The accuracy of the measurement of time and space domain signals is limited by the measurement system. The limitations are basically due to the finite bandwidth and the nonlinearities. The compensation of the finite bandwidth is called inverse filtering. Inverse filtering and the compensation of nonlinearities have many similarities. The compensation of nonlinearities in the case of strongly nonlinear and noisy environment introduce many new difficulties. Our department has long tradition and expertise in the field of inverse filtering. Our aim is to utilize this knowledge and develop new algorithms in the field of nonlinear compensation. The difficulty of compensation is that the measurement noise is amplified with a great extent on those parts of the nonlinear characteristic, where the slope of the inverse characteristic is large. Decreasing the slope introduces distortion of the useful signal. The solution is a compromise between the biased and the noisy compensations. Our aim is to develop different algorithms to compensate nonlinearities in different environments. In one case the unbiased reconstruction is required, in other cases the aim is to have a smooth reconstruction with no impulsive like noise. The results will be developed mainly to reconstruct and restore the sound of old movie films. The algorithms, however, will be applicable to the compensation of noninearities in other applications as well.