Physiological signal analysis often involves identifying events crucial to understanding biological dynamics. Many methods have been proposed to detect them, from handcrafted and supervised approaches to unsupervised techniques.All these methods tend to produce spurious events, mainly as they detect each event independently.This work introduces UNHaP (Unmix Noise from Hawkes Processes), a novel approach addressing the joint learning of temporal structures in events and the removal of spurious detections.By treating the event detection output as a mixture of structured Hawkes and unstructured Poisson events, UNHaP efficiently unmixes these processes and estimates their parameters.This approach significantly enhances event distribution characterization while minimizing false detection rates on simulated and real data.