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In this paper a fast algorithm for removing line scratches in old movies is presented. It is strongly based on exploiting the defect visibility in the image. To this aim the Weber's law can be applied to coefficients of an over-complete wavelet representation of the degraded image. The intensity of the defect, which is represented as a light diffraction effect, is then attenuated in the vertical and approximation sub-bands till the minimum threshold of visibility is reached. The experimental results are very satisfying: the image is completely recovered without local artifacts or annoying smoothing effects.