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 blockwise 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.

An embedding framework for video reconstruction using Gaussian mixture models In this paper, we propose a novel video reconstruction methodology which is built based on alternating direction method of multipliers (ADMM) algorithm. In this regard, a new enhanced ADMM model has been used which permits the user to apply image or video reconstruction techniques as subproblems being embedded to a denoising methodology. Correspondingly, we use conventional compressive sensing (CS) based Gaussian mixture models (GMM) as a subproblem of our proposed framework. On the other hand, sparse 3D transformdomain block matching (BM3D) is used as the denoiser of algorithm in order to remove the remaining artifacts and noise in the reconstructed video frames. Consequently, by considering both online and offline CSbased GMM frameworks, we are able to make two forms of GMM based video reconstruction algorithms which are represented as online and offline structures. Using the proposed algorithms, video reconstruction is more satisfactory in terms of visual quality in comparison with other state of the art techniques.