Optimal Coded Diffraction Patterns for Practical Phase Retrieval

Phase retrieval, a long-established challenge for recovering a complex-valued signal from its Fourier intensity measurements, has attracted significant interest because of its far-flung applications in optical imaging. To enhance accuracy, researchers introduce extra constraints to the measuring procedure by including a random aperture mask in the optical path that randomly modulates the light projected on the target object and gives the coded diffraction patterns (CDP). It is known that random masks are non-bandlimited and can lead to considerable high-frequency components in the Fourier intensity measurements. These high-frequency components can be beyond the Nyquist frequency of the optical system and are thus ignored by the phase retrieval optimization algorithms, resulting in degraded reconstruction performances. Recently, our team developed a binary green noise masking scheme that can significantly reduce the high-frequency components in the measurement. However, the scheme cannot be extended to generate multiple-level aperture masks. This paper proposes a two-stage optimization algorithm to generate multi-level random masks named $\textit{OptMask}$ that can also significantly reduce high-frequency components in the measurements but achieve higher accuracy than the binary masking scheme. Extensive experiments on a practical optical platform were conducted. The results demonstrate the superiority and practicality of the proposed $\textit{OptMask}$ over the existing masking schemes for CDP phase retrieval.

Towards Practical Single-shot Phase Retrieval with Physics-Driven Deep Neural Network

Phase retrieval (PR), a long-established challenge for recovering a complex-valued signal from its Fourier intensity-only measurements, has attracted considerable attention due to its widespread applications in digital imaging. Recently, deep learning-based approaches were developed that achieved some success in single-shot PR. These approaches require a single Fourier intensity measurement without the need to impose any additional constraints on the measured data. Nevertheless, vanilla deep neural networks (DNN) do not give good performance due to the substantial disparity between the input and output domains of the PR problems. Physics-informed approaches try to incorporate the Fourier intensity measurements into an iterative approach to increase the reconstruction accuracy. It, however, requires a lengthy computation process, and the accuracy still cannot be guaranteed. Besides, many of these approaches work on simulation data that ignore some common problems such as saturation and quantization errors in practical optical PR systems. In this paper, a novel physics-driven multi-scale DNN structure dubbed PPRNet is proposed. Similar to other deep learning-based PR methods, PPRNet requires only a single Fourier intensity measurement. It is physics-driven that the network is guided to follow the Fourier intensity measurement at different scales to enhance the reconstruction accuracy. PPRNet has a feedforward structure and can be end-to-end trained. Thus, it is much faster and more accurate than the traditional physics-driven PR approaches. Extensive simulations and experiments on a practical optical platform were conducted. The results demonstrate the superiority and practicality of the proposed PPRNet over the traditional learning-based PR methods.

SiPRNet: End-to-End Learning for Single-Shot Phase Retrieval

Traditional optimization algorithms have been developed to deal with the phase retrieval problem. However, multiple measurements with different random or non-random masks are needed for giving a satisfactory performance. This brings a burden to the implementation of the algorithms in practical systems. Even worse, expensive optical devices are required to implement the optical masks. Recently, deep learning, especially convolutional neural networks (CNN), has played important roles in various image reconstruction tasks. However, traditional CNN structure fails to reconstruct the original images from their Fourier measurements because of tremendous domain discrepancy. In this paper, we design a novel CNN structure, named SiPRNet, to recover a signal from a single Fourier intensity measurement. To effectively utilize the spectral information of the measurements, we propose a new Multi-Layer Perception block embedded with the dropout layer to extract the global representations. Two Up-sampling and Reconstruction blocks with self-attention are utilized to recover the signals from the extracted features. Extensive evaluations of the proposed model are performed using different testing datasets on both simulation and optical experimentation platforms. The results demonstrate that the proposed approach consistently outperforms other CNN-based and traditional optimization-based methods in single-shot maskless phase retrieval. The source codes of the proposed method have been released on Github: https://github.com/Qiustander/SiPRNet.