DeepPhaseCut: Deep Relaxation in Phase for Unsupervised Fourier Phase Retrieval

Area of Science:

• Signal Processing
• Computational Imaging
• Machine Learning

Background:

• Fourier phase retrieval aims to reconstruct a signal from its Fourier transform magnitude.
• Traditional Fienup-type algorithms can be trapped in local minima.
• Convex relaxation methods offer guarantees but are computationally expensive.

Purpose of the Study:

• To develop a novel, efficient, and accurate method for Fourier phase retrieval.
• To address limitations of existing algorithms, including local minima and high computational cost.
• To propose an unsupervised deep learning approach for immediate high-quality reconstruction.

Main Methods:

• A novel unsupervised feed-forward neural network is proposed.
• The network comprises two generators trained simultaneously: one for phase estimation (PhaseCut loss) and one for image reconstruction.
• The approach integrates physics-driven constraints within an unsupervised learning framework, avoiding matched data.

Main Results:

• The proposed method generates high-quality reconstructions immediately.
• It outperforms existing Fourier phase retrieval algorithms, including Fienup-type and convex relaxation methods.
• The network demonstrates effective signal restoration without supervised training data.

Conclusions:

• The novel unsupervised neural network provides a superior solution for Fourier phase retrieval.
• This physics-driven, feed-forward network offers an efficient and accurate alternative to conventional methods.
• The study highlights the potential of unsupervised deep learning for solving classical inverse problems.