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1、Restoration of Blurred Images Using Blind Deconvolution AlgorithmMs.S.Ramya Kalasalingam University, Anand Nagar, Krishnankoil Ms.T.Mercy Christial Kalasalingam University, Anand Nagar, KrishnankoilAbstract: Image restoration is the process of recovering the original image from the degraded image. A
2、spire of the project is to restore the blurred/degraded images using Blind Deconvolution algorithm. The fundamental task of Image deblurring is to de-convolute the degraded image with the PSF that exactly describe the distortion. Firstly, the original image is degraded using the Degradation Model. I
3、t can be done by Gaussian filter which is a low-pass filter used to blur an image. In the edges of the blurred image, the ringing effect can be detected using Canny Edge Detection method and then it can be removed before restoration process. Blind Deconvolution algorithm is applied to the blurred im
4、age. It is possible to renovate the original image without having specific knowledge of degradation filter, additive noise and PSF. To get the effective results1, the Penalized Maximum Likelihood (PML) Estimation Technique is used with our proposed Blind Deconvolution Algorithm.Key words： Blind Deco
5、nvolution Algorithm; Canny Edge Detection; Degradation Model; Image restoration; PML; PSF1 IntroductionImage deblurring is an inverse problem which whose aspire is to recover an image which has suffered from linear degradation. The blurring degradation can be spaceinvariant or space-in variant. Imag
6、e deblurring methods can be divided into two classes: nonblind, in which the blurring operator is known. And blind, in which the blurring operator is unknown2.Blurring is a form of bandwidth reduction of the image due to imperfect image formation process. It can be caused by relative motion between
7、camera and original image.Normally, an image can be degraded using low-pass filters and its noise. This low-pass filter is used to blur/smooth the image using certain functions.Image restoration is to improve the quality of the degraded image. It is used to recover an image from distortions to its o
8、riginal image. It is an objective process which removes the effects of sensing environment. It is the process of recovering the original scene image from a degraded or observed image using knowledge about its nature. There are two broad categories of image restoration concept such as Image Deconvolu
9、tion and Blind Image Deconvolution .Image Deconvolution is a linear image restoration problem where the parameters of the true image are estimated using the observed or degraded image and a known PSF (Point Spread Function). Blind Image Deconvolution is a more difficult image restoration where image
10、 recovery is performed with little or no prior knowledge of the degrading PSF. The advantages of Deconvolution are higher resolution and better quality.This paper is structured as follows: Section 2 describes the degradation model for blurring an image. Section 3 represents Canny Edge Detection. Sec
11、tion 4 describes the deblurring algorithm and overall architecture of this paper. Section 5 describes the sample results for deblurred images using our proposed algorithm. Section 6 describes the conclusion, comparison and future work.2 Degradation ModelIn degradation model, the image is blurred usi
12、ng filters and additive noise. Image can be degraded using Gaussian Filter and Gaussian Noise. Gaussian Filter represents the PSF which is a blurring function. The degraded image can be described by the following equation (1) （equation 1）In equation (1), g is degraded/blurred image, H is space invar
13、iant function (i.e.) blurring function3, f is an original image, and n is additive noise. The following Fig.1 represents the structure of degradation model. Fig.1 Degradation ModelImage deblurring can be done by the technique, Gaussian Blur. It is the convolution of the image with 2-D Gaussian funct
14、ion.A) Gaussian Filter:Gaussian filter is used to blur an image using Gaussian function. It requires two parameters such as mean and variance. It is weighted blurring. Gaussian function is of the following form (equation 2)where is variance and x and y are the distance from the origin in the horizon
