Fast Removal of Powerline Harmonic Noise From Surface NMR Datasets Using a Projection-Based Approach on Graphical Processing Units

Surface nuclear magnetic resonance (NMR) measurements are notorious for their low signal-to-noise ratio (SNR). Powerlines are probably the most common source of noise and give the greatest contribution to noise levels. The noise from powerlines manifests itself as sinusoidal signals oscillating at the fundamental powerline frequency (50 or 60 Hz) and at integer multiples of this frequency. Modeling and subtraction of the powerline noise have been demonstrated as a highly applicable method for improving SNR and are common practice today. However, the methods used to determine the parameters of the powerline noise are computationally expensive. Consequently, it is difficult to do real-time noise removal during the acquisition of field data and, therefore, also difficult to do a real-time quality inspection of data. Here, we demonstrate how the removal of powerline noise in surface NMR data can be significantly faster. We obtain this through two new developments. First, we apply a projection-based method to determine the powerline model, which is twice as fast as the commonly applied least-squares solution of a matrix equation. Second, we obtain a further 10–25 times speed-up by exploiting the high-performance parallel computations offered by graphical processing units (GPUs). We demonstrate the method on a noise-only field dataset with an embedded synthetic NMR signal.