The purpose of this study was to develop algorithms to lower the incidence of false arrhythmia alarms in the ICU using information from independent sources, namely electrocardiogram (ECG), arterial blood pressure (ABP) and photoplethysmogram (PPG). Our approach relies on robust adaptive signal processing techniques in order to extract accurate heart rate (HR) values from the different waveforms. Based on the quality of available signals, heart rate was either estimated from pulsatile waveforms using an adaptive frequency tracking algorithm or computed from ECGs using an adaptive mathematical morphology approach. Furthermore, we developed a supplementary measure based on the spectral purity of the ECGs to determine whether a ventricular tachycardia or flutter/fibrillation arrhythmia has taken place. Finally, alarm veracity was determined based on a set of decision rules on HR and spectral purity values. The proposed method was evaluated on the PhysioNet/CinC Challenge 2015 database, which is composed of 1250 life-threatening alarm recordings, each categorized into either bradycardia, tachycardia, asystole, ventricular tachycardia or ventricular flutter/fibrillation arrhythmia. This resulted in overall true positive rates of 95%/99% and overall true negative rates of 76%/80% on the real-time and retrospective subsets of the test dataset, respectively.