Multiplierless Design of Biorthogonal Dual-Tree Complex Wavelet Transform using Lifting Scheme

In this work, we present the design, implementation and application of two families of biorthogonal dual-tree complex wavelet transform (CWT) filters using lifting scheme. The first design is achieved using exhaustive search with coding gain, DC leakage and directional selectivity as the fundamental criteria. The second set of filters are derived from the biorthogonal design procedure that was recently suggested by Selesnick. Furthermore, this paper also introduces a new theorem that suggests that lifting implementation of filters that are time-reversals of each other is closely related. Various applications are presented to validate the proposed design scheme, including performance in denoising as well as in the JPEG-2000 image coding standard.