用提升格式构造二次平均插值小波

提升格式是小波研究的新热点，提升格式的运用有两个不同的层次，即用提升格式来实现已有的小波变换和构造新的小波，首先用提升格式构造了二次平均插值小波，并用构造出的小波对灰度图象做变换，然后对变换后的系数采用最优比特率分配的方法来做编码，取得了与JPEG2000推荐的D9/7双正交小波图象编码基本一致的结果，但是，二次平均插值小波的提升格式要比D9/7双正交小波的提升格式简单得多，这意味着消耗的计算资源也少得多。

Constructing Average Interpolating Wavelets Via Lifting Scheme

Lifting scheme, the new hotspot of wavelets research, can be used to implement the existent wavelets and to construct completely new wavelets. Seen from the theory of lifting scheme, any transform constructed by lifting scheme is some kind of generalized wavelet transform. What's more, many digital signals are from the integral average of analog signals over certain interval or area. Considering the above two facts, the concept of average interpolating is presented in this paper. The average interpolating wavelet of 2 degree is constructed and is applied to image coding. After the wavelet transform for image data, Optimal Bit Allocation, which combines embedded quantization and entropy coding of binary system arithmetic coding together, is applied to get an optimal coding result by reaching the least distortion with the expected bits number. Finally, an image coding result is got as good as, if not better than, that of the D9/7 recommended by JPEG2000 draft. The lifting steps of the average interpolating wavelet is much simpler than that of the commonly used D9/7, which means the computational resources consumed here is much less.