基于小波变换的分形插值反演问题

The Inverse Problem of Fractal Interpolation Function Based on the Wavelet Transform

通过对分形反演问题的研究方法和特点的分析，讨论了小波处理分形反演问题和在Hausdorff测度空间中分形插值函数的构造、小波变换零点的的自相似特征，给出了分形插值函数反演的解及算法，并通过算例表明了该方法的有效性和可行性。

By analyzing the research approaches and characters of fractal inversion problems,we discuss the way to deal with fractal inversion problems,fractal interpolation function structure in Hausdorff measure space,and self- similar characteristics of zero points of wavelet transformation.The solution and the algorithm of the inversion of fractal interpolation function are given with examples to illustrate its availability and feasibility.