Lorentzian-Model-Based Bayesian Analysis for Automated Estimation of Attenuated Resonance Spectrum

Extracting information from a signal exhibiting damped resonances is a challenging task in many practical cases due to the presence of noise and high attenuation. The interpretation of the signal relies on a model whose order (i.e., the number of resonances) is in general unknown. In this study, the signal is modeled as a sum of Lorentzian lineshapes, and a Bayesian framework is designed to simultaneously remove the baseline distortion, select the number of resonances, and recover the parameters of each line-shape including frequency, damping factor, resonance amplitude, and noise magnitude. The Bayesian problem is solved resorting to a reversible jump Markov chain Monte Carlo (RJ-MCMC) sampling scheme. The algorithm is tested on synthetic signals as well as experimental data from a resonant ultrasound spectroscopy experiment aiming to measure elastic properties. The results show that, compared to the well-known linear prediction singular value decomposition method, the RJ-MCMC method achieves a better performance with the advantages of joint model selection, high accuracy estimation, and uncertainty evaluation. We found that when the signal-to-noise-ratio is larger than 20 dB, the average relative error for frequency extraction is smaller than 0.5%. Such an algorithm enables to estimate the number of resonances and extract tens of resonance parameters from a highly attenuated spectrum, which can significantly facilitate the automated processing of signals exhibiting damped resonances.