Research On Bidemensional Empirical Mode Decomposition Based On Unconstrained Optimization Method

Hilbert-Huang transform is a novel time-frequency analysis method,proposed by the Norden e.Huang in 1989.This method is suitable for processing nonlinear nonstationary signal analysis,which includes empirical mode decomposition and Hilbert spectrum analysis.It has high research value and a very broad prospects for applications.The proposed EMD has opened the post-wavelet era.Based on the theory of one-dimensional empirical mode decomposition,J Nunes et al.proposed two-dimensional data EMD,i.e.,bidemensional empirical mode decomposition(BEMD),which is capable of dealing with the most non-stationary grayscale images in the world.Similar to the EMD with incomplete mathematical theory,there are many problems in BEMD,including mode mixing,end-point/edge effects,over-decomposition and under-decomposition,and heavy computation burden.This thesis reviews the principles and algorithms of EMD and BEMD and analyzes their differences.The BEMD is described in detail,including the acquisition of extreme points in the case of two-dimensional data,how to obtain the upper and lower envelope surfaces through extreme points,and the sifting process termination conditions.And the reasons for the existence of problems in the BEMD is analyzed.The thesis makes attempts to improve the BEMD algorithm to solve the inherent problems in the BEMD.This thesis constructs the objective function and constraints through the characteristics of the intrinsic mode component and the local mean component produced by the decomposition.Then,the constraint problem is changed into an unconstrained optimization problem through the dual function.The intrinsic mode component and local mean component can be obtained by one-step operation.Next,the local mean component is used for the next solution.After multiple operations until the obtained local mean component has no extreme point inside the image,the iteration is stopped and the decomposition is completed.The one-step operation of this improved algorithm need not multiple sifting process iterations,does not accumulate errors,and reduces endpoint effects.At the same time,one-step operation reduces the amount of computation and prevents over-decomposition and under-decomposition.The proposed BEMD is employed for image analysis.Similar to hyperspectral multiple channels,a feature vector can be constructed for each point.The image achieved by the BEMD decomposition includes more information.Thus,it is worth analyzing the data of a layer or multi-layer.In this thesis,the multiple channels decomposed by the leather image are used to detect leather defects,which can reduce the influences of textures and light and shadow.Finally,the improved BEMD is employed for IC solder joint inspection.the components decomposed by the IC solder joint image are used for defect classification based on deep neural network.