Discontinuous Galerkin Neural Operator for Pathology Defocus Deblurring

2026-05-22

AI Summary

This work addresses the challenge of spatially varying and locally discontinuous defocus blur in pathological microscopy images, which conventional deep learning approaches struggle to model effectively due to their reliance on translation invariance and lack of interpretability. The study introduces the Discontinuous Galerkin Neural Operator (DGNO), the first integration of the discontinuous Galerkin (DG) method into neural operators. By parameterizing integral kernels through local volume operators and interface numerical fluxes, DGNO rigorously adheres to the physical laws of optical imaging while simultaneously capturing local heterogeneity and global consistency. This approach overcomes the limitation of existing vision-based neural operators that depend on globally smooth kernels, achieving significantly superior performance across multiple experiments—yielding sharper reconstructions, robust handling of spatially varying blur, and strong scalability at high resolutions.

Abstract

Defocus deblurring in pathological microscopy remains challenging due to the spatially varying and locally discontinuous nature of optical blur induced by a position-dependent integral imaging process. Existing deep learning methods, constrained by shift-invariance assumptions and limited interpretability, are not well suited to such heterogeneous blur patterns. Neural operators provide a principled alternative by modeling defocus formation directly as an integral operator, offering a new perspective on defocus deblurring. However, most existing neural operator architectures for low-level vision rely on globally parameterized kernels that assume smoothness and stationarity, limiting their ability to model heterogeneous and locally discontinuous blur patterns. To address this limitation, we propose the Discontinuous Galerkin Neural Operator (DGNO), which parameterizes the integral kernel using a discontinuous Galerkin formulation with element-local volume operators and interface numerical fluxes. DGNO provides a principled combination of locality, heterogeneity modeling, and global coherence while preserving the underlying physics of optical image formation. Extensive and insightful experiments demonstrate that DGNO surpasses state-of-the-arts, delivering sharper reconstructions, robust handling of spatially varying blur, and scalable high-resolution performance. The code will be released at https://github.com/DeepMed-Lab-ECNU/Single-Image-Deblur.

Problem

• defocus deblurring
• pathological microscopy
• spatially varying blur
• locally discontinuous blur
• heterogeneous blur patterns

Innovation

• Discontinuous Galerkin
• Neural Operator
• Defocus Deblurring
• Pathology Microscopy
• Integral Kernel