An operator factorization method for restoration of blurred images
Abstract
A problem of restoration of images blurred by spaceinvariant pointspread 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 Wiener 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 orthonormal harmonic sinusoids called the sine transform, and the eigenvector expansion of the Wiener filter equation can be numerically achieved via a fastsinetransform algorithm which is related to the fastFouriertransform (FFT) algorithm.
 Publication:

IEEE Transactions on Computers
 Pub Date:
 November 1977
 Bibcode:
 1977ITCmp..26.1061J
 Keywords:

 Blurring;
 Computer Techniques;
 Image Enhancement;
 Image Processing;
 Operators (Mathematics);
 Wiener Filtering;
 Algorithms;
 Boundary Value Problems;
 Covariance;
 Eigenvectors;
 Polynomials;
 Transformations (Mathematics);
 Instrumentation and Photography