Time-domain Bayesian detection and estimation of noisy damped sinusoidal signals applied to NMR spectroscopy

The problem of model detection and parameter estimation for noisy signals arises in different areas of science and engineering including audio processing, seismology, electrical engineering, and NMR spectroscopy. We have adopted the Bayesian modeling framework to jointly detect and estimate signal resonances. This considers a model of the time-domain complex free induction decay (FID) signal as a sum of exponentially damped sinusoidal components. The number of model components and component parameters are considered unknown random variables to be estimated. A Reversible Jump Markov Chain Monte Carlo technique is used to draw samples from the joint posterior distribution on the subspaces of different dimensions. The proposed algorithm has been tested on synthetic data, the 1H NMR FID of a standard of l-glutamic acid and a blood plasma sample. The detection and estimation performance is compared with Akaike information criterion (AIC), minimum description length (MDL) and the matrix pencil method. The results show the Bayesian algorithm superior in performance especially in difficult cases of detecting low-amplitude and strongly overlapping resonances in noisy signals.