基于小波的图像去噪方法研究
摘要
一般说来,在现实中各种方式获取的图像,都一定程度被噪声所污染,从而对我们日常的应用和分析带来了困难。图像去噪的目的是减少和消除图像中的噪声,从而改善图像质量。近年来,小波在数学、信号处理和图像处理领域受到很大关注,也有很多学者对基于小波的图像去噪方法展开了大量详尽的研究。由Donoho首先提出的小波阈值法因为简单,有效成为了一种主流的方法。已有多种方法提出,到目前为止,仍有许多学者在其基础上进行研究。但是由于小波阈值法对于去除噪声和保留图像边缘细节有天然的设计上的缺陷,即不可能提出一种阈值方法都能完美的将噪声和图像有效信息分开,所以传统的阈值去噪法不能同时达到去噪和保持边缘信息的两个目的。图像边缘检测的目的方法是检测到图像的有效边缘信息的同时,抑制我们不需要的例如噪声等不需要的信息。传统的边缘检测算子可以较为有效的检测出图像边缘,但是对于噪声图像非常敏感。在小波域中,利用小波间系数相关性进行边缘检测是一个可以有效抑制噪声的方法。由于考虑到了噪声点与正常系数随尺度变换而衰减的不同情况,将相关性系数相乘可以有效检测出边缘信息同时抑制噪声。但是该方法往往不如传统边缘检测算子的检测效果好,同时要考虑尺度变换导致的系数偏移情况。
本文的具体内容如下:
我们在第一章中,首先介绍了我们选题的背景意义,以及图像去噪的发展和去噪方法的评价标准,最后简单介绍了小波图像去噪方法的发展历程。
第二章的内容是我们之后工作的基础,其中我们主要介绍了小波变换的基本理论,二维小波变换及提升小波理论,在最后通过文献我们着重分析了小波变换后噪声点和正常系数的分布规律。
第三章主要介绍了小波去噪理论和几种基本方法。首先我们介绍了阈值的选取方法,包括硬阈值、软阈值、半软阈值等。其次,我们介绍了几种门限准则。例如通用阈值法、极大极小阈值、Stein无偏风险阈值、贝叶斯阈值等。
在第四章中,我们首先详细介绍了贝叶斯阈值的具体算法,包括如何估计噪声点的方差,已经如何计算阈值——逐点阈值法和逐块阈值法。
第五章,首先研究了基于小波的边缘检测方法。其中主要包括利用传统边缘算子的方法和小波系数相关性的算法。这两种算法各有各的特点。提出了我们的改进方法。有效的将两种算法结合,从而给出了我们检测边缘信息的算法。
最后,我们在给出算法的基础上进行了大量的实验,实验表明,我们的算法可以有效的提取图像边缘,同时,该边缘有效抑制了噪声,因此在去噪的效果上,我们的算法不仅去噪效果明显,同时更能体现边缘。在峰值信噪比上,我们的算法比传统的Bayes阈值去噪法以及类零树Bayes阈值去噪法,都有了一定的提高。从理论和实验结果都证明,相对于传统的Bayes阈值法和改进的Bayes阈值去噪法,我们给出的算法的去噪结果稳定、快速、同时更加有效的。
Generally, the images obtained in various ways in reality, are contaminated by noise to some extent and the difficulties come with it in our daily application and analysis. The purpose of image denoising is to reduce or eliminate the image noise, thus improving image quality. In recent years, in mathematics, signal processing and image processing, wavelet has received much attention, meanwhile many scholars have started their researches on the wavelet-based image denoising method. Because wavelet threshold method which is first proposed by Donoho is very simple, effective becomes a mainstream approach. Many methods proposed so far, but there are still many scholars based on their research. However, because wavelet threshold has a natural defect on removing noise and keeping the edge detail, which can not propose a threshold method can perfectly valid information will be separated from the noise and image. so the traditional threshold denoising method can not simultaneously achieve and maintain the edge information of two purposes. The purpose of edge detection method is effective to detect the image edge information, inhibit some noise which we do not need. The traditional edge detection operators can more effectively detect image edge, but the image is very sensitive to noise. In the wavelet domain, wavelet coefficients of correlation between the edge detection are an effective way to suppress noise. In consideration of the noise is normal with the scale transformation and attenuation coefficient of different situations, the correlation coefficient multiplication can detect the edge information while suppressing noise. However, this method is often not as good as the traditional edge detection operator detection effect, and coefficient offset is also should be taken into account.
