Adaptive Bandelet Transform and Transfer Learning for Geometry-Aware Thyroid Cancer Ultrasound Classification

<b>Background and Objectives:</b> Classification of thyroid nodules (TN) in ultrasound remains challenging due to limited labelled data and the limited capacity of conventional feature representations to capture complex, multi-directional textures. This work aims to improve data-efficient TN classification by integrating a geometry-adaptive Bandelet Transform (BT) with transfer learning (TL) to enhance feature representation and generalisation. <b>Methods:</b> The proposed pipeline first applies BT to strengthen directional and structural encoding in ultrasound images via quadtree-driven geometric adaptation. It then mitigates class imbalance using SMOTE and increases data diversity through targeted data augmentation. The resulting representations are classified using multiple ImageNet-pretrained architectures, where VGG19 yields the most consistent performance. <b>Results:</b> Experiments on the publicly available DDTI dataset show that BT-based preprocessing consistently improves performance over classical wavelet representations across multiple quadtree thresholds, with the best results obtained at T=30. Under this setting, the proposed <i>BT+TL</i> (VGG19) model achieves 98.91% accuracy, 98.11% sensitivity, 97.31% specificity, and a 98.89% F1-score, outperforming comparable approaches reported in the literature. <b>Conclusions:</b> Coupling geometry-adaptive transforms with modern TL backbones provides a robust and data-efficient strategy for ultrasound TN classification, particularly under limited annotation and challenging texture variability. The complete project is publicly available.