PiLocNet: Physics-informed neural network on 3D localization with rotating point spread function

2024-10-17

arXiv.org

AI Summary

To address degraded 3D single-molecule localization accuracy caused by inaccurate modeling of rotationally variant point spread functions (PSFs) and poor noise robustness, this paper proposes a physics-informed neural network (PINN) framework. The method uniquely embeds a differentiable PSF forward model as a hard physical constraint within the network architecture and incorporates a variational regularization term to enforce solution plausibility and stability. By jointly optimizing a data-fitting loss—adapted to Poisson or Gaussian noise—and a physics-consistency constraint, the model integrates model-driven accuracy guarantees with data-driven generalization capability. In experiments with rotationally variant single-lobe PSFs, the approach achieves sub-pixel 3D localization accuracy, reducing localization error by 27% and 35% compared to pure optimization-based and pure learning-based methods, respectively, and improving stability under strong noise by over 40%. The framework significantly enhances interpretability and robustness.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: Localization, Mapping, and Navigation
• Search and Optimization: Local Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• 3D localization with PSF engineering
• Combining model-based and neural network approaches
• Improving robustness against image noise

Innovation

• Physics-informed neural network
• Incorporates forward-model-based information
• Regularization terms from variational method