Constructing Average Interpolating Wavelets Via Lifting Scheme
用提升格式构造二次平均插值小波

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.