Physics-Informed Ellipsoidal Coordinate Encoding Implicit Neural Representation for high-resolution volumetric wide-field microscopy

Wide-field fluorescence microscopy through axial scanning provides a simple way for volumetric imaging of cellular and intracellular activities, but the optical transfer function (OTF) of wide-field microscopy suffers from axial frequency deficiencies, leading to strong interference from out-of-focus fluorescence signals and reduced imaging quality. Richardson-Lucy (RL) deconvolution and its variants are commonly employed to reduce inter-plane signal interference of wide-field microscopy. However, these methods are still affected by the "missing cone" issue inherent in the OTF, compromising both the axial resolution and optical sectioning capability. Existing deep learning methods could realize high-fidelity 3D image stack restoration, but relying on high-quality paired datasets or specific assumptions about sample distributions. Here, we propose a novel method named physics-informed ellipsoidal coordinate encoding implicit neural representation (PIECE-INR), to tackle the challenges of background signal interference and resolution loss in axial scanning image stacks using the wide-field microscopy. In PIECE-INR, we integrate the wide-field fluorescence imaging model with the self-supervised INR network for high-fidelity reconstruction of 3D fluorescence data without the need of additional ground truth data for training. We further design a novel ellipsoidal coordinate encoding based on the systems OTF constraints and incorporate implicit priors derived from the physical model as the loss function into the reconstruction process. Our approach enables block-wise reconstruction of large-scale images by using localized physical information. We demonstrate state-of-the-art performance of our PIECE-INR method in volumetric imaging of live HeLa cells, large-volume C. elegans whole-embryo, and mitochondrial dynamics.