Discontinuous Galerkin Neural Operator for Pathology Defocus Deblurring

Shaoqing Duan, Haofei Song, Xintian Mao, Qingli Li, Yan Wang
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:27028-27044, 2026.

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 experiments demonstrate that DGNO surpasses state-of-the-art methods, delivering sharper reconstructions, robust handling of spatially varying blur, and scalable high-resolution performance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-duan26e, title = {Discontinuous Galerkin Neural Operator for Pathology Defocus Deblurring}, author = {Duan, Shaoqing and Song, Haofei and Mao, Xintian and Li, Qingli and Wang, Yan}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {27028--27044}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/duan26e/duan26e.pdf}, url = {https://proceedings.mlr.press/v306/duan26e.html}, 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 experiments demonstrate that DGNO surpasses state-of-the-art methods, delivering sharper reconstructions, robust handling of spatially varying blur, and scalable high-resolution performance.} }
Endnote
%0 Conference Paper %T Discontinuous Galerkin Neural Operator for Pathology Defocus Deblurring %A Shaoqing Duan %A Haofei Song %A Xintian Mao %A Qingli Li %A Yan Wang %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-duan26e %I PMLR %P 27028--27044 %U https://proceedings.mlr.press/v306/duan26e.html %V 306 %X 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 experiments demonstrate that DGNO surpasses state-of-the-art methods, delivering sharper reconstructions, robust handling of spatially varying blur, and scalable high-resolution performance.
APA
Duan, S., Song, H., Mao, X., Li, Q. & Wang, Y.. (2026). Discontinuous Galerkin Neural Operator for Pathology Defocus Deblurring. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:27028-27044 Available from https://proceedings.mlr.press/v306/duan26e.html.

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