The specific content of this article are as follows:
The background of our topics of significance is introduced in the first chapter, as well as the development of image denoising and evaluation criteria of image denoising. In the last, development process of wavelet image denoising method is introduced.
The second chapter is the basis of the work after which we introduced mainly introduced the basic theory of wavelet transform, two-dimensional wavelet transform and enhance of the wavelet theory. we focus in the final analysis of literature after the wavelet transform coefficients of noise points and normal Distribution of.
The third chapter introduces the theory of wavelet denoising and several basic methods. First, we introduced the threshold selection methods, including hard threshold and soft threshold, half-soft threshold value. Secondly, we introduced several threshold criteria. Such as universal threshold, minimax threshold, Stein unbiased risk threshold, Bayesian threshold value.
In the fourth chapter, we first described in detail the specific algorithm for Bayesian threshold, including how to estimate the variance of noise points, has been how to calculate the threshold - the threshold point by point-by-block method and threshold method.
Through literature, our analysis of the classical Bayes threshold and several improved Bayes threshold, the analysis of their advantages and disadvantages. In addition, we also analyzed the wavelet transform, image factor and noise point of characteristic coefficients. We put forward our strategy based on edge detection threshold Bayes foundation.
In chapter five, we first studied the wavelet-based edge detection method. Which mainly include the use of traditional methods of edge operator and wavelet coefficients of correlation algorithms. The two algorithms each have their own characteristics.
Relative to traditional edge detection method, we can find edge and hold-up noise. We not only consider intra-scale dependencies, but also inter-scale dependencies. Because our method not conflict with traditional edge detection, so it is feasible in theory.
At last, we give an algorithm based on a large number of experiments, the result is stable, fast and effective. At the same time than the traditional Bayes threshold denoising with some improvements.
本文的具体内容如下:
我们在第一章中,首先介绍了我们选题的背景意义,以及图像去噪的发展和去噪方法的评价标准,最后简单介绍了小波图像去噪方法的发展历程。
第二章的内容是我们之后工作的基础,其中我们主要介绍了小波变换的基本理论,二维小波变换及提升小波理论,在最后通过文献我们着重分析了小波变换后噪声点和正常系数的分布规律。
第三章主要介绍了小波去噪理论和几种基本方法。首先我们介绍了阈值的选取方法,包括硬阈值、软阈值、半软阈值等。其次,我们介绍了几种门限准则。例如通用阈值法、极大极小阈值、Stein无偏风险阈值、贝叶斯阈值等。
在第四章中,我们首先详细介绍了贝叶斯阈值的具体算法,包括如何估计噪声点的方差,已经如何计算阈值——逐点阈值法和逐块阈值法。
第五章,首先研究了基于小波的边缘检测方法。其中主要包括利用传统边缘算子的方法和小波系数相关性的算法。这两种算法各有各的特点。提出了我们的改进方法。有效的将两种算法结合,从而给出了我们检测边缘信息的算法。
最后,我们在给出算法的基础上进行了大量的实验,实验表明,我们的算法可以有效的提取图像边缘,同时,该边缘有效抑制了噪声,因此在去噪的效果上,我们的算法不仅去噪效果明显,同时更能体现边缘。在峰值信噪比上,我们的算法比传统的Bayes阈值去噪法以及类零树Bayes阈值去噪法,都有了一定的提高。从理论和实验结果都证明,相对于传统的Bayes阈值法和改进的Bayes阈值去噪法,我们给出的算法的去噪结果稳定、快速、同时更加有效的。
Generally, the images obtained in various ways in reality, are contaminated by noise to some extent and the difficulties come with it in our daily application and analysis. The purpose of image denoising is to reduce or eliminate the image noise, thus improving image quality. In recent years, in mathematics, signal processing and image processing, wavelet has received much attention, meanwhile many scholars have started their researches on the wavelet-based image denoising method. Because wavelet threshold method which is first proposed by Donoho is very simple, effective becomes a mainstream approach. Many methods proposed so far, but there are still many scholars based on their research. However, because wavelet threshold has a natural defect on removing noise and keeping the edge detail, which can not propose a threshold method can perfectly valid information will be separated from the noise and image. so