Image restoration is an estimation process that attempts to recover an ideal high-quality image from a given degraded version. The Wiener filter method derived from the minimum mean square error criterion is widely used in image restoration to restore degraded images. In this method the constant Γ, which is an a priori representation of the signal-to-noise ratio for the complete image plane, is unknown and its value is supplied by the user and adjusted by the trial-and-error approach. A new estimation process of Γ is proposed. First of all, a second image is constructed from the given degraded image (referred to as the first image) using Lagrange's interpolation technique. Lagrange's interpolation technique used here is actually a modified version of the original approach. Secondly, an expression for Γ[u,v], the ratio of the power spectrum of the noise to the power spectrum of the first image is obtained using the power spectra of the first and the second images. However, the Wiener filter only needs Γ for the complete image plane. Therefore an arithmetic mean of a selected set of Γ[u,v] values is calculated. This arithmetic mean is then used as Γ in the Wiener filter to restore the first image.