| Wavelet analysis is an important tool in signal processing, im-age processing areas. But in the treatment of high dimensional sig-nal or image anisotropic problem (such as edge), wavelet is not veryideal. The reason is that high dimensional wavelet is formed by onedimensional wavelet through the tensor product, which is not goodat directional treatment. According to this problem, the researchershave proposed many other wavelets, such as Ridgelet, Curvelet, Ban-delet, Contourlet and Shearlet. This paper mainly studies Shearlet,because of its good property in direction, and shearlet can check outthe orientation of mutations of signals, and the corresponding seriescan express the information of signal efectively.The advantages of orthogonal wavelet (Haar wavelet) are obvi-ous, but Shearlet is short of orthogonality. In wavelet analysis, whenwe can’t build the orthogonal wavelet, we can establish the biorthogo-nal wavelet according to the framework theory. Therefore, it is neces-sary to consider whether we should establish the biorthogonal Shear-let. The frst part of this paper study the following contents:(1)Establishing the multiscale analysis structure for a kind of biorthogo- nal Shearlet;(2) Discussing the relationship which the correspondingflter need to satisfy for the Shearlet biorthogonal theory.In addition, when people construct Shearlet, one way is usingpseudo polar in the frequency domain, another way is construct it inthe time domain directly. W.Q. Lim has constructed Shearlet in thetime domain, and given the fast algorithm. According to the waveletanalysis, decomposition algorithm of wavelet includes fast algorithmand Mallat algorithm. Therefore, Shearlet theory should also havecorresponding Mallat algorithm. The second part of the paper studythe following results:(1) Discrete Shearlet transformation is studiedand Mallat algorithm are given on the base of fast algorithm.(2) Inthe numerical calculation, the decomposition algorithm is presentedwith the Mallat algorithm. |
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