关于分形图像压缩的收敛性

提出弱双曲迭代函数系统压缩方法，证明了其吸引子的存在性和解码序列的收敛性。使用弱IFS的优点在于变换可以是非线性的，而且放宽了对压缩因子的要求，这有利于变换的选取和构造，同时可以由较少的变换对图像进行分形编码，有利于提高压缩比。理论和数值实例，用本的方法进行图像压缩，可选择更广泛、更灵活的变换，能获得更好的图像质量和更高的压缩效率。

On Relaxing Condition on Compression Factor in Fractal Image

Fractal image compression based on IFS (iterated function system) theory is a new and efficient method, but its requirement about compression factor is too severe, thus limiting increase of compression rate and causing computational complexity. Therefore we propose weak IFS theory whose requirement about compression factor is much less severe. Using the weak IFS theory we can select its transforms in a range much larger than is possible with IFS theory, and this much wider choice is conducive to obtaining higher compression rate and to reducing computational complexity. In section 1, we prove theorem 1, which ensures existence of the attractor in weak IFS theory; we also prove theorems 2 and 3, which ensure the convergence of the decoding sequence in weak IFS theory. Numerical examples in section 2 do show that weak IFS theory is conducive to obtaining higher compression rate and to reducing computational complexity.