Reconstruction of nonlinearly distorted signals with regularized inverse characteristics

A signal distorted by static, invertible, nonlinear characteristics can be exactly restored in the absence of noise. In this case the inverse of the characteristics can be used. When noise is superimposed to the distorted signal, the inverse characteristics may not be proper, because the noise is strongly amplified. This noise has to be suppressed in the reconstructed signal, which can be accomplished only at the price of bias. This article presents a method to compensate the effect of static nonlinearities in the presence of noise. The method is based on Tikhonov regularization operators and provides a compromise between noisy and biased estimates. The proposed algorithm has been successfully applied to reconstruct the sound of old movie-films