# FunKAN: Functional Kolmogorov-Arnold Network for Medical Image Enhancement and Segmentation

arXiv: https://arxiv.org/abs/2509.13508 · HTML: https://mlsanity.com/paper/2509.13508/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 37 references that are in the map.
- First posted on arXiv 16 Sep 2025.

## Builds on (most cited first, 13 of 13)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [UNet++: A Nested U-Net Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1807.10165/) (2018)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Medical Transformer: Gated Axial-Attention for Medical Image Segmentation](https://mlsanity.com/paper/2102.10662/) (2021)
- [UNeXt: MLP-based Rapid Medical Image Segmentation Network](https://mlsanity.com/paper/2203.04967/) (2022)
- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [Improved Residual Networks for Image and Video Recognition](https://mlsanity.com/paper/2004.04989/) (2020)
- [UnO: Unsupervised Occupancy Fields for Perception and Forecasting](https://mlsanity.com/paper/2406.08691/) (2024)
- [Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomials](https://mlsanity.com/paper/2406.02583/) (2024)

## Built on by (most cited first, 1 of 1)

- [Hardware-Aware Functional Kolmogorov-Arnold Networks for Efficient Medical Image Enhancement and Segmentation](https://mlsanity.com/paper/2609.36134/) (2026)

## Abstract (arXiv)

Medical image enhancement and segmentation are critical yet challenging tasks in modern clinical practice, constrained by artifacts and complex anatomical variations. Traditional deep learning approaches often rely on complex architectures with limited interpretability. While Kolmogorov-Arnold networks offer interpretable solutions, their reliance on flattened feature representations fundamentally disrupts the intrinsic spatial structure of imaging data. To address this issue we propose a Functional Kolmogorov-Arnold Network (FunKAN) -- a novel interpretable neural framework, designed specifically for image processing, that formally generalizes the Kolmogorov-Arnold representation theorem onto functional spaces and learns inner functions using Fourier decomposition over the basis Hermite functions. We explore FunKAN on several medical image processing tasks, including Gibbs ringing suppression in magnetic resonance images, benchmarking on IXI dataset. We also propose U-FunKAN as state-of-the-art binary medical segmentation model with benchmarks on three medical datasets: BUSI (ultrasound images), GlaS (histological structures) and CVC-ClinicDB (colonoscopy videos), detecting breast cancer, glands and polyps, respectively. Experiments on those diverse datasets demonstrate that our approach outperforms other KAN-based backbones in both medical image enhancement (PSNR, TV) and segmentation (IoU, F1). Our work bridges the gap between theoretical function approximation and medical image analysis, offering a robust, interpretable solution for clinical applications.