Bayesian Blind Identification of Nonlinear Distortion with Memory for Audio Applications

Whenever an audio device introduces unwanted nonlinear distortions into the manipulated signal, finding a tractable system to approximately model and estimate such degradations can be instrumental to recover the undistorted audio. This paper approaches such blind estimation task (for which classical identification tools are unsuitable) by bringing into the Bayesian framework a Hammerstein system model: the cascade of a static memoryless nonlinearity with a memory-inducing linear filter, which has been shown to be effective in describing many real systems. By assuming the underlying clean audio signal is autoregressive in short sections, the proposed method identifies the distorting system by simulating, in a Markov-Chain Monte Carlo context, the posterior distribution of the model parameters conditioned on the distorted signal. To deal with the resulting non-standard posterior distribution, a combination of the Metropolis-Hastings (MH) algorithm and the Gibbs Sampling is adopted. MH proposals are based on the Laplace approximation of the posterior distribution thanks to its almost Gaussian shape around modes. A heuristic that forces a broad region of the parameter space to be visited on an occasional basis prevents the Markov Chain from getting stuck around local maxima. A series of experiments with artificially distorted music recordings attests the effectiveness of the proposed algorithm.