A method for obtaining an approximate Wiener filter

Abstract

The Wiener restoration filter yields the minimum mean-square error between the restored image and the true object function. However, it has found limited use because, in its usual formulation, it requires information about the object power spectrum which is generally unknown. In this paper, it is shown that the Wiener filter can be derived from the noise-free image power spectrum, and a method is presented for estimating this from the observed data. From this estimate an approximate Wiener filter was calculated. The method was tested on three sets of simulated data which included a constant background, rectangular defects, and Gaussian defects at varying contrast and noise levels. The performance of the approximate Wiener filter was compared both to the true Wiener filter and to the standard 1-2-1 three-point smooth. The results confirmed that the approximate Wiener filter adapted to the information content of the observed data and closely matched the performance of the true Wiener filter. The approximate Wiener filter outperformed the three-point smooth in all cases, especially at low contrast and high noise levels. The approximate Wiener filter can be calculated without operator intervention and requires little additional computation time over conventional Wiener filter techniques.