【作者】 杨国梁；

【导师】 汪西莉；

【作者基本信息】 陕西师范大学 ， 计算机软件与理论， 2006， 硕士

【摘要】 由于图像中总存在许许多多的噪声,为了更好地对图像进行分析和通信,在图像预处理中必须减少图像中的噪声。传统的去噪方法在去噪的同时使得图像的细节变得模糊。近年来,随着小波理论的不断发展和完善,小波分析已经渗透到各学科领域中去。同样,小波在图像去噪中也得到了广泛的应用,并提出了许多小波图像去噪算法。 小波变换由于具有“数学显微镜”的作用,在去噪的同时能保持图像的细节,得到原图像的最佳恢复。Ridgelet是继小波变换(Wavelet)后提出的一种新型的多尺度分析方法。对于图像中的直线状和超平面的奇异性问题,Ridgelet变换体现了比Wavelet变换更好的处理效果。在众多小波去噪方法中,Donoho小波阈值收缩法提出较早且被重视,但Donoho给出的阈值有“过扼杀”小波系数的倾向,重建误差较大。因此,针对阈值的选取以及对阈值的处理方法,人们作了大量的研究。 本论文主要围绕Ridgelet变换及其在图像处理中的应用来进行研究。主要进行了以下几个方面的工作: (1)对常用的图像去噪方法和小波去噪进行了研究,比较了各种方法的特点。 (2)对传统的小波收缩阈值进行了研究,并且对Lakhwinder Kaur等人针对Donoho阈值的存在问题提出的NormalShrink阈值法作了进一步的改进。 (3)对传统的阈值处理方法进行了研究,提出软硬折中的阈值处理函数。 (4)对Ridgelet变换作了初步研究并将其用于图像去噪。 (5)将改进的自适应阈值结合软硬折中阈值处理法用于Ridgelet变换对图像进行去噪,并与小波图像去噪及利用传统方法的Ridgelet变换图像去噪结果进行了对比。针对特征以直线为主的图像,试验结果表明该方法的去噪效果较传统的小波图像去噪效果好,峰值信噪比和去噪后的视觉效果较优。更多还原

【Abstract】 Many real-images are always corrupted by noise. In order to further image analysis and communication, the noise needs to be reduced in image pre-processing. Traditional methods can filter noise, but at the same time they make the image details blurred. Recently, with the development of wavelet theory, wavelet analysis has been applied in many fields. Meanwhile, wavelet is applied in image denoising successfully. And many new image denoising algorithms based on wavelet have been proposed.Wavelet transfonn has the characteristic of "mathematics microscope", thus it cannot only wipe off noise but also retain the image detail. Ridgelet transform is a new kind of multiscale analysis technique after wavelet transfonn. For image processing, ridgelet transform is more effective than the wavelet transform in representing linear and super-plane singularities. Among the wavelet denoising methods, Donoho’s wavelet shrinkage appears early and is recognized by many researchers, but this method tends to kill too many wavelet coefficients that might contain useful image information, and the reconstruction error is a little bigger. Therefore, aiming at the threshold selection and how to deal with the threshold, people make much research.The content of this dissertation is Ridgelet transform and its application in image processing. The content is as followed:First, the common and wavelet image denoising methods are discussed, and the characteristics of these methods are compared;Then we study the traditional wavelet shrinkage threshold and improve Lakhwinder Kaur’s NormalShrink by aiming at the defect of Donoho’s VisuShrink. Third, based on the traditional threshold method, we propose the soft-hard threshold tradeoff function. Fourth, we analyze the Ridgelet transfonn and the image denoising algorithm based on it. Finally, we use soft-hard threshold tradeoff function to the finite ridgelet transform for image denoising applying the new adaptive shrinkage shreshold, and compare the traditional method on wavelet transform and Ridgelet transform for image denoising. For images feature by straight lines, the experimental results show our method is better than the one we apply the traditional method on wavelet transform. The PSNR and vision perceive are better.更多还原