A K-iterated scheme for the first-order Gaussian recursive filter with boundary conditions

Recursive Filters (RFs) are a well known way to approximate the Gaussian convolution and are intensively used in several research fields. When applied to signals with support in a finite domain, RFs can generate distortions and artifacts, mostly localized at the boundaries of the computed solution. To deal with this issue, heuristic and theoretical end conditions have been proposed in literature. However, these end conditions strategies do not consider the case in which a Gaussian RF is applied more than once, as often happens in several realistic applications. In this paper, we suggest a way to use the end conditions for such a K-iterated Gaussian RF and propose an algorithm that implements the described approach. Tests and numerical experiments show the benefit of the proposed scheme.