the traditional threshold denoising method can not simultaneously achieve and maintain the edge information of two purposes. The purpose of edge detection method is effective to detect the image edge information, inhibit some noise which we do not need. The traditional edge detection operators can more effectively detect image edge, but the image is very sensitive to noise. In the wavelet domain, wavelet coefficients of correlation between the edge detection are an effective way to suppress noise. In consideration of the noise is normal with the scale transformation and attenuation coefficient of different situations, the correlation coefficient multiplication can detect the edge information while suppressing noise. However, this method is often not as good as the traditional edge detection operator detection effect, and coefficient offset is also should be taken into account.
The specific content of this article are as follows:
The background of our topics of significance is introduced in the first chapter, as well as the development of image denoising and evaluation criteria of image denoising. In the last, development process of wavelet image denoising method is introduced.
The second chapter is the basis of the work after which we introduced mainly introduced the basic theory of wavelet transform, two-dimensional wavelet transform and enhance of the wavelet theory. we focus in the final analysis of literature after the wavelet transform coefficients of noise points and normal Distribution of.
The third chapter introduces the theory of wavelet denoising and several basic methods. First, we introduced the threshold selection methods, including hard threshold and soft threshold, half-soft threshold value. Secondly, we introduced several threshold criteria. Such as universal threshold, minimax threshold, Stein unbiased risk threshold, Bayesian threshold value.
In the fourth chapter, we first described in detail the specific algorithm for Bayesian threshold, including how to estimate the variance of noise points, has been how to calculate the threshold - the threshold point by point-by-block method and threshold method.
Through literature, our analysis of the classical Bayes threshold and several improved Bayes threshold, the analysis of their advantages and disadvantages. In addition, we also analyzed the wavelet transform, image factor and noise point of characteristic coefficients. We put forward our strategy based on edge detection threshold Bayes foundation.
In chapter five, we first studied the wavelet-based edge detection method. Which mainly include the use of traditional methods of edge operator and wavelet coefficients of correlation algorithms. The two algorithms each have their own characteristics.
Relative to traditional edge detection method, we can find edge and hold-up noise. We not only consider intra-scale dependencies, but also inter-scale dependencies. Because our method not conflict with traditional edge detection, so it is feasible in theory.
At last, we give an algorithm based on a large number of experiments, the result is stable, fast and effective. At the same time than the traditional Bayes threshold denoising with some improvements.
引文
[1] Donovan G, Geronimo, J.S. Hardin D. and Massopust P,Construction of Orthogonal Wavelets Using Fractal Interpolation Function. SLAM J. Math. Anal, 1996,Vol 27:1158-1192.
[2] Daubechies L, Gorssam A. and Meyer Y., Painless Nonorthogonal Expansion. Math,Phys., 1986, Vol 27: 1271-1283.
[3] Donoho D L, Johnstone I M. Ideal Spatial Adaptation by Wavelet Shrinkage. Stanford University, CA, 94305-4065,USA.
[4] B.Vidakovic. Statistical Modeling by Wavelets. Wiley Series in Probability and Statistics. John Wiley & Sons, Inc, 1999.
[5] Thierry Blu and Florian Luisier.The SURE-LET Approach to Image Denoising, IEEE Transactions on Image Processing, July 113, 2007.
