Adaptive signal averaging method which enhances the sensitivity of continuous wave magnetic resonance and other analytical measurements

A method of signal processing for repetitively acquired noisy signals obtained by magnetic resonance or other analytical measurements involving a deterministic signal obscured by noise in order to obtain enhanced physical, chemical or biological information from the noisy signals due to improved signal to noise ratio comprising:

• using a single measurement device in order to acquire repeated measurements and generate a first set of signals, each signal corresponding to one of the measurements and each signal of the first set of signals having a constant noise variance;
• providing a signal processing device having a processor and a non-transitory computer readable memory containing an adaptive algorithm which utilizes a reference signal in order to generate a filtered signal;
• using the signal processing device in order to perform the following steps:
• a) conventionally averaging at least two noisy signals from the first set of signals in order to generate an initial reference;
• b) executing the adaptive algorithm using the initial reference in step (a) in order to filter a subsequent noisy signal from the first set of signals in order to obtain a filtered signal;
• c) conventionally averaging the subsequent noisy signal with the initial reference in order to update the initial reference;
• d) executing the algorithm using the updated reference in order to filter a next subsequent noisy signal in order to obtain another filtered signal;
• e) conventionally averaging the next subsequent noisy signal with the updated reference in order to further update the reference;
• f) repeating steps (d) and (e) in order to obtain a set of filtered signals;
• g) averaging the set of filtered signals in order to generate a final signal that has a noise variance equal to a prediction error variance of the adaptive filter divided by a number of signals used in steps (b) through (f), in order to create a measure that is lower than the noise variance in any of the signals corresponding to the measurements as well as the noise variance for the average of these measurements;
• h) identifying the physical, chemical or biological information from the final filtered signal that has been, or is, enhanced because the information is no longer being obscured by noise;
• and
• i) providing the identified and enhanced information as the output of the signal processing device.