Computation of the singular system for a class of integral operators related to data inversion in confocal microscopy

In this paper the authors propose a numerical method for the computation of the singular system of certain compact integral operators related to the problem of data inversion in confocal microscopy. The method is based on the sampling theorem for functions whose Hankel transform has a bounded support. In this way the original integral equation is transformed into an infinite-dimensional linear system for the values of the unknown function at the sampling point. The singular values of the infinite-dimensional matrix coincide with the singular values of the integral operator. Approximations of the singular systems are obtained by considering finite sections of the infinite-dimensional matrix.