arXiv subjects

Andrey Krylov

Publications and source records attributed to Andrey Krylov.

5 recordsLinked to original sources

arXiv2026

Universal Approximation of Continuous Functionals on Compact Subsets via Linear Measurements and Scalar Nonlinearities

We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear measurements of the inputs and then combine these measurements through continuous scalar nonlinearities. We also extend the approximation principle to maps with values in a Banach space, yielding finite-rank approximations. These results provide a compact-set justification for the common ``measure, apply scalar nonlinearities, then combine'' design pattern used in operator learning and imaging.

cs.LG↗

arXiv2025

MGRegBench: A Novel Benchmark Dataset with Anatomical Landmarks for Mammography Image Registration

Robust mammography registration is essential for clinically relevant applications like tracking disease progression in breast tissue. However, progress has been limited by the absence of transparent public datasets and reproducible standardized benchmarks. Existing studies are often not directly comparable, as they use private data and inconsistent evaluation frameworks. To address this, we present MGRegBench, a patient-disjoint, leakage-controlled evaluation protocol for mammography registration, comprising over 5,000 image pairs, each with a breast segmentation mask, and 100 pairs with manually annotated anatomical landmarks, plus standardized train/evaluation splits and ready-to-run baselines. Using this resource, we benchmark diverse registration methods -- including classical (ANTs), learning-based (VoxelMorph, TransMorph), implicit neural representation (IDIR), a mammography-specific approach, and a recent deep learning method MammoRegNet, with implementations adapted to this modality, and validate generalization on the independent SDM-MCs dataset. Our contributions are: (1) the first public dataset of this scale with manual landmarks and masks for mammography registration; (2) a transparent, leakage-controlled benchmark enabling the first like-for-like comparison of diverse classical and machine learning-based methods; (3) external validation on SDM-MCs to test whether the main trend transfers beyond MGRegBench; and (4) an extensive analysis of deep learning-based registration. We publicly release our code and data to establish a foundational resource for fair, reproducible, and clinically relevant comparisons and catalyze future research in AI-driven medical imaging.

cs.CV↗

arXiv2025

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

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.

cs.CV↗

arXiv2018

3D Inception-based CNN with sMRI and MD-DTI data fusion for Alzheimer's Disease diagnostics

In the last decade, computer-aided early diagnostics of Alzheimer's Disease (AD) and its prodromal form, Mild Cognitive Impairment (MCI), has been the subject of extensive research. Some recent studies have shown promising results in the AD and MCI determination using structural and functional Magnetic Resonance Imaging (sMRI, fMRI), Positron Emission Tomography (PET) and Diffusion Tensor Imaging (DTI) modalities. Furthermore, fusion of imaging modalities in a supervised machine learning framework has shown promising direction of research. In this paper we first review major trends in automatic classification methods such as feature extraction based methods as well as deep learning approaches in medical image analysis applied to the field of Alzheimer's Disease diagnostics. Then we propose our own design of a 3D Inception-based Convolutional Neural Network (CNN) for Alzheimer's Disease diagnostics. The network is designed with an emphasis on the interior resource utilization and uses sMRI and DTI modalities fusion on hippocampal ROI. The comparison with the conventional AlexNet-based network using data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset (http://adni.loni.usc.edu) demonstrates significantly better performance of the proposed 3D Inception-based CNN.

cs.CV↗

arXiv2018

3D CNN-based classification using sMRI and MD-DTI images for Alzheimer disease studies

Computer-aided early diagnosis of Alzheimers Disease (AD) and its prodromal form, Mild Cognitive Impairment (MCI), has been the subject of extensive research in recent years. Some recent studies have shown promising results in the AD and MCI determination using structural and functional Magnetic Resonance Imaging (sMRI, fMRI), Positron Emission Tomography (PET) and Diffusion Tensor Imaging (DTI) modalities. Furthermore, fusion of imaging modalities in a supervised machine learning framework has shown promising direction of research. In this paper we first review major trends in automatic classification methods such as feature extraction based methods as well as deep learning approaches in medical image analysis applied to the field of Alzheimer's Disease diagnostics. Then we propose our own algorithm for Alzheimer's Disease diagnostics based on a convolutional neural network and sMRI and DTI modalities fusion on hippocampal ROI using data from the Alzheimers Disease Neuroimaging Initiative (ADNI) database (http://adni.loni.usc.edu). Comparison with a single modality approach shows promising results. We also propose our own method of data augmentation for balancing classes of different size and analyze the impact of the ROI size on the classification results as well.

cs.CV↗