A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
Journal of the ACM (JACM)
Toeplitz Matrix Inversion: The Algorithm of W. F. Trench
Journal of the ACM (JACM)
Fast computational techniques for pseudoinverse and wiener image restoration.
Fast computational techniques for pseudoinverse and wiener image restoration.
Image Restoration, Modelling, and Reduction of Dimensionality
IEEE Transactions on Computers
IEEE Transactions on Computers
Generalized Wiener Filtering Computation Techniques
IEEE Transactions on Computers
The Application of Constrained Least Squares Estimation to Image Restoration by Digital Computer
IEEE Transactions on Computers
IEEE Transactions on Computers
Technical Note: A fast parallel Gauss Jordan algorithm for matrix inversion using CUDA
Computers and Structures
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A problem of restoration of images blurred by space-invariant point-spread functions (SIPSF) is considered. The SIPSF operator is factorized as a sum of two matrices. The first term is a polynomial of a noncirculant operator P and the second term is a Hankel matrix which affects only the boundary observations. The image covariance matrix is also factorized into two terms; the covariance of the first term is a polynomial in P and the second term depends on the boundary values of the image. Thus, by modifying the image matrix by its boundary terms and the observations by the boundary observations, it is shown that the wieWir filter equation is a function of the operator P and can be solved exactly via the eigenvector expansion of P. The eigenvectors of the noncirculant matrix P are a set of orthronormal harmonic sinusoids called the sine transform, and the eigenvector expansion of the Wiener filter equation can be numerically achieved via a fast-sine-transform algorithm which is related to the fast-Fourier-transform (FFT) algorithm. The factorization therefore provides a fast Wiener restoration scheme for images and other random processes. Examples on 255 X 255 images are given.