RgeoJSD: Robust Geometric Jensen-Shannon Divergence Noise-Tolerant Loss for Cerebral Emboli Classification

Cerebral emboli, solid or gaseous particles circulating in the cerebral blood stream, can obstruct arteries and are a major cause of stroke. Transcranial Doppler (TCD) ultrasonography uniquely enables continuous, long-term monitoring, particularly with portable devices. Deep learning methods offer the potential to capture complex microemboli patterns in TCD signals, improving emboli identification. However, the development of such techniques relies heavily on labeled data, which are often noisy due to experts’ uncertainty. Enhancing the robustness of training to label noise not only alleviates the experts’ labeling burden but also facilitates the integration of unannotated data through semi-automatic annotation. In this work, we propose the Robust geometric Jensen-Shannon Divergence (RgeoJSD) loss function, which leverages the favorable mathematical properties of geometric JSD (geoJSD). We show that geoJSD can be decomposed into a cross-entropy-like term and an additional term that enhances noise robustness. By weighting these components, RgeoJSD achieves tolerance to label noise. We evaluated RgeoJSD on a TCD dataset comprising 1 232 labeled spectrograms from 35 subjects, recorded using a TCD-X Holter device. Spectrograms were annotated into three classes: solid emboli, gaseous emboli, and artifacts. Under synthetic symmetric noise conditions, RgeoJSD performed comparably to standard cross-entropy loss when labels were clean, and significantly outperformed it under noise, improving the accuracy by up to 4.4% and 9.9% at noise rates of 0.2 and 0.4, respectively. These findings indicate that RgeoJSD is a promising solution for training deep learning models on noisy TCD data, and a strong candidate for enabling reliable, automated cerebral emboli classification.