基于Cauchy分布的非下采样Shearlet HMT模型及其图像去噪应用  

Cauchy Distribution NSST-HMT Model and Its Applications in Image Denoising

作　　者：王相海[1,2] 朱毅欢 吕芳 苏欣[2] 宋传鸣[1] WANG Xiang-Hai;ZHU Yi-Huan;LV Fang;SU Xin;SONG Chuan-Ming(School of Computer and Information Technology,Liaoning Normal University,Dalian,Liaoning 116029;School of Mathematics,Liaoning Normal University,Dalian,Liaoning 116029)

机构地区：[1]辽宁师范大学计算机与信息技术学院,辽宁大连116029 [2]辽宁师范大学数学学院,辽宁大连116029

出　　处：《计算机学报》2018年第11期2496-2508,共13页Chinese Journal of Computers

基　　金：国家自然科学基金项目(41671439;61402214);辽宁省高等学校创新团队支持计划(LT2017013)资助~~

摘　　要：Shearlet变换作为后小波时代的一个重要的多尺度几何分析工具具有良好的各向异性和方向捕捉性,同时它也可以对诸如图像等多维信号进行一种近最优的稀疏表示.非下采样Shearlet变换(NSST)在保持Shearlet变换特性的同时还具有平移不变特性,这在具有丰富纹理和细节信息的图像处理中发挥着重要作用.该文首先对图像NSST方向子带内系数的概率密度分布进行分析,获得系数的稀疏统计特性和Cauchy分布拟合子带内系数的有效性;其次对NSST方向子带间系数的联合概率分布进行分析,获得方向子带系数间所具有的持续和传递特性,确定了一种NSST子带间树形架构的系数对应关系,进而提出一种NSST域隐马尔可夫模树模型(C-NSSTHMT),该模型通过Cauchy分布来拟合NSST系数,更好地揭示图像NSST变换后相同尺度子带内和不同尺度子带间系数的相关性.进一步提出一种基于所提出C-NSST-HMT模型的图像去噪算法,该算法对于含噪声方差为30和40的噪声图像,其去噪后的PSNR(Peak Signal to Noise Ratio)较NSCT-HMT方法分别提高了1.995dB和1.193dB.特别对纹理和细节丰富的图像,该算法在去噪的同时,有效地保留了图像的几何信息.With the rapid development of science and technology,as the carrier of multimedia communication,the application of image in life becomes more and more extensive.Due to the external or in situ imaging system,the image produces a lot of noise during the transmission.These noises not only affect the visual effects of the image,but even change the content and quality of the image,which cause great interference in image segmentation,image retrieval,feature extraction and other subsequent digital image processing operations.The purpose of image denoising is to filter out the noise from the noise polluted image and get the original“pure”image,but it also need to ensure that the image of the internal edge and texture structure are not affected too much.In the past few years,the method of image denoising based on the wavelet transform has been concerned.However,although the wavelet transform represent the singular points of images very well,it can not capture the line singularity of the high dimensional signal and the abundant texture information and direction information in the image effectively.In order to overcome the above weakness of wavelet transform,other multi-scale analysis tools,for instance Shearlet transform,Bandelet transform,Ridgelet transform,Curvelet transform,Contourlet transform and Directionlet transform,etc.,have been proposed in recent years to provide a better representation for the high dimensional singular features of images.Further more,it is a hot issue that how to represent and correlate the image subband coefficients of these multiscale geometric transform effectively.As an important multi-scale geometric analysis tool in the post-wavelet era,Shearlet transform has a good directional sensitivity and anisotropy,and it is a near-optimal sparse representation of multidimensional functions.The Non-Subsampled Shearlet Transform(NSST)maintains the property of Shearlet transformation and also has a translation invariance,which plays an important role in image processing with rich texture and detai

关 键 词：非下采样Shearlet变换 隐马尔可夫树模型 NSST-HMT Cauchy分布 支持向量机 图像去噪 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]