© 2018 SPIE. To further accelerate the calculations associated with point-cloud-based holograms, wavelet shrinkage-based superpositIon (WASABI) has been proposed. Wavelet shrinkage eliminates the small wavelet coecient values of the light distribution emitted from a point cloud, resulting in an approximated light distribution calculated from a few representative wavelet coecients. Although WASABI can accelerate the hologram calculations, the approximated light distribution tends to lose the high-frequency components. To address this issue, random sampling was applied to the light distribution.