Non-separable three dimensional discrete wavelet transform with adaptive directional prediction

In this report, we introduce a directionally adaptive three dimensional (3D) prediction to the non-separable 3D discrete wavelet transform (DWT). The proposed 3D DWT has less lifting steps and better prediction performance comparing to the existing separable 3D DWT with fixed filter coefficients. The 3D DWT can be applied to compress data volume of volumetric medical images or motion pictures. It is also applicable to analyze such kind of multi-dimensional signals. The proposed method has compatibility with the conventional DWT defined by the JPEG 2000 international standard.