Optimized Update/Prediction Assignment for Lifting Transforms on Graphs

Transformations on graphs can provide compact representations of signals with many applications in denoising, feature extraction or compression. In particular, lifting transforms have the advantage of being critically sampled and invertible by construction, but the efficiency of the transform depends on the choice of a good bipartition of the graph into update (U) and prediction (P) nodes. This is the update/prediction (U=P) assignment problem, which is the focus of this paper. We analyze this problem theoretically and derive an optimal U=P assignment under assumptions about signal model and filters. Furthermore, we prove that the best U=P partition is related to the correlation between nodes on the graph and is not the one that minimizes the number of conflicts (connections between nodes of same label) or maximizes the weight of the cut. We also provide experimental results in randomly generated graph signals and real data from image and video signals that validate our theoretical conclusions, demonstrating improved performance over state of the art solutions for this problem.This work was supported in part by NSF under Grant CCF-1018977 and in part by the Spanish Ministry of Economy and Competitiveness under Grants TEC2014-53390-P, TEC2014-52289-R, TEC2016-81900-REDT/AEI and TEC2017-83838-RPublicad