多小波变换的提升格式及其在图象编码中的应用

在简要介绍提升格式和多小波之后，提出了一种新的实现多小波变换的提升格式模型，由于这个模型主要由若干个单小波变换的提升格式搭建而成，因而不必自己推演提升格式的内部结构和参数，另外，这个模型还可以根据实际应用的需要选用不同的单小波，该文还给出用D9／7双正交（单）小波变换的提升格式构造的多小波变换的实例，并把这样构造的多小波变换应用于图象编码，结果表明，该方法可取得比常用的GHM多小波图象编码更好的效果。

A Lifting Scheme for Multiwavelet Transforms and its Application to Image Coding

Lifting scheme is not only a fast algorithm of existing wavelet transforms, but also a tool to produce new wavelet transforms. Multiwavelets are a new kind of wavelets and have found many new applications to signal processing. In this paper we present a framework of lifting scheme for multiwavelet transforms, in which the existing lifting schemes designed originally for wavelet (not multiwavelet) transforms can be used as building blocks. Thus we needn't concern about the internal structures and parameters of these building blocks. What we need to do is to choose different wavelets for different applications and then make use of the lifting schemes for these wavelets to build a new lifting scheme. This new lifting scheme is equivalent to a multiwavelet transform. We build such a lifting scheme by using the lifting schemes for D9/7 biorthogonal wavelet transform and then apply this new lifting scheme to image coding. We have achieved better results than that obtained by the commonly-used GHM multiwavelet image coding.