The Research Of Characteristics For Fractional Semi-orthogonal Multi-wavelet Frames And Image Fusion Strategies

Wavelet analysis is a new branch of mathematics that has developed rapidly for nearly three decades.It is a new signal analysis method based on Fourier analysis and functional analysis.Its application involves many aspects in natural science and engineering technology.Wavelet analysis has been widely used in signal processing,image processing,biomedicine,sampling theory,quantum mechanics,differential equation solution and other fields.Wavelet frame theory is an important part of wavelet analysis.Firstly,the research background and current situation of wavelet analysis and image fusion are reviewed,and the concepts and properties of wavelet frame,semi-orthogonal wavelet frame,fractional wavelet frame,Gabor frame and wave packet frame are presented.The classification and evaluation indices of image fusion are introduced.Secondly,based on the semi-orthogonal multi-wavelet frame and fractional wavelet frame,the concept of strictly semi-orthogonal fractional multi-wavelet frame in2L(R)is proposed.Through time-frequency analysis method and functional analysis method,the properties of semi-orthogonal fractional multi-wavelet frame are studied.The equivalent conditions for strictly semi-orthogonal fractional multi-wavelet frame are obtained.It is proved that the semi-orthogonal fractional Parseval multi-wavelet frame is equivalent to the fractional Parseval multi-wavelet frame associated with generalized multi-resolution analysis.Thirdly,a multi-focus image fusion algorithm based on undecimated dual-tree complex wavelet domain is proposed.For low-frequency sub-band coefficients,the non-negative matrix decomposition for the block principal component rotation is used.The high frequency sub-band coefficients are selected by Gaussian weighted region energy and regional standard deviation.A new method of image fusion is obtained.The experimental results show that the algorithm is of effectiveness.In order to overcome the shortcomings of the infrared visible image fusion method,two new adaptive multi-directional image fusion methods based on fast finite shearlet transform are proposed in the fourth part of the paper.One image fusion method is to use a sparseness constraint added to the original nonnegative matrix factorization algorithm for low frequency sub-band coefficients,and the direction weight contrast is selected for the high frequency sub-band coefficients.The experimental results show that the fusion image has clearly overall outline and the objective evaluation also has some improvement.Another kind of image fusion method is to use the gradient information correlation method for low frequency sub-band coefficients.A fusion rule for joint direction characteristic contrast and gray correlation analysis is designed for high frequency sub-band coefficients.The simulation results show that the fusion strategy have better effect on the subjective vision and the objective evaluation.Finally,by means of compactly supported shearlet transform,a new method of image fusion based on optimal gradient non-negative matrix decomposition algorithm and direction characteristic contrast is designed.The simulation results indiate that this method is effective and have some progress in subjective vision or objective evaluation.