Abstract: Acording to the character of second bandelet transform，a novel image denoising scheme is proposed by combining redundant version with multi-level thresholding based on blocks.Bandelet transform is able to achieve optimal approximation and represent image of sparse for utilizing image geometrical regularity.Standard bandelet transform is lack of translation-invariation，a new version with redundant is presented.During bandeletization，thresholding estimating with no risk is introduced to reduce influence of noise on geometrical flow，and then make use of Bayes shrinkage denoising in bandelet domain.The numerical experiments indicated that the redundant approach with adaptive thresholding for image denoising is much better than wavelet and curvelet also contourelet.Especially，Bandelet denoising can preserve much more details of the images and have better visual quality because of no Psedudo-Gibbs.

Key words: image processing, image denoising, redundant Bandelet transform, adaptive multi-thresholding, geometry regularity

摘要： 结合第二代Bandelet变换的特点，提出了基于分割块的自适应多阈值冗余Bandelet图像去噪方法。首先采用冗余的二维小波变换实现图像的多分辨率表示，通过稀疏的观点，而不是率失真的观点而定义拉格朗日函数在各个高频子带进行Bandelet化，在Bandelet化的过程采用没有风险的估计阈值来寻找最佳几何流方向和完成最优四叉树分割，最后通过Bayes软阈值萎缩法实现在Bandelet域去噪。实验结果表明：该算法的去噪效果要优于经典小波以及curvelet和contourlet，去噪后图像的边缘没有伪Gibbs效应，具有好的图像的视觉质量。

关键词: 图像处理, 图像去噪, 冗余Bandelet变换, 自适应多阈值, 几何正则性