  We propose and analyze an iterative refinement of a modified Lavrentiev
regularization method for deconvolution of the discrete Helmholtz-type
differential filter. The modification for the Lavrentiev regularization method
exploits the properties of the Helmholtz filter, and we prove that the
modification reduces the error bound between the original solution and the
approximated solution. Furthermore, we derive an optimal stopping condition on
the number of iterations necessary for the regularization. We provide numerical
examples demonstrating the benefits of this iterative modified Lavrentiev
regularization over a family of Tikhonov regularization methods.