[6]曲天书,戴逸松,王树勋.基于SURE无偏估计的自适应小波阈值去噪.电子学报, 2002, 2, 30(2):266-268.
[7] S.G.Chang,B .Yu and M .Vetterli, Image Denoising via Lossy Compression and Wavelet Thresholding,IEEE Int. Conf. Image Processing, Nov,1997,Vol.1:640-607.
[8] F.Abramovich, T.Sapatinas and B.W. Sliverman.“Wavelet Thresholding via a Bayesian Approach”, tech.rep. Math Department, University of Bristol, Bristol BS8 1TW,UK,Nov, Vol. 6,1996.
[9]王红霞.基于复数小波变换增强带噪图像的空间自适应方法.计算机辅助设计与图形学学报, 2005, 9(9):1911-1916.
[10] DL Donoho. Sparse component analysis and optimal atomic decomposition .Constructive Approximation,1998,vol.17:353-382.
[11] Candès EJ ,DL Donoho. Curvelets [R]. USA:Deartment of Statistics, Stanford University,1999.
[12] E L Pennec ,S Mallat. Image compression with geometrical wavelets, [A]. In Proc. of ICIP’2000[C]. Vancouver ,Canada ,September, 2000. pp:661- 664.
[13] MNDo , M.Vetterli. Contourlets [A]. J Stoeckler , GV Welland. Beyond Wavelets. Academic Press,2002.
[14]薛丽霞,汪林林,李永树,王佐成.一种新的遥感影像边缘检测方法.计算机科学,34(7):235-237, 2007.
[15]傅博,王相海.一种基于细尺度间小波系数相关性的图像去噪方法.计算机科学,35(10):246-249,2008.
[16]傅一平,李志能,袁丁.利用小波系数的相关性提取噪声图像边缘.计算机辅助设计与图形学学报,16(2):174-179,2004.
[17] Yansun Xu, John B.Weaver, Dennis M.Healy, Jr., and Jian Lu,“Wavelet transform domain filters:a spatially selective noise filtration technique”. IEEE Transactions on Image Processing, 3(6):747-758, Nov,1994.
[18] Wei Liu, Z. Ma“Threshold Wavelet Based on Detection Image Denoising Edge”, IMACS Multiconference on "Computational Engineering in Systems Applications" (CESA), October 4-6, 2006, Beijing, China.
[20]文山,李葆青.基于小波分层的多方向图像边缘检测.自动化学报,33(5):480-487, 2007.
[21]傅一平,李志能,袁丁.利用小波系数的相关性提取噪声图像边缘.计算机辅助设计与图形学学报,16(2):174-179,2004.
[22] Buades, A. and Coll, B. and Morel, J. M. A non-local algorithm for image denoising. IEEE Computer Society Conference on Computer Vision and Pattern Recognition , Vol.2: 60–65,2005
[23] Alexey, L. A Multiresolution Approach for Improving Quality of Image Denoising Algorithms. IEEE international conference on Acoustics. Speech and Signal processing, 2006.
[24] Liu Yanli. A Robust and Fast Non-local Means Algorithm for Image Denoising. Comput. Sci. & Technol. 200x, Vol.21.
[25]王相海,宋传鸣.图像及视频可分级编码[M].北京:科学出版社,2009.1.
[26] C. Liu, H. Wang and Y. Wang.“Image Denoising Based on Wavelet Edge Detection by Scale Multiplication”IEEE International Conference on Integration Technology March 20-24,2007,Shenzhen,China
[27]傅博.基于多尺度变换的图像去噪方法研究.辽宁师范大学硕士论文,2009年
[2] Daubechies L, Gorssam A. and Meyer Y., Painless Nonorthogonal Expansion. Math,Phys., 1986, Vol 27: 1271-1283.
[3] Donoho D L, Johnstone I M. Ideal Spatial Adaptation by Wavelet Shrinkage. Stanford University, CA, 94305-4065,USA.
