| Since the introduction by Daubechies of compactly supported orthogonal wavelet bases in R? various new wavelet bases have been constructed and applied successfully in image processing, numerical computation, statistics, and etc. Many of these applications, such as image compression, employ bidimensional wavelets and wavelet packets. Bidimensional wavelets have been often constructed by means of tensor product. The bidimensional wavelets and wavelet packets constructed by this method inherit the size and other features of one dimensional wavelets and wavelet packets. But the tensor product method imposes an unnecessary product structure on the plane, which is artificial for natural signals as well as images. We hope to establish a more isotropic analysis to overcome this drawback. The wavelets and wavelet packets related to the matrix are used in quincunx subsampling of image processing in two dimensions. In this thesis, wavelet packet decompositions related to the matrix M are obtained, this thesis is organized as follows. In Chapter 1, bidimensional orthogonal wavelet packets related to M are constructed. In Chapter 2, bidimensional non-orthogonal wavelet packet decomposition related to M is obtained. In Chapter 3, biorthogonal wavelet bases related to M is discussed. In Charter 4, biorthogonal wavelet packet decomposition related to M is obtained.
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