The accuracy of measurement systems is limited by the finite bandwidth of the system and by its nonlinearity. The limitations might be either technical or financial. In both cases the result is a distorted signal. If the distortion is not acceptable, the measurement can be partly compensated for it by digitally post processing the measured data. This procedure is generally called inverse filtering. We developed algorithms to compensate for the static nonlinearity even having large amount of measurement noise. We successfully applied the proposed algorithms to restore the distorted sound of old movie films. We also developed methods to compensate measurement systems for the effect of the finite bandwidth of the system, and adapted the algorithms to compensate the distortion of optical measurement systems.