Variable-smoothing local regularization methods for first-kind integral equations

We consider the local regularization problem for integral equations of the first kind, generalizing previous work which applied only to problems of Volterra type. Our approach allows for local control of the regularization process, allowing for resolution of fine/sharp features of solutions without having to resort to nondifferentiable optimization techniques. In addition, we present examples illustrating the numerical implementation of one version of the resulting local regularization algorithm and show that, under quite reasonable assumptions, the operation count of the local method compares well with that of standard Tikhonov regularization.