Comparison between the Diffusion and the ADMM Filter and Combined Results

In this paper we compare two different methods to filter prediction signals in video coding: The anisotropic diffusion filter modeled using a (modified) heat equation and the ADMM (Alternating Direction Method of Multipliers) filter using directional total variation. The two methods are based on the same idea, namely using the structures in the underlying prediction signal to control the direction of the smoothing. It is shown here, that mathematically, in a continuous setting for a certain choice of parameters, the solutions of the two problem formulations are the same.Both filters are compared in the setting of a software based on HEVC (High Efficiency Video Coding). While the results for the diffusion filter method involve the testing of four different filters of uniform and signal adaptive type, the ADMM filter results feature only one type of filter configuration that can be en- or disabled in a block-wise manner. Despite the fact that both methods rely on the same idea, it is illustrated that the overall gains of the combination are higher than the RD gains of the individual tools. In particular, it is demonstrated that this is still the case if the filters are combined in an exclusive way. This proves that there is an additional value for each of the filter methods.