Removal of Co-Frequency Powerline Harmonics From Multichannel Surface NMR Data

Powerline harmonics are often the primary noise source in surface nuclear magnetic resonance (NMR) measurements. State-of-the-art techniques, such as notch filtering, Wiener filtering, and model-based subtraction, have been demonstrated to greatly mitigate powerline harmonic noise, but these approaches break down when one of the powerline harmonics has a frequency close to or coincident with the Larmor frequency $f_{L}$ , referred to as a co-frequency harmonic. We propose a hybrid scheme where model-based subtraction of powerline harmonics is coupled with data from a synchronous reference coil to specifically subtract the co-frequency harmonic component. In standard model-based subtraction of powerline harmonics, a sinusoidal model of all harmonic components is fit to the data and subtracted. In the new approach, the amplitude and phase of the co-frequency harmonic are determined by a sinusoidal model fit to the synchronous noise-only data recorded in a reference coil. From the reference coil co-frequency model, the co-frequency harmonic in the primary coil is estimated using relationships between the amplitude and phase of the co-frequency harmonic in the two coils established during noise-only segments. By utilizing data from the reference coil to model the co-frequency harmonic, accidental fitting of the surface NMR signal is avoided. We investigate the efficiency of the method using a synthetic surface NMR signal embedded in noise-only data recorded in Denmark. Our results demonstrate that the co-frequency powerline harmonic can be removed efficiently without distorting the surface NMR signal and the new method performs better than standard methods.