Generalized lapped biorthogonal transforms using lifting steps

In this paper, a large class of lapped biorthogonal transforms using lifting steps(LLBT) is presented. The transform cofficients are parametarized as a basic matrix and a series of lifting steps, providing fast, efficient in-place computation of them. Our main motivation of the new transform is its application in image coding. The LLBT has several long overlapped basis functions of the synthesis bank for representing smooth signals to avoid annoying blocking artifacts. The bases of the synthesis bank covering high-frequency bands are constrained to be short to reduce ringing artifacts. Moreover, the analysis bandpass filters provide better stopband attenuation. Comparing to the popular 8×8 DCT,the LLBT only requires several more additions and shifting operations. However, image coding examples show that the LLBT is far superior to the DCT and 8×16 LOT in both objective and subjective coding performance.