In recent years, neural networks have been used to solve phase retrieval
problems in imaging with superior accuracy and speed than traditional
techniques, especially in the presence of noise. However, in the context of
interferometric imaging, phase noise has been largely unaddressed by existing
neural network architectures. Such noise arises naturally in an interferometer
due to mechanical instabilities or atmospheric turbulence, limiting measurement
acquisition times and posing a challenge in scenarios with limited light
intensity, such as remote sensing. Here, we introduce a 3D-2D Phase Retrieval
U-Net (PRUNe) that takes noisy and randomly phase-shifted interferograms as
inputs, and outputs a single 2D phase image. A 3D downsampling convolutional
encoder captures correlations within and between frames to produce a 2D latent
space, which is upsampled by a 2D decoder into a phase image. We test our model
against a state-of-the-art singular value decomposition algorithm and find
PRUNe reconstructions consistently show more accurate and smooth
reconstructions, with a x2.5 - 4 lower mean squared error at multiple
signal-to-noise ratios for interferograms with low (< 1 photon/pixel) and high
(~100 photons/pixel) signal intensity. Our model presents a faster and more
accurate approach to perform phase retrieval in extremely low light intensity
interferometry in presence of phase noise, and will find application in other
multi-frame noisy imaging techniques.

近年来，神经网络已被用于解决成像中的相位恢复问题，比传统技术具有更高的准确性和速度，特别是在存在噪声的情况下。然而，在干涉成像的背景下，现有的神经网络结构很少解决相位噪声问题。本文介绍了一种 3D-2D 相位恢复 U-Net (PRUNe) 模型，它以噪声和随机相位移的干涉图作为输入，并输出一张 2D 相位图像。经过 3D 降采样卷积编码器和 2D 解码器的处理，模型能更准确、平滑地恢复相位图像，在低光强（<1 个光子 / 像素）和高光强（~100 个光子 / 像素）信噪比的干涉图像上，均表现出比现有算法更低 2.5-4 倍的均方误差。该模型为在极低光强干涉成像中进行相位恢复提供了更快速和更准确的方法，并将在其他多帧噪声成像技术中应用。