15、tal axis and vertical axis Gaussian Filter has an efficient implementation of that allows it to create a very blurry blur image in a relatively short time.B) Gaussian Noise:The ability to simulate the behavior and effects of noise is central to image restoration. Gaussian noise is a white noise with
16、 constant mean and variance. The default values of mean and variance are 0 and 0.01 respectively.C) Blurring Parameter:The parameters needed for blurring an image are PSF, Blur length, Blur angle and type of noise. Point Spread Function is a blurring function. When the intensity of the observed poin
17、t image is spread over several pixels, this is known as PSF. Blur length is the number of pixels by which the image is degraded. It is number of pixel position is shifted from original position. Blur angle is an angle at which the image is degraded. Available types of noise are Gaussian noise, Salt
18、and pepper noise, Poisson noise, Speckle noise which are used for blurring. In this paper, we are using Gaussian noise which is also known as White noise. It requires mean and variance as parameters.D) Algorithm for Degradation ModelInput:Load an input image fInitialize blur length lInitialize blur
19、angle thetaAssign the type of noise nPSF (Point Spread Function), hProcedure Ih=create (f, l, theta) %Creation of PSFBlurred image (g) = f*h + ng= filter (f, h, n,”convolution”)If g contains “ringing” at its edge thenRemove ringing effect using edge taper functionElseGo to Procedure IIEnd Procedure
20、I3 Canny Edge Ddtection And Ringing EffectThe Discrete Fourier Transform used by the deblurring function creates high frequency drop-off at the edges of images. This high frequency drop-off can create an effect called boundary related ringing in deblurred images. For avoiding this ringing effect at
21、the edge of image, we have to detect the edge of an image. There are various edge detection methods available to detect an edge of the image4.The edge can be detected effectively using Canny Edge Detection method. It differs from other edge-detection methods such as Sobel, Prewitt, Roberts, Log in t
22、hat it uses two different thresholds foe detecting both strong and weak edges. Edge provides a number of derivative (of the intensity is larger than threshold) estimators. The edge can be detected for checking whether there exists ringing effect in an input image.A) Canny Edge DetectorCanny edge det
23、ection method finds edges by looking for local maxima of the gradient of f(x, y). The gradient is calculated using the derivative of a Gaussian Filter. The method uses two thresholds to detect strong and weak edges, and includes the weak edges in the output only if they are connected to strong edges
24、. Therefore, this method is more likely to detect true weak edges.Steps involved in canny method:The image is smoothed using Gaussian Filter with a specified standard deviation, , to reduce noiseThe local gradient, g(x, y) and edge direction are computed at each point.The edge point determined give
25、rise to ridges in the gradient magnitude image. This ridge pixels are then thresholds, T1& T2, with T1T2.Ridge pixels with values greater than T2 are said to bestrong edge pixels. Ridge pixels with values between T1 &T2 are said to be weak edge pixels.B) Edgetaper for Ringing Effect:The ringing effe
26、ct can be avoided using edge taper function. Edgetaper function is used to preprocess our image before passing it to the deblurring functions. It removes the high frequency drop-off at the edge of an image by blurring the entire image & then replacing the center pixels of the blurred image with the
27、original image.4 Overall Architecture And Deblurring AlgorithmThe following Fig. 2 represents the overall architecture of this paper.The original image is degraded or blurred using degradation model to produce the blurred image. The blurred image should be an input to the Deblurring algorithm. Vario
