Hybrid CNN with Chebyshev Polynomial Expansion for Medical Image Analysis

TL;DR

This work tackles automated pulmonary nodule detection and classification in CT scans, where variability in nodule morphology challenges traditional CNNs. It introduces a Chebyshev polynomial-based augmentation to CNNs (the Chebyshev-CNN), enriching spatial-spectral feature representations to improve benign/malignant discrimination. Evaluated on the LUNA16 and LIDC-IDRI datasets, the model achieves state-of-the-art performance, with an overall accuracy of 97.5% and statistically significant improvements over baselines. The approach demonstrates the value of embedding principled mathematical function approximators within deep learning for medical imaging and informs future hybrid models for clinical decision support.

Abstract

Lung cancer remains one of the leading causes of cancer-related mortality worldwide, with early and accurate diagnosis playing a pivotal role in improving patient outcomes. Automated detection of pulmonary nodules in computed tomography (CT) scans is a challenging task due to variability in nodule size, shape, texture, and location. Traditional Convolutional Neural Networks (CNNs) have shown considerable promise in medical image analysis; however, their limited ability to capture fine-grained spatial-spectral variations restricts their performance in complex diagnostic scenarios. In this study, we propose a novel hybrid deep learning architecture that incorporates Chebyshev polynomial expansions into CNN layers to enhance expressive power and improve the representation of underlying anatomical structures. The proposed Chebyshev-CNN leverages the orthogonality and recursive properties of Chebyshev polynomials to extract high-frequency features and approximate complex nonlinear functions with greater fidelity. The model is trained and evaluated on benchmark lung cancer imaging datasets, including LUNA16 and LIDC-IDRI, achieving superior performance in classifying pulmonary nodules as benign or malignant. Quantitative results demonstrate significant improvements in accuracy, sensitivity, and specificity compared to traditional CNN-based approaches. This integration of polynomial-based spectral approximation within deep learning provides a robust framework for enhancing automated medical diagnostics and holds potential for broader applications in clinical decision support systems.

Figures (3)

• Figure 1: Architecture overview of the Chebyshev-enhanced CNN pipeline for lung nodule detection.
• Figure 2: Training and validation loss/accuracy curves of the Chebyshev-CNN model.
• Figure 3: Confusion matrix for the Chebyshev-CNN model on the test set.