Lifting Scheme及其在小波图象编码中的应用

Lifting Scheme是构造第二代小波的关键技术。相对于第一代小波而言，Lifting Scheme是一种比Mallat算法更快、更简单和更容易操作的算法，也是JPEG2000推荐的算法，为了将其应用到小波图象编码中，提出了一种对Lifting Scheme作适当改进以用于小波图象编码的方法。该方法就是先用Lifting Scheme来实现D9/7双正交小波变换，然后再用这种技术实现的D9/7双正交小波变换来进行图象压缩编码。在将Lifting Scheme算法用于小波图象编码的过程中，对该算法做了必要的简化，以便保证每个提升(lifting）环节都是FIR滤波。同时，根据能量守恒的原则，重新调整了尺度因子。实验结果表明，这种经过改进的Lifting Scheme取得了比Mallat算法更好的图象编码效果。

Lifting Scheme and Its Application to Wavelet Image Coding

Lifting scheme is honored as the key tool to the construction of second generation wavelets. As for the first generation wavelets, lifting scheme is a new way of implementation faster, simpler and easier than the commonly used Mallat algorithm. Lifting scheme is also the one recommended by JPEG2000, a new image coding international standard scheduled to be formally published this year. In order to apply the lifting scheme to wavelet image coding, we make some improvement to the lifting scheme. We first implement the D9/7 bi orthogonal wavelet transform through lifting scheme and then apply the transform to wavelet image coding. In doing so, we improve the procedure of implementation to make sure that each lifting step is FIR filtering. At the same time, we adjust the value of scale factor under the guide of energy conservation. The scale factor obtained this way is different from that recommended by JPEG2000. The experimental results presented in this paper show that our improved lifting scheme has achieved the image coding gain better than that achieved by Mallat algorithm.