Pulse Shape Estimation for Bio-Magnetic Signals Under Low SNR via Translation-Invariant Denoising and Phase Retrieval

The human body naturally emits magnetic fields whose detection is vital for diagnosing various health conditions. In our lab, we have previously demonstrated a wearable sensor that detects the magnetic field of the heart. Unfortunately, the sensed bio-magnetic signals are usually very weak, resulting in a noisy signal. In this work, we overcome this limitation by proposing a method that denoises and reconstructs a semi-periodic bio-magnetic signal using its analytical model. The approach is based on segmenting the signal into several windows, and then averaging the magnitude of the Discrete Fourier Transform (DFT) of each window. Once that is complete, phase retrieval is done on the signal's derived analytical model to reconstruct the noise-free signal. Simulation results show that the proposed approach achieves an error of less than 5.71% with SNR= −7.45 dB when compared to a signal that is perfectly periodic. The proposed approach is expected to have significant impact on the detection of bio-magnetic signals that can be obtained in a non-contact and non-invasive manner but suffer from noise.