Deblurring Gaussian Blur

Deblurring Gaussian Blur
By:"Robert A. Hummel","B. Kimia","Steven W. Zucker","Courant Institute of Mathematical Sciences. Computer Science Department","NEW YORK UNIV NY COURANT INST OF MATHEMATICAL SCIENCES."
Published on 1986 by

Gaussian blur, or convolution against a Gaussian kernel, is a common model for image and signal degradation. In general, the process of reversing Gaussian blur is unstable, and cannot be represented as a convolution filter in the spatial domain. If we restrict the space of allowable functions to polynomials of fixed finite degree, then a convolution inverse does exist. We give constructive formulas for the deblurring kernels in terms of Hermite polynomials, and observe that their use yields optimal approximate deblurring solutions among the space of bounded degree polynomials. The more common methods of achieving stable approximate deblurring include restrictions to band-limited functions or functions of bounded norm. Keywords: approximate inverse method; heat equation.

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