A preliminary study on the extraction of MRI Gradient-Induced potential from noisy ECG and its application to build a simple mathematical model

•Large bandwidth potential acquisition during MRI has a positive effect on denoising.•Wavelet decomposition effectively extract high bandwidth gradient-induced potentials.•For a specific MRI sequence, there is best wavelet for induced potential extraction.•Gradient-induced potentials are strongly pseudo-periodic and can be modelled.•Modelling constitutes a database that can be used for deep learning filter denoising. Magnetic resonance imaging (MRI) is the medical imaging technique that benefits most from recent technological innovations, particularly the constant proposal of new MRI sequences that refine clinical information from the obtained images. However, this generates new gradient-induced potential (GIP) morphologies. These induced potentials (IPs) pollute the electrophysiological signals possibly recorded simultaneously. Several algorithms developed to eliminate this noise rely on modelling the shape of the IP. As each new sequence has a different shape of IP, it might be interesting to find a mathematical approach to building sequence-specific models. In this article, we present a preliminary study that includes wavelet decomposition of contaminated electrocardiographic (ECG) to extract IP morphologies and whose time–frequency characterization allows the elaboration of a harmonic model, using sinusoidal decomposition. The in vitro IPs are used to select analyzing wavelets. A broadband sensor (3.5Khz), placed inside a 3 T MRI scanner, is used to collect 3-lead ECGs while activating three sequences that generate very high noise levels. The in vivo IPs extracted from the polluted ECGs are characterized to verify their quasi-periodicity. Parameters of the sinusoidal model (amplitude, frequency, phase) are estimated using the Broyden-Fletcher-Goldfard-Shano optimization algorithm. Four wavelets (sym7, coif3, bior2.2, bior3.3) showed efficient in vivo IP extraction results. Three evaluation criteria for the modelling algorithm, allowing the calculated models to be compared with the shapes of the extracted IPs, showed promising results. For example, for the chosen efficiency criterion Nash-Sutcliffe efficiency, the values obtained for the three leads are between 0.99980 and 1. Promising preliminary results have been obtained for the extraction on modelling of different IPs from noisy ECG signals. Continuing this preliminary study on more MRI sequences and subjects could help build a database of IP models to initiate deep learning filtering. Since these m