Blind identification of Hammerstein nonlinear distortion models

Compensation of nonlinear distortions is an issue of importance for the restoration of degraded audio material. However, it remains a very challenging task, especially in cases when only a single instance of the degraded audio signal is available. Compared to other sources of distortion, such as additive noise (hiss) or signal gaps, even the fundamental limits achievable by the restoration are yet unknown. We consider a particular distortion model of the Hammerstein type (instantaneous nonlinear distortion followed by an all pole filter) for which only the output signal is observed. We argue that the tasks of identifying the distortion model and restoring the signal should be handled separately and focus on the former one. The proposed method estimates the distortion model from a large number of signal frames using a sub-optimal iterative framework.