Abstract
This paper presents a new framework for a biorthogonal lapped transform that consists of long and short basis functions called the VLLBT. It is shown that when the biorthogonal long basis functions of the VLLBT are given, the optimal short basis functions in the energy compaction sense are derived by solving an eigenvalue problem without iterative searching techniques. We also provide design and image coding examples of the VLLBT. The resulting VLLBT attains high coding gain comparing to other lapped transforms. Moreover, experimental results show that the proposed VLLBT is superior to other conventional transforms in terms of PSNR at high compression ratio. Furthermore, it significantly reduces the annoying blocking artifacts. These results may imply that the proposed VLLBT with the optimal Short functions is a promising technique in the field of image coding.
