Image restoration using spectrum estimation

Abstract

A stochastic approach to image restoration is proposed by using various spectrum estimation techniques. In order to estimate the original image from the knowledge of observed image, the minimum mean square error filter or Wiener filter is known to be optimum in the sense of minimizing the mean square error. The optimality of Wiener filter, however, holds only when the power spectra of the original image and noise are given in addition to the transfer function of the imaging system. In practice, the information of the original image is generally not available. In the present paper additive noise is assumed to be white with known variance and the Wiener filter is implemented using various estimation techniques for the original spectrum. The proposed method shows significant improvement over the conventional methods, such as the Wiener filter using constant signal-to-noise power ratio, particularly for images with low signal-to-noise ratio.