Hybrid CNN with Chebyshev Polynomial Expansion for Medical Image Analysis

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.