Noise bias correction in accumulated modulus NMR signal recovery

We discuss Nuclear Magnetic Resonance (NMR) signal detection in unstable magnetic field B and low Signal-to-Noise Ratio (SNR) condition. To improve SNR many acquisitions are accumulated and, because of B instability, inphase and quadrature components (I&Q) cannot be accumulated since carrier frequency changes from one acquisition to another. Carrier frequency dependence is removed by modulus S calculation, allowing S accumulation. Resulting accumulated S has improved SNR by a factor √k, but suffers from a noise error, sometimes called “noise bias”, arising from Rice statistics of S. We propose a technique to compensate such an error from knowledge of the original SNR of each acquisition of I&Q components. Usually SNR is estimated from acquisition with zero NMR signal, by switching off RF generator or, in NMR Imaging (MRI), from background pixels. Our technique is new since we estimate original SNR without switching off the signal to measure noise alone, but by calculation of modulus variance from accumulated S and S². We describe the compensation technique, showing both simulated results and real world results confirming goodness of our approach.