Lifting Wavelet Design by Block Wavelet Transform Inversion

Abstract

Due to its intuitive structure and efficient implementation, such as integer wavelets, lifting style wavelets gained high popularity. Following the natural correspondence between subband and lifting filters, this paper proposes a new approach to the design of wavelets indirectly through the optimisation of its corresponding block wavelet transform (BWT). BWT is a matrix transform which is generated from subbands, and it describes the relation between these two transform approaches. The BWT optimisation is achieved by making the matrix close to a particular Karhunen-Loeve transform (KLT) of interest. It has been observed that lifting-style wavelets have their constrains in the BWT matrix structure, therefore the minimisation of the difference between a KLT and a BWT derived from a lifting style wavelet becomes a non-trivial task. This paper briefly describes the vanishing moment and orthogonality constraints of the BWT, and introduces the first attempts to obtain single stage lifting wavelet filters that satisfies the constrained minimisation. Experimental results are provided.