The shifted inverse-gamma model for noise-floor estimation in archived audio recordings

In this paper a new model for audio signals in additive noise is presented in a time–frequency formulation. It is assumed that signal and noise coefficients are both complex Gaussian random variables, but that the (unknown) variance of the signal component is scaled relative to the (also unknown) noise variance. Under this assumption we find that an appropriate prior distribution for the unknown scalings of signal coefficient variances relative to noise variance can be specified in terms of a shifted inverse-gamma distribution. Incorporating this prior distribution into a Bayesian model, the marginal conditional distribution for the noise variance may be computed in closed form using just tabulated values of the incomplete gamma function, which is readily available in mathematical programming languages. We test our method using both simulated and real noise environments, demonstrating successful and promising results under quite challenging conditions.