Approximating the DCT with the lifting scheme: systematic design and applications
Jie Liang, Trac Duy Tran · 2002
A systematic approach to design two families of multiplierless approximations of the DCT with the lifting scheme is presented, based on Chen's (1977) and Loeffler's (1989) factorizations of the DCT matrix, respectively. The analytical values of all the lifting steps are derived, which can be approximated by dyadic values to enable fast implementations with only shifts and additions. Different trade-offs between the complexity and the performance can be easily obtained. A scaled lifting structure is proposed to further reduce its complexity. The performance of the lifting-based DCT implementation is demonstrated in the frameworks of JPEG and H.263+. Besides, the lossless compression capability is also presented.