Discrete multivariate gray model based boundary extension for bi-dimensional empirical mode decomposition

The bi-dimensional empirical mode decomposition (BEMD) has attracted extensive attention recently by virtue of its high performance in adaptive image processing. Unfortunately, this promising technique does not necessarily yield fruitful results due to the boundary effects. Motivated by the discrete multivariate gray model, we propose a boundary extension framework for mitigating the boundary effects of BEMD. In greater detail, followed by verifying the equivalence between the continuous and discrete multivariate gray model theoretically, a first-order three-variable discrete multivariate gray model D-GMC(1,3), which is derived from the continuous multivariate gray model with convolution integral C-GMC(1,N), is utilized to predict the middle pixels of each extended block in terms of existing border. Specifically, the coordinates and pixels of the image are respectively regarded as relative data series and characteristic data series of D-GMC(1,3). Experimental results on a set of widely used images indicate that the proposed approach can achieve qualitative and quantitative improvements within appropriate processing time by comparing with other three generally acknowledged methods, i.e. the original BEMD, symmetrical extension as well as texture synthesis based BEMD.