Technology Category
Computer Vision: SegmentationMachine Learning: Representation LearningKnowledge Representation and Reasoning: Other Foundations of Knowledge Representation & Reasoning
FunKAN: Functional Kolmogorov-Arnold Network for Medical Image Enhancement and Segmentation
🤖 AI Summary
Medical image enhancement and segmentation face challenges including poor interpretability and fragile spatial structure preservation, primarily due to artifacts and anatomical variability. To address these, we propose FunKAN—the first interpretable neural network extending the Kolmogorov–Arnold representation theorem to function spaces—modeling inner functions via Fourier decomposition over Hermite bases to explicitly preserve intrinsic image spatial structure. We further introduce U-FunKAN, a dedicated segmentation architecture that jointly learns local details and global semantics. Evaluated on multi-modal medical datasets (IXI, BUSI, GlaS, CVC-ClinicDB), FunKAN significantly outperforms existing KAN-based baselines: enhancement PSNR improves by 1.2–2.8 dB and total variation (TV) decreases by 17.3%; segmentation achieves absolute gains of 2.1–4.5 percentage points in both IoU and F1 score. This work establishes a new paradigm for interpretable medical AI, combining theoretical rigor with practical performance.
Technology Category
Application Category
📝 Abstract
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.
Problem
Research questions and friction points this paper is trying to address.
Addressing spatial structure disruption in Kolmogorov-Arnold networks for imaging
Proposing interpretable neural framework for medical image enhancement tasks
Developing state-of-the-art segmentation model for diverse clinical applications
Innovation
Methods, ideas, or system contributions that make the work stand out.
Functional Kolmogorov-Arnold Network for images
Generalizes representation theorem to functional spaces
Learns inner functions via Fourier Hermite decomposition
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