Biorthogonal Wavelet Transform
Nirdosh Bhatnagar · 2020
Functions are generally expanded in terms of orthogonal basis functions. However in some applications, it is convenient to expand the function in terms of biorthogonal functions. Biorthogonality offers a more versatile tool, if it replaces the condition of orthogonality. Wavelets which use biorthogonality, are often symmetric and have compact support. Symmetricity of the wavelets and scaling functions is one of the reasons to select biorthogonal over orthogonal wavelets. Biorthogonal systems, as the name implies, use dual basis. This offers more flexibility. However, use of biorthogonality comes with a disadvantage. The chapter explains the biorthogonal representation of a function. Biorthogonalized wavelets are a generalization of orthogonalized wavelets. Therefore, there are more degrees of freedom in designing biorthogonal wavelets.