基于分数维变换的图象恢复

Image Restoration Based on the Fractional Fourier Transform

对时不变退化模型的图象恢复可采用估计时间为Ｏ（ＮｌｏｇＮ）的“Ｗｉｅｎｅｒ线性滤波，对某些具有时变退化模型或非平稳过程的图象进行恢复，若进行线性估计，则需用Ｏ（Ｎ２）时间完成．这里提出的采用分数维傅里叶变换域滤波的方法，在实现时间为Ｏ（ＮｌｏｇＮ）下，可获得比在普通傅里叶变换域中滤波进行估计所具有的ＭＳＥ小；且没有附加代价。实验中，对不同的退化过程（ｃｈｉｒｐ函数等）引起的退化图象进行恢复，结果显示此方法是有效的．

The Wiener filter. which can be implement in O(NlogN)time, is suited for time-invariant degradation models. For time-variant and non-stationary processes. however, the optimal linear estimate requires O(N2).Optimal filtering in fractional Fourier domains permits reduction of the error compared, with ordinary Fourier domain filtering for certain types of degradation and noise while requiring O(NlogN) implementation time. Thus, improved performance is achieved at no additional cost. The blurred images that have several different degradation models are restored ill the experiments. The results show that the method presented in this paper is valid.