Non separable 3D lifting structure compatible with separable quadruple lifting DWT

This report reduces the total number of lifting steps in a 3D quadruple lifting DWT (discrete wavelet transform). In the JPEG 2000 international standard, the 9/7 quadruple lifting DWT has been widely utilized for image data compression. It has been also applied to volumetric medical image data analysis. However, it has long delay from input to output due to cascading four (quadruple) lifting steps per dimension. We reduce the total number of lifting steps introducing 3D direct memory accessing under the constraint that it has backward compatibility with the conventional DWT in JPEG 2000. As a result, the total number of lifting steps is reduced from 12 to 8 (67 %) without significant degradation of data compression performance.