NOVEL DECONVOLUTION OF NOISY GAUSSIAN FILTERS WITH A MODIFIED HERMITEEXPANSION

We have shown (J. Appl. Phys., 1990, 1415-1420) that deconvolving an i mage which was blurred by a Gaussian filter is equivalent to antidiffu sing the image for an appropriate duration of time. However, the antid iffusion algorithm used to show this, based on backward integration of the diffusion equation, is extremely sensitive to noise with numerica l errors increasing exponentially with time. Thus, an extremely high s ignal to noise ratio is required for reconstruction of a blurred image via antidiffusion. In this paper, we introduce a new antidiffusion al gorithm which is substantially more robust with respect to noise. This is because each functional component in the series of the reconstruct ed image is obtained analytically from a corresponding component of th e blurred image. We show that the algorithm yields accurate reconstruc tions of Gaussian-smeared signals and images with extremely low signal to noise ratios. (C) 1994 Academic Press, Inc.