ECGs are currently acquired during magnetic resonance examinations. This "hostile" environment highly distorts ECG signals, due to the high-static magnetic field, RF pulses and fast switching magnetic gradients. Specific signal processing is then required since the ECG signal is used for image synchronization with heart activity (or triggering) and for patient monitoring. A new set of two magnetic field gradient (MFG) artifact reduction methods, based on ECG and MFG artifact modelings and Bayesian filtering, is herein presented and will be called Bayesian gradient artifact reduction monitoring (BAGARRE-M) and BAGARRE-triggering. These algorithms overcome the limitations of state-of-the-art methods and enable accurate processing of very noisy ECG acquisitions during MRI. Whether for triggering or monitoring purposes, the presented methods overcome state-of-the-art techniques with both better QRS detection accuracy and signal denoising quality.