用物理约束提升3D定位精度，让神经网络结果更可信。
PiLocNet: Physics-informed neural network on 3D localization with rotating point spread function
- 将物理模型融入神经网络，通过数据拟合损失保证结果符合光学规律。
- 在泊松和高斯噪声下仍保持高精度，相比传统方法鲁棒性更强。
- 适合需要可解释性的显微成像、量子传感等依赖已知物理过程的领域。
针对基于点扩散函数（PSF）工程的三维定位问题，本文提出一种改进型定位神经网络PiLocNet，其为物理信息神经网络（PINN）。以往研究多分为基于模型的优化与神经网络两类方法，PiLocNet融合二者优势：通过正向模型驱动的数据拟合损失项，使网络输出符合物理规律。同时引入变分法中的正则化项，显著提升在泊松与高斯噪声下的鲁棒性。该框架赋予神经网络可解释性，实验表明其性能优越。尽管聚焦于单瓣旋转PSF编码全三维位置，但该方法可推广至其他受已知前向过程约束的PSF与成像问题。
原文摘要 · Abstract (English)
For the 3D localization problem using point spread function (PSF) engineering, we propose a novel enhancement of our previously introduced localization neural network, LocNet. The improved network is a physics-informed neural network (PINN) that we call PiLocNet. Previous works on the localization problem may be categorized separately into model-based optimization and neural network approaches. Our PiLocNet combines the unique strengths of both approaches by incorporating forward-model-based information into the network via a data-fitting loss term that constrains the neural network to yield results that are physically sensible. We additionally incorporate certain regularization terms from the variational method, which further improves the robustness of the network in the presence of image noise, as we show for the Poisson and Gaussian noise models. This framework accords interpretability to the neural network, and the results we obtain show its superiority. Although the paper focuses on the use of single-lobe rotating PSF to encode the full 3D source location, we expect the method to be widely applicable to other PSFs and imaging problems that are constrained by known forward processes.
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