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

For the 3D localization problem using point spread function (PSF) engineering, we propose an enhancement of our previously introduced localization neural network, LocNet. The improved network is a physics-informed neural network 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 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 this paper focuses on the use of a 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 well-modeled forward processes.