Research On Fractional Wavelet Theory And Applications

As a new time-frequency analysis tool,the Fractional Wavelet Transform(FRWT)extend the traditional analysis method of the Wavelet Transform(WT)based on time–frequency domain to the method based on time-fractional frequency domain,which can characterize signal localization features in time and fractional-frequency domain,so it has some high scientific value in the studies of FRWT theory and application.This thesis studies the theory and applications of Discrete Orthogonal Wavelet Transform(DFRWT),and the main research work and innovations are as follows:(1)The equivalence property between the DFRWT and the theory of the two channel filter banks in fractional domain.The FRWT provides an adaptive localization analysis method in the time-fractional frequency domain,which decomposes the signal into the sum of time domain components representing the subbands of the fractional domain.In the analysis of the generalized orthogonal multi-resolution framework,the paper discusses the method of the fractional orthogonal wavelet construction,analyzed the intrinsic equivalence between DFRWT and the theory of two channel filter banks in the fractional fourier domain.The conclusion shows that the transfer relationships of function spaces determined by the generalized second scale equations corresponding the fractional domain space division by the fractional domain filter banks and FRWT provides a broad sense of multi-resolution analysis in the time domain and the fractional fourier domain respectively.(2)The algorithm about the coefficients decomposition and reconstruction of the DFRWT.In order to facilitate DFRWT application,this paper deduces one-dimensional and two-dimensional algorithms of the orthogonal discrete fractional wavelet based on the orthogonal projection principle of function space in the generalized orthogonal MRA,and realizes the coefficient decomposition and reconstruction process based on DFRWT.The algorithm is based on traditional Mallat algorithm added coefficient modulation link,which has the upper and lower sampling process of the fractional convolution(3)The method of image threshold de-noising and enhancement based on DFRWT.When p order changes near 1,the modulus values of the high-frequency subband coefficients are still sparseness while changing.The coefficients of variation affects the threshold value of the image,so the image processing effect is not the same.Methods of denoising image and enhancing image based on DFRWT with flexibility and selectivity are proposed.The results of image processing are superior to the traditional wavelet domain methods and other methods.(4)The method of image fusion based on DFRWT.Against the existing problems in image fusion,according to the non-sparsity character of mode coefficient in different p order of Fractional wavelet transform,the paper proposes new image fusion methods of regional maximum value and regional variance matching base on DFRWT for the Multi-focus images and the medical images.The compared experiments were done to test using different gray distribution features image and discuss the selection of p order.Compared with the traditional DWT fusion method,experimental results show that the proposed methods effectively suppress the pseudo-Gibbs effect,fusion effect and objective evaluationis are obviously improved.Compared with the method of Non-Subsampled Contourlet Transform(NSCT),fusion time is much shorter while ensuring the fusion of quality.(5)The dual digital watermarking method based on generalized transformation domain.In the traditional method based on time-frequency domain for the watermarking,the watermark algorithm becomes more complex and the imbedding watermark results to a lack of selectivity due to the disequilibrium of transformation coefficient distribution.For this reason,this paper proposes a new robust watermark method based on the generalized time-frequency transform(Fractional Fourier Transform and Fractional Wavelet Transform)domains.Antisymmetric dual watermarking are obtained based on the characteristics of image's fractional Fourier transform and are inserted into the coefficients of different subbands of the host image's fractional wavelet transform in the low p order.Experimental results show that the dual watermarks possess strong robustness to resist shear attack,and the equilibrium of the energy of subband coefficient distribution and key sensitivity guarantee that the embedded watermark in low p order has good transparency and security and change the traditional method of watermark embedding.The proposed method is shown to be simple,more flexible,and more robust as compared with traditional methods.