# Discontinuous Galerkin Neural Operator for Pathology Defocus Deblurring

arXiv: https://arxiv.org/abs/2605.23282 · HTML: https://mlsanity.com/paper/2605.23282/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 38 references that are in the map.
- First posted on arXiv 22 May 2026.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Deep Multi-scale Convolutional Neural Network for Dynamic Scene Deblurring](https://mlsanity.com/paper/1612.02177/) (2016)
- [MambaIR: A Simple Baseline for Image Restoration with State-Space Model](https://mlsanity.com/paper/2402.15648/) (2024)
- [Scale-recurrent Network for Deep Image Deblurring](https://mlsanity.com/paper/1802.01770/) (2018)
- [Rethinking Coarse-to-Fine Approach in Single Image Deblurring](https://mlsanity.com/paper/2108.05054/) (2021)
- [Cell Detection with Star-convex Polygons](https://mlsanity.com/paper/1806.03535/) (2018)
- [Defocus Deblurring Using Dual-Pixel Data](https://mlsanity.com/paper/2005.00305/) (2020)
- [Interpreting Super-Resolution Networks with Local Attribution Maps](https://mlsanity.com/paper/2011.11036/) (2020)
- [MambaIRv2: Attentive State Space Restoration](https://mlsanity.com/paper/2411.15269/) (2024)
- [Iterative Filter Adaptive Network for Single Image Defocus Deblurring](https://mlsanity.com/paper/2108.13610/) (2021)
- [Super-Resolution Neural Operator](https://mlsanity.com/paper/2303.02584/) (2023)
- [Benchmarking the Robustness of Deep Neural Networks to Common Corruptions in Digital Pathology](https://mlsanity.com/paper/2206.14973/) (2022)
- [Gaussian Kernel Mixture Network for Single Image Defocus Deblurring](https://mlsanity.com/paper/2111.00454/) (2021)
- [A Unified Framework for Microscopy Defocus Deblur with Multi-Pyramid Transformer and Contrastive Learning](https://mlsanity.com/paper/2403.02611/) (2024)
- [DiffFNO: Diffusion Fourier Neural Operator](https://mlsanity.com/paper/2411.09911/) (2024)
- [CellTranspose: Few-shot Domain Adaptation for Cellular Instance Segmentation](https://mlsanity.com/paper/2212.14121/) (2022)
- [EAMamba: Efficient All-Around Vision State Space Model for Image Restoration](https://mlsanity.com/paper/2506.22246/) (2025)
- [Ring deconvolution microscopy: exploiting symmetry for efficient spatially varying aberration correction](https://mlsanity.com/paper/2206.08928/) (2022)

## Abstract (arXiv)

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.