摘要
本文首先证明了小波域中去除了均值的分形小波变换算子M可以在有限步迭代中逼近其固定点,从而使得分形小波变换编码可以在不是完全压缩的条件下完成收敛;然后对这种放宽了收敛条件的编码算法给出了压缩因子的一个上界,并据此对Fisher提出的终值压缩性思想作出了有效的解释。
For the operator M which is a mean shifted version of IFS(Iterated Function System) in wavelet domain is proved that in practical circumstances the same fixed point can be reached in only few iterations. So, the IFS in wavelet domain may converge without being fully contractive. Then, a contraction factor's upper bound is obtained after relaxing the collage theorem bound and the idea of eventual contractivity introduced by Fisher is explained.
关键词
分形小波变换
有线迭代收敛
图像压缩编码
Fractal wavelet transform, Self-quantization of subtrees, Image compression, Eventually contractive convergence
