A Q-SERIES APPROACH TO DEBLURRING THE DISCRETE GAUSSIAN

A method is presented for deblurring an image blurred by the discrete Gaussian. The method, based on classical theorems of Jacobi and Ramanu jan, not only provides exact formulas for the deblurring, but also con dition numbers and error bounds estimating the agreement between the o riginal and reconstructed image. The use of the Jacobi Triple Product Theorem provides a convenient factorization of the formulas used in th e inversion process into a product of three infinite series. These thr ee series correspond to a constant together with a Toeplitz operator a nd its transpose. In the finite setting this factorization corresponds to the factorization of a matrix into the product of Toeplitz matrice s, where the entries can be computed using simple recursion formulas, For selected choices of a, condition numbers are calculated for these operators. The results are similar to a method developed by Kimia and Zucker. (C) 1997 Academic Press.