A wavelet-based 3D surfacelet transform

In this paper, we propose a new multiscale version 3D surfacelet tranform, named wavelet-based surfacelet transform (WBST). The surfacelet transform (ST) is constructed by combining the 3D directional filter banks with a multiscale pyramid structure. But the redundancy of the pyramid structure will affects the performance of ST in some redundant-sensitivity applications. To avoid the redundancy, we use the non-redundant 3D wavelet transform instead of the pyramid structure. The new structure reduces the redundancy factor of ST from 4.02 to 3. The experimental results show that the proposed WBST has the better performance in non-linear approximation (NLA) in comparison the ST. And the small redundancy makes the WBST has a large potential in 3D signal compression.