A Three Dimensional Combinative Lifting Algorithm for Wavelet Transform Using 9/7 Filter

Three dimensional-discrete wavelet transform (3D-DWT) shows its advantages in the volumetric data compression. Some algorithms and architectures have been proposed for the 3D-DWT, but most of them perform the transform by applying three separate 1D transforms, or by applying inter-frame transform and spatial transform separately. In this paper, we choose 9/7 filter along the three directions to do the transform based on lifting scheme. Using multilinear algebra (L.D. Lathauwer, 1997), this paper let X_n operation stand for a high order tensor´s linear transform in its nth dimension. Then we successfully extend spatial combinative lifting algorithm (SCLA)(H. Meng and Z. Wang, 2000) to its 3D application. Matrices A,B,C,D,E for lifting algorithm of 9/1 filter (H. Meng and Z. Wang, 2000) can be multiplied step by step to get the final result of one level decomposition of 3D-DWT. The operation on matrix A could be represented as X₁A X₂A X₃A.