Multi-Channel Non-Local Means Algorithm Based on Hermite Approximation for Denoising Two-Dimensional Magnetocardiography

Magnetocardiography (MCG) is gaining prominence in medical technology. However, owing to the semi-open magnetic shielding, MCG is still severely interfered by low-frequency, non-Gaussian noise, particularly in clinical settings. The spatial distribution of low-frequency non-Gaussian noise is not accurately captured by linear mixing models. In addition, this noise completely overlaps with MCG signals in both the time and frequency domains, distorting the physiological information encoded in the waveform morphology and two-dimensional MCG image, which is important for diagnosis. To address this, we propose a multi-channel non-local means (NLM) method based on Hermite approximation, exploiting the high synchronization between channels and the repeatability within each channel without requiring additional reference channels. First, a matrix that contains magnetocardiographic image morphology information is computed through Hermite approximation of the reference channels. Next, clustering is performed on all data, and the standard deviation of the clustering results is utilized to calculate the adaptive Gaussian smoothing parameters. Finally, the multi-channel adaptive NLM algorithm is applied to denoise the MCG signals. Simulation, semi-physical, and real-case experiments using self-developed MCG equipment demonstrate that the proposed method effectively restores the waveform characteristics and time-frequency domain information of MCG images under low-frequency non-Gaussian noise. This method outperforms existing techniques in noise reduction and establishes a solid foundation for future clinical applications.