ML estimation of memoryless nonlinear distortions in audio signals

Many real-world signals are subjected to nonlinear distortions that can be approximately modeled as memoryless and invertible. In Audio applications, they are typical of magnetic recordings but can also result of dynamic compression employed in vinyl recordings etc. Such an effect can be disturbing to a modern audience which is used to higher quality material. This paper proposes an iterative algorithm to maximize the likelihood function of the distortion function parameters, based solely on samples of the degraded signal, and then recover the original signal. The method assumes the original signal to be autoregressive and Gaussian in short sections - a standard model for audio - and the nonlinearity to be time-invariant throughout the signal, thus allowing the use of all samples in the model estimation. Additionally, a simple and time-efficient alternative technique to estimate the nonlinear function is proposed; it can be used either as a fast and reliable stand-alone procedure or as a initialization routine for the more sophisticated maximum likelihood approach. The robustness of the proposed techniques is verified through application to artificial and real signals nonlinearly distorted.