computational cost mainly caused by the
parameter updates of the untrained NN, we develop an accelerated algorithm that
adaptively trades off between explicit and implicit regularization.
Experimental results indicate that the proposed algorithm outperforms existing
untrained NN-based algorithms with fewer computational resources and even
performs competitively against trained NN-based algorithms.