Chinese Journal of Computers   Full Text
Title	Design of Two-Channel Neville-Lagrange Lifting Wavelet Filter Banks with Linear Phase
Authors	CHEN Dong ZHANG Tian-Wen LI Dong
Address	(School of Computer Science and Technology, Harbin Institute of Technology, Harbin 150001)
Year	2009
Issue	No.7(1413—1423)
Abstract &   Background	Abstract The second generation wavelets based on lifting scheme can be obtained by applying the Euclidean algorithm to Laurent polynomial of the first generation wavelets. To design the second generation wavelets fit into lifting scheme is a focus problem that need to be studied deeply. This paper constructs the two-channel Neville-Lagrange lifting wavelet filter banks with linear phase by combining the Neville filer theory and Lagrange interpolation theory. Furthermore, the linear phase property is proved and the normalization of two-channel Neville-Lagrange lifting wavelet filter banks is discussed. As an example, the two-channel Neville-Lagrange-44 (N-L-44 for short) is given, and the comparison with 9/7 wavelet of JPEG2000 for image compression is discussed. Experimental results show that the N-L-44 lifting wavelet filter bank is better than the 9/7 wavelet filter bank of JPEG2000 for image compression obviously, and compared to the lifting scheme of 9/7 wavelet, N-L-44 lifting wavelet filter bank improves the image compression performance at low bit rate (bpp<1). In addition, two-channel Neville-Lagrange lifting wavelet filer banks with linear phase show the great potential advantages, such as the design of adaptive lifting wavelet filter bank, the construction of the True-2D lifting wavelet filter bank. Keywords Neville filter; Lagrange interpolation; lifting wavelet; image compression; linear phase Background This research is an important part of the National Natural Science Foundation of China (No.60875013 and No.60475011). The main objective of the two programs is to study the design of wavelet filter banks and the algorithm for image compression. Discrete wavelet transform (DWT) is the dominant method of image compression and becomes the core technique of static image compression standard of JPEG2000. The second wavelet theory based on lifting is the development and improvement of classic DWT, and the powerful wavelet filter banks for image compression can be designed using lifting. The Neville filter theory is a useful tool for constructing the lifting wavelet filter banks, Neville filter theory and Lagrange interpolation are combined in our research and the new filter banks that named “two-channel Neville-Lagrange lifting wavelet filter banks with linear phase” are constructed. Test result shows that the new filter banks improve the image compression performance at low bit rate and shows the great potential advantages, such as the design of adaptive lifting wavelet filter bank, the construction of the True-2D lifting wavelet filter bank.