BIORTHOGONAL WAVELET TRANSFORMATIONS

This chapter explains how to construct a biorthogonal filter pair that can be used to generate wavelet transformation matrices. It also explains how to construct short biorthogonal filter pairs. The chapter then develops techniques utilizing symmetric filters that minimize the problems caused by wrapping rows in the transformation. Before developing general algorithms for symmetric biorthogonal wavelet transformations and their inverses, one needs to know more about the relationship of the lengths of symmetric biorthogonal filter pairs. The chapter presents an algorithm for applying the symmetric biorthogonal transformation constructed from odd‐length biorthogonal filter pairs applied to vectors of even length N without justification. It also describes an algorithm for computing the symmetric biorthogonal transformation for even‐length filter pairs. Finally, the chapter presents the application of image compression and investigates the application of image pansharpening to which the biorthogonal wavelet transform is well‐suited.