| Empirical mode decomposition(EMD)is an important nonlinear non-stationary signal analysis method,which is widely used in medical,military,environmental monitoring and other fields.This paper focuses on improving computing efficiency of the bidimensional multivariate empirical mode decomposition(BMEMD),and has done the following research work:(1)The paper makes a systematic theoretical introduction to the basic knowledge of EMD algo-rithm,and focuses on the concept of intrinsic mode function(IMF),and the recursive sifting process to obtain IMF.On this basis,the two main extension directions of the EMD algorithm(multivariate signal and multidimensional signal)are sorted out,including the multivariate empirical mode de-composition(MEMD)algorithm and the two-dimensional empirical mode decomposition(BEMD)algorithm.Then the paper elaborates a BMEMD algorithm for two-dimensional multivariate signal processing,and analyzes its advantages and disadvantages.(2)The paper then introduces a derivative algorithm of EMD in recent years: variational mode Decomposition(VMD).The extended algorithm in two-dimensional signal processing,named bidi-mensional variational mode decomposition(BVMD),is also analyzed with advantages and disadvan-tages.The above work reflects the superiority of BMEMD in the field of two-dimensional multivariate signal processing,and further illustrates the necessity of studying the fast algorithm of BMEMD.(3)This paper proposes a fast BMEMD algorithm based on mean surface approximation,which obtains the mean surface no longer by averaging the maximum surface and the minimum surface,but by interpolating extreme points directly.Based on this,the paper proposes a fast BMEMD algorithm(Mean Approximation Bidimensional Multivariate Empirical Mode Decomposition,MA-BMEMD)based on mean surface estimation.Then through the artificial synthetic texture images decomposition and the real images fusion,it is verified that MA-BMEMD not only guarantees the advantages of the BMEMD algorithm,but also greatly reduces the complexity of the algorithm and improves the efficiency of the BMEMD.(4)The paper also proposes a fast BMEMD algorithm which estimates surface based on order statistic filters.The core idea of the algorithm is to use a simple but effective convolution operation to estimate the maximum(minimum)value surface instead of the traditional surface interpolation method.At the same time,the size of the filter is completely driven by data,which is adaptive.Based on this,the paper proposes a fast adaptive BMEMD algorithm(FA-BMEMD)using local extremum filters.On the other hand,inspired by MA-BMEMD,the paper also proposes a BMEMD algorithm for fast mean surface estimation using a mean filter(FMA-BMEMD).The results of synthetic tex-ture images decomposition and real image fusions prove that both FA-BMEMD and FMA-BMEMD greatly improve the computational efficiency while retaining the pattern alignment and texture anal-ysis properties.EMD has great research significance for nonlinear and non-stationary signal analysis,and its derived BMEMD algorithm performs best in the field of bidimensional multivariate signals compared with other algorithms.This paper mainly studies the rapid implementation of the BMEMD algorithm.While ensuring the original function of the algorithm,the time complexity of the algorithm is reduced as much as possible,which lays the foundation for its real-time application in the industry. |
