The Application of Constrained Least Squares Estimation to Image Restoration by Digital Computer

Abstract

Constrained least squares estimation is a technique for solution of integral equations of the first kind. The problem of image restoration requires the solution of an integral equation of the first kind. However, application of constrained least squares estimation to image restoration requires the solution of extremely large linear systems of equations. In this paper we demonstrate that, for convolution-type models of image restoration, special properties of the linear system of equations can be used to reduce the computational requirements. The necessary computations can be carried out by the fast Fourier transform, and the constrained least squares estimate can be constructed in the discrete frequency domain. A practical procedure for constrained least squares estimation is presented, and two examples are shown as output from a program for the CDC 7600 computer which performs the constrained least squares restoration of digital images.