A new structure of lifting wavelet for reducing rounding error

The 5/3 wavelet transform with double lifting steps in JPEG 2000 can reconstruct a signal without any loss. It has been utilized for lossless coding. The 9/7 wavelet transform contains two more lifting steps and scaling operations to improve performance for lossy coding. The loss is due to (1) quantization of band signals, (2) rounding of signals after scaling and (3) finite word length expression of scaling coefficients. This paper analyzes conditions on word length of coefficients and bit depth of rounded signals for no loss. It also proposes a new structure of lifting wavelet by changing order of the lifting step and the scaling. As a result, the rounding error is not scattered by the lifting steps and the error is minimized in mini-max sense.