Abstract
Since its first introduction, the lifting scheme has become a powerful method to perform wavelet transforms and many other orthogonal transforms. Especially for integer-to-integer wavelet transforms, the lifting scheme is an indispensable tool for lossless image compression. Earlier work has shown that the number of lifting steps can have an impact on the transform performance. The fidelity of integer-to-integer transforms depends entirely on how well they approximate thir original wavelet transforms. The predominant source of errors is due to the rounding-off of the intermediate real result to an integer at each lifting step. Hence, a wavelet transform with a large number of lifting steps would automatically increase the approximation error. In the case of lossy compression, the approximation error is less important because it is usually masked out by the transform coefficient quantization error. However, in the case of lossless compression, the compression performance is certainly affected by the approximation error. Consequently, the number of lifting steps in a wavelet transform is a major concern. The new lifting method presented in this paper reduces the number of lifting steps substantially in lossless data compression. Thus, it also significantly improves the overall rounding errors incurred in the real-to-integer conversion process at each of the lifting steps. The improvement of the overall rounding errors is more pronounced in the integer-to-integer orthogonal wavelet transforms, but the improvement in the integer-to-integer biorthogonal wavelet transforms is also significant. In addition, as a dividend, the new lifting method further saves memory space and decreases signal delay. Many examples on popular wavelet transforms are included.
