由于小波具有良好的时频特性,对于平滑图像,利用固定尺寸的小波滤波器滤波可以获得良好的分解结果.然而对于具有较多突变点的图像而言,采用固定尺寸的小波滤波器进行滤波并不是一个理想的选择.基于Heijman等人提出的2维自适应更新提升格式,本文提出了一种双自适应的小波变换算法,在更新与预测过程均采用自适应算法.最后,对标准图像进行测试分析,实验结果表明该算法在图像精确重构不需要额外的附加信息,且可以提高图像的峰值信噪比（PSNR）.

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.