  This paper presents a novel approach to construct regularizing operators for
severely ill-posed Fredholm integral equations of the first kind by introducing
parametrized discretization. The optimal values of discretization and
regularization parameters are computed simultaneously by solving a minimization
problem formulated based on a regularization parameter search criterion. The
effectiveness of the proposed approach is demonstrated through examples of
noisy Laplace transform inversions and the deconvolution of nuclear magnetic
resonance relaxation data.
