Auxiliary image construction by Lagrange's interpolation for estimation of Γ in image restoration

Abstract

In image restoration process the Wiener filter method, derived from the minimum mean square error criterion, is probably the most popular. In this method the constant (Gamma) , which is an a priori representation of the signal-to-noise ratio for the complete image plane, is supplied by the user and adjusted by trial and error method. In a previous paper an estimation process for (Gamma) was introduced. An expression for (Gamma) [i, j], which is an a priori representation of the signal-to-noise ratio for the pixel [i, j], was derived assuming that two degraded images of the same object are provided. The expression depends on the correlation between the two degraded images and the point spread function involved in blurring the original image. The estimate for (Gamma) was obtained by taking a statistical average of the values of (Gamma) [i, j]. However, it may not always be possible to have the second image, in which case this process of estimation of (Gamma) cannot be used. In this paper, a new algorithm is proposed to construct the second image based on Lagrange's interpolation technique so that the above method of estimating (Gamma) can still be used when the second image is not available.