Application Of Canonical Correlation Analysis In Separation Of Mixed Signals And Color Images

This thesis has carried out a series of research based on canonical correlation analysis(CCA).The main work is as follows:The first,we propose an integrated image feature extraction method of partial differential equations(PDEs)+one-directional two-dimensional CCA(2D-CCA),and focuses on the influence of PDEs on Cumulative Contribution Rate(CCR)in 2D-CCA.Experimental results show that the evolution of PDEs can not only weaken the choice of CCR in 2D-CCA does not even need to consider the choice of CCR.Compared with the algorithm of Lei et al.,it can obtain better recognition accuracy with fewer evolution times of PDEs,even up to 100%recognition accuracy.The second,we propose a CCA-based signals+colors image mixing and separation method,and separately studies the advantages and disadvantages of using different convolution kernels for equal-size convolution and PDEs as feature extraction methods,and using CCA and PDEs+CCA as separation methods.The experimental results show that when using uniform filter feature extraction and CCA separation,the proposed method is very effective for the mixed separation of dual-signal+dual-color image and multi-signal+colorful image.Then,in order to avoid loss of discriminant information caused by reshaping of image data in the separation and extraction process,a new signals+color images separation and extraction method named a 2D-CCA-based signal+color image hybrid separation method is proposed for image data with the same rows and columns.The use of different convolution kernel performs equal-size convolution and PDEs as the feature extraction method,using 2D-CCA and PDEs+2D-CCA as the advantages and disadvantages of the separation method.The experimental results show that the method can be used for uniform filtering feature extraction and 2D-CCA separation.While getting better signal and color image restoration effect,the time for separation is greatly shortened.The last,in order to solve the problem of image data with different row and column numbers,a two-directional two-dimensional CCA((2D)~2-CCA)-based signals+color images mixing and separation method is proposed.Four kinds of common filters are used to extract image features by unequal convolution.The experimental results show that when using uniform filter feature extraction and(2D)~2-CCA separation,the recovery effect of the signal and color image is further improved,and the time required for separation is further shortened.And applies the research results on the functional magnetic resonance imaging(f MRI)data found that music therapy is have a therapeutic effect on depression,because the auditory stimulation activates nerve cells in the hippocampus in the brain,making negative memories more debilitating and erasing the emotional impulses of bad memories,thus alleviating the trauma of the memory.