Construction Of Compactly Supported Symmetric-Antisymmetric Orthogonal Multiwavelet

Wavelet analysis is the most glorious inheritance, summary and development of the Fourier analysis in the latest 170 years. It plays an important role in inheriting traditions and breaking new grounds for the future. Theoretical study of wavelet analysis combined closely with its applications. Multiwavelet theory is a new wavelet construction theory which developed on the basis of wavelet theory, it has a unique advantage as opposed to single wavelet, so the theory can be applied to the process of signal and image processing. Now the wavelet analysis is an important content of scientific and technological research work, it has brought the information industry and information technology to a new era. The two aspects of the structure theory of multiwavelet and application of wavelet transform are studied in this paper.Multiwavelet has the disadvantages that the single wavelet can not simultaneously satisfy the symmetry, orthogonality, compact support and higher-order vanishing moments in theory. On the basis of multiwavelets constructed theory, the single compactly supported symmetric orthogonal wavelet function is used to construct bivariate compactly supported symmetric-antisymmetric orthogonal multiwavelets through multipling with an orthogonal matrix after translation and this method is extended to the circumstances of r multiplicity, thus compactly supported symmetric-antisymmetric orthogonal multi-wavelet function is reconstructed in this way. The constructed multiwavelets not only have the nature of compact support and symmetry-antisymmetry, but also orthogonality.Based on the Canny algorithm and wavelet transform algorithm, an edge detection method that based on the image fusion in application is proposed in this paper. It has improved the question of the traditional wavelet transform discontinuity at the edge and the weak ability to suppress noise and gaven an improved method of wavelet transform. Two methods, wavelet transform and Canny operator, are used to extract the edge separately, and the results of the two methods are fused together. The fusion method combined the advantages of the two kinds of edge detection method to achieve complete and accurate positioning results.