| In the research of the cost function for the quaternion filtering and neural network domain,the least mean square algorithm(LMS)based on the minimum mean square error(MSE)update criterion has been widely used since it has low computational complexity and excellent performance in various applications.However,it is found that the MSE criterion does not perform well in non-Gaussian or nonlinear environment,and its perfor-mance loss is commonly degraded with the influence of large impulsive noise.Therefore,after introducing the concept of ”entropy” to measure the similarity of random variables,the maximum correlation entropy criterion(MCC)is applied to the adaptive filtering al-gorithm,and thus obtaining robustness.In terms of neural network,MCC criterion has also been proved to be applied in wind energy prediction,face recognition and other real-number scenes.Therefore,this thesis combined MCC criterion with the current filtering algorithm and multi-layer perceptron algorithm in the field of quaternion.The main con-tent of this thesis can be divided into the following aspects:Firstly,the quaternion gradient update of quaternion linear filter based on both MSE and MCC is derived based on the real-number LMS algorithm.At the same time,combin-ing robust estimation with MCC,a novel robust linear quaternion algorithm is proposed to deal with the quaternion non-Gaussian noise.The parameter selection is discussed through simulation experiments,and the correctness and practicability of the algorithm are verified under the simulation with optimal parameters.Secondly,according to the above proposed gradient update criterion,the gradient derivation operation process is introduced based on the characteristics of quaternion in-volution and conjugate involution based on HR calculus gradient operation,which are used to simplify the calculus gradient operation process in HR.Finally,the quaternion nonlinear filter weight update formula based on the MCC is derived and verified by robust regression experiment.Compared with the traditional nonlinear quaternion filtering algo-rithm based on MSE,the proposed algorithm has better performance in dealing with com-mon non-Gaussian environmental noise.The derivation of the update formula provides convenience and foundation for the subsequent derivation of quaternion MLP algorithm in the next chapter.Finally,this thesis discusses the multi-layer perceptron algorithm in quaternion.The theory of network parameters,forward propagation and reverse update of the multi-layer perceptron structure is firstly reviewed,and then by utilizing the gradient update of net-work parameters and generalized involution characteristics of quaternion,this thesis fi-nally obtain the QMLP update algorithm based on MCC criterion.After verifying the correctness of the algorithm in robust regression,it is applied to the image codec com-pression application.This thesis reaches to the conclusion that the proposed algorithm can process the non-Gaussian noise of the input image,so that the peak signal-to-noise between the original image and the output image is higher which means the processing result is better than the traditional quaternion multi-layer perceptron based on MSE.In this thesis,the combination of MCC criterion and robust estimation is applied to quaternion linear filtering,and the M-QMCC algorithm is innovatively proposed,and the application of MCC in quaternion nonlinear filtering and multi-layer perceptron al-gorithm is discussed,take advantage of the robustness of the criterion against common non-Gaussian ambient noise.After verifying the correctness of the algorithm through simulation and experiments,it is concluded that the combination of quaternion filtering and perceptron algorithm with MCC criterion has better robustness than the quaternion algorithm under the traditional MSE criterion.The final error turns out to be smaller. |
