On Solving Fredholm Integral Equations of the First Kind

Abstract

A method for numerical solution of Fredholm integral equations of the first kind is derived and illustrated The solution f(x) of the integral equation is assumed to be a sample function of a wide-sense stationary random process with known autocorrelaUon function. From the set of permissible solutions, the solution that “best” satisfies the statistical properties of the random process is admitted as the correct solution With a kernel matrix A, the search for this solution is carried out by introducing the orthogonal frame of reference of the symmetrized matrix ATA and then suitably adjusting the components along the principal axes with small eigenvalues of ATA (1 e small singular values ofA), The method is illustrated for an example first considered by Philhps and also for another problem from the area of image processing. © 1977, ACM. All rights reserved.