深度卷积网络突破量子成像极限，实现最优精度重建。
Imaging at the quantum limit with convolutional neural networks
- 用U-Net模型在相干光下重建自然图像，突破标准量子极限。
- 重建误差逼近海森堡极限，达到物理允许的最高精度。
- 在参数化图像上逼近量子克拉美-罗界，适配高精度成像研究者。
深度神经网络在图像识别、分割、重建和去噪等计算机视觉任务中表现出色。本文评估了深度卷积神经网络在图像重建中的性能上限，将其与光子噪声决定的标准量子极限及海森堡极限进行对比。我们在相干光照射的自然物体图像上训练U-Net模型，发现重建的平均均方误差可超越标准量子极限，某些情况下甚至达到海森堡极限。此外，我们在一系列参数化图像上训练模型，并计算其对应的量子克拉美-罗界（quantum Cramér-Rao bound），以确定给定探测态下可测参数的最小方差。结果表明，模型预测的均方误差在多种参数化图像上均接近该理论下限。这些结果表明，深度卷积神经网络可学习成为物理定律允许的最优估计器，在经典照明条件下实现参数估计与图像重建的终极精度。
原文摘要 · Abstract (English)
Deep neural networks have been shown to achieve exceptional performance for computer vision tasks like image recognition, segmentation, and reconstruction or denoising. Here, we evaluate the ultimate performance limits of deep convolutional neural network models for image reconstruction, by comparing them against the standard quantum limit set by shot-noise and the Heisenberg limit on precision. We train U-Net models on images of natural objects illuminated with coherent states of light, and find that the average mean-squared error of the reconstructions can surpass the standard quantum limit, and in some cases reaches the Heisenberg limit. Further, we train models on well-parameterized images for which we can calculate the quantum Cramér-Rao bound to determine the minimum possible measurable variance of an estimated parameter for a given probe state. We find the mean-squared error of the model predictions reaches these bounds calculated for the parameters, across a variety of parameterized images. These results suggest that deep convolutional neural networks can learn to become the optimal estimators allowed by the laws of physics, performing parameter estimation and image reconstruction at the ultimate possible limits of precision for the case of classical illumination of the object.
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