基于小波的多重分形图像去噪新算法

针对多重分形分析很难估计有限长离散数据的多重分形谱这一问题,提出了一种基于奇异性分析的多重分形图像去噪算法.通过定义基于小波系数矩的配分函数,给出了一种有限长离散数据序列多重分形谱估计方法.图像去噪算法中图像的性质由多重分形谱决定,对噪声的类型没有提出任何假设条件,而是通过定义一个基于二维微局域(2-mi-crolocal)分析的变换算子对每一点的Hausdorff指数进行处理,使处理后的图像中大多数点位于平滑区域的同时,谱的相对强度没有变化,从而取得最佳效果.实验结果表明,该方法在去除噪声的同时可很好地保留原始图像的纹理信息.

New wavelet-based algorithm for denoising of multifractal images

A novel multifractal image denoising approach based on singularity structure analysis is proposed to overcome the difficulty in estimating the multifractal spectrum of discrete data for multifractal analysis. By defining the partition function for moments of the wavelet coefficients, a new estimator for multifractal spectrum is given. There is no assumption for the type of noise or global smoothness of original data, and the image is characterized by its multifractal spectrum. The Hausdorff exponent of the image is processed by defining a new transformation operation, so that most of the points in the denoised image lie in the smooth regions while the relative strength of the singularities is preserved. Experimental results show that the method proposed leads to a smooth image and preserves the texture information of original images very well.