The decomposition and reconstruction algorithms based on semi-biorthogonal wavelets
Lixia Chen · Journal of Guilin University of Electronic Technology · 2009
Wavelet decomposition and reconstruction algorithms are a critical step for wavelets towards the practical application.The semi-biorthogonal wavelets are introduced according to the established bracket products multiresolution analysis and the construction of a new class of wavelets.Based on the analysis of scaling space and wavelet space,together with the relationship between the corresponding bases of the spaces,the decomposition and reconstruction algorithms of semi-biorthogonal wavelets are proposed.The further discussion showed that the algorithms could be converted to solve pairs of Toeplitz linear equations.Furthermore,as the scaling functions φ and ■ are biorthogonal,the algorithms could be degenerated to the existing decomposition and reconstruction algorithms of biorthogonal wavelets.