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 ArA and then suitably adjusting the components along the
principal axes with small eigenvalues ofATA (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.
