Discontinuous Galerkin Neural Operator for Pathology Defocus Deblurring

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.

Spatially-Variant Degradation Model for Dataset-free Super-resolution

This paper focuses on the dataset-free Blind Image Super-Resolution (BISR). Unlike existing dataset-free BISR methods that focus on obtaining a degradation kernel for the entire image, we are the first to explicitly design a spatially-variant degradation model for each pixel. Our method also benefits from having a significantly smaller number of learnable parameters compared to data-driven spatially-variant BISR methods. Concretely, each pixel's degradation kernel is expressed as a linear combination of a learnable dictionary composed of a small number of spatially-variant atom kernels. The coefficient matrices of the atom degradation kernels are derived using membership functions of fuzzy set theory. We construct a novel Probabilistic BISR model with tailored likelihood function and prior terms. Subsequently, we employ the Monte Carlo EM algorithm to infer the degradation kernels for each pixel. Our method achieves a significant improvement over other state-of-the-art BISR methods, with an average improvement of 1 dB (2x).Code will be released at https://github.com/shaojieguoECNU/SVDSR.

I$^3$Net: Inter-Intra-slice Interpolation Network for Medical Slice Synthesis

Medical imaging is limited by acquisition time and scanning equipment. CT and MR volumes, reconstructed with thicker slices, are anisotropic with high in-plane resolution and low through-plane resolution. We reveal an intriguing phenomenon that due to the mentioned nature of data, performing slice-wise interpolation from the axial view can yield greater benefits than performing super-resolution from other views. Based on this observation, we propose an Inter-Intra-slice Interpolation Network (I$^3$Net), which fully explores information from high in-plane resolution and compensates for low through-plane resolution. The through-plane branch supplements the limited information contained in low through-plane resolution from high in-plane resolution and enables continual and diverse feature learning. In-plane branch transforms features to the frequency domain and enforces an equal learning opportunity for all frequency bands in a global context learning paradigm. We further propose a cross-view block to take advantage of the information from all three views online. Extensive experiments on two public datasets demonstrate the effectiveness of I$^3$Net, and noticeably outperforms state-of-the-art super-resolution, video frame interpolation and slice interpolation methods by a large margin. We achieve 43.90dB in PSNR, with at least 1.14dB improvement under the upscale factor of $\times$2 on MSD dataset with faster inference. Code is available at https://github.com/DeepMed-Lab-ECNU/Medical-Image-Reconstruction.