New methods for restoring motion-blurred images derived from edge error considerations

Abstract

On the basis of a previous analysis of the edge error in image restorations by the authors, two new classes of Fourier-domain restoration methods for motion-blurred images are proposed in this paper. In the spectral interpolation methods, the restoration problem is reduced to the estimation of a number of indeterminate spectral coefficients of the image. If we require that the restored image have the smallest possible variance, all the indeterminate spectral coefficients may be set to zero. Even such a simple implementation of the spectral interpolation method proves to be equivalent to the sophisticated spatial-domain method proposed by Sondhi. This suggests that the spectral interpolation method has great potential when used in conjunction with appropriate sophisticated methods for the interpolation of spectral coefficients. In the pixel difference interpolation method, a restoration is computed on the basis of the estimates of the differences in the intensity of adjacent pixels. A characteristic of this method is that we have the freedom to choose the locations at which the estimates are to be made. For images with patches of uniform intensity, the pixel differences within the regions of uniform intensity are small and can be accurately estimated. This fact may be exploited to obtain near-perfect restoration of such images, as demonstrated in actual restorations of test images. Even for highly textured images, restorations obtained using this method are found to be of a quality comparable to those obtained using Sondhi's and Ku and Hu's methods. © 1991.