Because of the better temporal and frequency properties

the wavelet approximation with constant size filter can get better decomposition effects for the smooth image. However

standard wavelet approximation techniques cannot achieve similar results for images which are not smooth. The structures of wavelet transforms based on the adaptive lifting scheme with perfect reconstruction presented by Heijman et al.

this paper proposed the double adaptive wavelet transform which adopts the adaptive transform in both the update and prediction processes. The transform can perform perfect reconstruction without any overhead cost. At last

the experiment results demonstrate that the algorithm not only allows perfect reconstruction without any overhead cost but also can improve the PSNR of the image.