Phase retrieval with physics informed zero-shot network

On the use of deep learning for phase recovery

Phase recovery (PR) refers to calculating the phase of the light field from its intensity measurements. As exemplified from quantitative phase imaging and coherent diffraction imaging to adaptive optics, PR is essential for reconstructing the refractive index distribution or topography of an object and correcting the aberration of an imaging system. In recent years, deep learning (DL), often implemented through deep neural networks, has provided unprecedented support for computational imaging, leading to more efficient solutions for various PR problems. In this review, we first briefly introduce conventional methods for PR. Then, we review how DL provides support for PR from the following three stages, namely, pre-processing, in-processing, and post-processing. We also review how DL is used in phase image processing. Finally, we summarize the work in DL for PR and provide an outlook on how to better use DL to improve the reliability and efficiency of PR. Furthermore, we present a live-updating resource ( https://github.com/kqwang/phase-recovery ) for readers to learn more about PR.

Physics-informed neural network for phase imaging based on transport of intensity equation

Non-interferometric quantitative phase imaging based on Transport of Intensity Equation (TIE) has been widely used in bio-medical imaging. However, analytic TIE phase retrieval is prone to low-spatial frequency noise amplification, which is caused by the illposedness of inversion at the origin of the spectrum. There are also retrieval ambiguities resulting from the lack of sensitivity to the curl component of the Poynting vector occurring with strong absorption. Here, we establish a physics-informed neural network (PINN) to address these issues, by integrating the forward and inverse physics models into a cascaded deep neural network. We demonstrate that the proposed PINN is efficiently trained using a small set of sample data, enabling the conversion of noise-corrupted 2-shot TIE phase retrievals to high quality phase images under partially coherent LED illumination. The efficacy of the proposed approach is demonstrated by both simulation using a standard image database and experiment using human buccal epitehlial cells. In particular, high image quality (SSIM = 0.919) is achieved experimentally using a reduced size of labeled data (140 image pairs). We discuss the robustness of the proposed approach against insufficient training data, and demonstrate that the parallel architecture of PINN is efficient for transfer learning.

SiSPRNet: end-to-end learning for single-shot phase retrieval

With the success of deep learning methods in many image processing tasks, deep learning approaches have also been introduced to the phase retrieval problem recently. These approaches are different from the traditional iterative optimization methods in that they usually require only one intensity measurement and can reconstruct phase images in real-time. However, because of tremendous domain discrepancy, the quality of the reconstructed images given by these approaches still has much room to improve to meet the general application requirements. In this paper, we design a novel deep neural network structure named SiSPRNet for phase retrieval based on a single Fourier intensity measurement. To effectively utilize the spectral information of the measurements, we propose a new feature extraction unit using the Multi-Layer Perceptron (MLP) as the front end. It allows all pixels of the input intensity image to be considered together for exploring their global representation. The size of the MLP is carefully designed to facilitate the extraction of the representative features while reducing noises and outliers. A dropout layer is also equipped to mitigate the possible overfitting problem in training the MLP. To promote the global correlation in the reconstructed images, a self-attention mechanism is introduced to the Up-sampling and Reconstruction (UR) blocks of the proposed SiSPRNet. These UR blocks are inserted into a residual learning structure to prevent the weak information flow and vanishing gradient problems due to their complex layer structure. Extensive evaluations of the proposed model are performed using different testing datasets of phase-only images and images with linearly related magnitude and phase. Experiments were conducted on an optical experimentation platform (with defocusing to reduce the saturation problem) to understand the performance of different deep learning methods when working in a practical environment. The results demonstrate that the proposed approach consistently outperforms other deep learning methods in single-shot maskless phase retrieval. The source codes of the proposed method have been released in Github [see references].