[4] B.Vidakovic. Statistical Modeling by Wavelets. Wiley Series in Probability and Statistics. John Wiley & Sons, Inc, 1999.
[5] Thierry Blu and Florian Luisier.The SURE-LET Approach to Image Denoising, IEEE Transactions on Image Processing, July 113, 2007.
[6]曲天书,戴逸松,王树勋.基于SURE无偏估计的自适应小波阈值去噪.电子学报, 2002, 2, 30(2):266-268.
[7] S.G.Chang,B .Yu and M .Vetterli, Image Denoising via Lossy Compression and Wavelet Thresholding,IEEE Int. Conf. Image Processing, Nov,1997,Vol.1:640-607.
[8] F.Abramovich, T.Sapatinas and B.W. Sliverman.“Wavelet Thresholding via a Bayesian Approach”, tech.rep. Math Department, University of Bristol, Bristol BS8 1TW,UK,Nov, Vol. 6,1996.
[9]王红霞.基于复数小波变换增强带噪图像的空间自适应方法.计算机辅助设计与图形学学报, 2005, 9(9):1911-1916.
[10] DL Donoho. Sparse component analysis and optimal atomic decomposition .Constructive Approximation,1998,vol.17:353-382.
[11] Candès EJ ,DL Donoho. Curvelets [R]. USA:Deartment of Statistics, Stanford University,1999.
[12] E L Pennec ,S Mallat. Image compression with geometrical wavelets, [A]. In Proc. of ICIP’2000[C]. Vancouver ,Canada ,September, 2000. pp:661- 664.
[13] MNDo , M.Vetterli. Contourlets [A]. J Stoeckler , GV Welland. Beyond Wavelets. Academic Press,2002.
[14]薛丽霞,汪林林,李永树,王佐成.一种新的遥感影像边缘检测方法.计算机科学,34(7):235-237, 2007.
[15]傅博,王相海.一种基于细尺度间小波系数相关性的图像去噪方法.计算机科学,35(10):246-249,2008.
[16]傅一平,李志能,袁丁.利用小波系数的相关性提取噪声图像边缘.计算机辅助设计与图形学学报,16(2):174-179,2004.
[17] Yansun Xu, John B.Weaver, Dennis M.Healy, Jr., and Jian Lu,“Wavelet transform domain filters:a spatially selective noise filtration technique”. IEEE Transactions on Image Processing, 3(6):747-758, Nov,1994.
[18] Wei Liu, Z. Ma“Threshold Wavelet Based on Detection Image Denoising Edge”, IMACS Multiconference on "Computational Engineering in Systems Applications" (CESA), October 4-6, 2006, Beijing, China.
[20]文山,李葆青.基于小波分层的多方向图像边缘检测.自动化学报,33(5):480-487, 2007.
[21]傅一平,李志能,袁丁.利用小波系数的相关性提取噪声图像边缘.计算机辅助设计与图形学学报,16(2):174-179,2004.
[22] Buades, A. and Coll, B. and Morel, J. M. A non-local algorithm for image denoising. IEEE Computer Society Conference on Computer Vision and Pattern Recognition , Vol.2: 60–65,2005
[23] Alexey, L. A Multiresolution Approach for Improving Quality of Image Denoising Algorithms. IEEE international conference on Acoustics. Speech and Signal processing, 2006.
[24] Liu Yanli. A Robust and Fast Non-local Means Algorithm for Image Denoising. Comput. Sci. & Technol. 200x, Vol.21.
[25]王相海,宋传鸣.图像及视频可分级编码[M].北京:科学出版社,2009.1.
[26] C. Liu, H. Wang and Y. Wang.“Image Denoising Based on Wavelet Edge Detection by Scale Multiplication”IEEE International Conference on Integration Technology March 20-24,2007,Shenzhen,China
[27]傅博.基于多尺度变换的图像去噪方法研究.辽宁师范大学硕士论文,2009年