28、us algorithms are available for deblurring. In this paper, we are going to use Blind Deconvolution Algorithm. The result of this algorithm produces the deblurring image which can be compared with our original image5.Fig.2 Overall ArchitectureA) Blind Deconvolution Algorithm:Blind Deconvolution Algor
29、ithm can be used effectively when no information of distortion is known. It restores image and PSF simultaneously. This algorithm can be achieved based on Maximum Likelihood Estimation (MLE) 6.Algorithm for Deblurring:Input:Blurred image gInitialize number of iterations iInitial PSF hWeight of an im
30、age w % pixels considered for restorationa=0 (default) %Array corresponding to additive noiseProcedure IIIf PSF is not known thenGuess initial value of PSFElseSpecify the PSF of degraded imageRestored Image f= Deconvolution (g, h, i, w, a)End Procedure II5 Sample RrsultsThe below images represent th
31、e result of degradation model using Gaussian blur. First image represented the original image and its edge can be estimated by Canny Edge detection method.Fig.3 Original ImageThe edge detection can be applicable to Gray Image. Therfore the origianl RGB image can be converted to gray image. After tha
32、t Canny Edge Detection is applied for getting the Edges of the original image.Fig.4 Edges of original ImageThe original can be blurred using gaussian low pass filter by specifying the blur parameters. The following image is depicted as blurred image.Fig.5 Blurred ImageFig.6 Edge of Blurred ImageThe
33、sample image after applying the proposed algorithm will be as follows.Fig.7 Restored Image6 ConclusionWe have presented a method for blind image deblurring. The method differs from most other existing methods by only imposing weak restrictions on the blurring filter, being able to recover images whi
34、ch have suffered a wide range of degradations. Good estimates of both the image and the blurring operator are reached by initially considering the main image edges.The restoration quality of our method was visually and quantitatively better than those of the other algorithms such as Wiener Filter al
35、gorithm, Regularization algorithm and Lucy-Richardson with which it was compared.The advantage of our proposed Blind Deconvolution algorithm is used to deblur the degraded image without prior knowledge of PSF and additive noise. But in other algorithms, we should have the knowledge over the blurring
36、 parameters.The future work of this paper is to increase the speed of the deblurring process that is reducing the number of iterations used for deblurring the image for achieving better quality image.Rrferences1 Mariana S.C. Almeida and Luis B. Almeida., Blind and Semi-Blind Deblurring of Natural Im
37、ages, IEEE Transactions on Image Processing, Vol 19, pp.36-52, No. 1,January 2010.2 Michal Sorel and Jan Flusser, Senior Member, IEEE., Space-Variant Restoration of Images Degraded by Camera Motion Blur, IEEE Transactions on Image Processing, Vol 17, pp.105-116, No. 2,February 2008.3 Jian-Feng Cai,
38、hui ji, Chaoqiang liu, Zuowei Shen., “Blind Motion deblurring using multiple images”, journal of Computational physics.,pp. 5057-5071, 2009.4 Shao-jie, WU Qiong, li Guo-hui., “Blind Image deconvolution for single motion-blurred image”, Journal., 2009.5 D. Kundur and D. Hatzinakos, “Blind image decon
39、volution,” IEEE Sig.Process. Mag., pp. 4364, May 1996.6 Rafael C.Gonzalez, Richard E. Woods, Steven L. Eddins, Digital Image Processing Using MATLAB (Pearson Education, Inc., 2006)模糊图像的盲反卷积复原算法Ms.S.Ramya Kalasalingam University, Anand Nagar, Krishnankoil Ms.T.Mercy Christial Kalasalingam University,
40、 Anand Nagar, Krishnankoil摘要：图像复原是从退化图像恢复原始图像的过程。该项目的Aspire是恢复模糊/使用退化图像盲反卷积算法。图像清晰化的根本任务是根据可准确描述退化图像失真的点扩散函数进行逆运算。首先对原始图像退化模型的使用。它可以通过一种用于图像模糊的低通滤波器高斯滤波器来完成。在图像边缘模糊，铃声效果可以检测使用Canny边缘检测方法，然后可以在恢复过程中删除。盲解卷积算法应用于模糊的图像。这是可能的翻新，而不必降解过滤，加性噪声和PSF具体知识的原始图像1。为了获得有效的结果，惩罚最大似然法（PML）的估计方法是使用我们所提出的盲反卷积算法。关键词：盲反卷
41、积算法；Canny边缘检测；退化模型；图像恢复；惩罚最大似然法；点扩散函数1导言图像清晰化是一个逆问题，它的渴望，是要收回一个已经从线性退化遭受的形象。可降解的模糊spaceinvariant或空间中的变体。图像清晰化方法可分为两大类：nonblind，其中的模糊算子是众所周知的。和盲目，其中模糊算子是未知的2。模糊是一种图像的带宽由于不完善的形象形成过程中减少的形式。它可以通过摄像头和原image.Normally之间相对运动造成的，可降解的图像使用低通滤波器和噪声。该低通滤波器是用来模糊/平滑图像使用某些功能。图像复原是提高图像质量的退化。它是用来从扭曲的形象恢复到原来的形象。这是一个客观
42、的过程，消除了感知环境的影响。它是从一个恢复退化或观察图片的原始场景图像使用及其自然知识的过程。有两大类的图像恢复的概念，如图像卷积和图像盲反卷积。图像解卷积是一种线性图像复原问题那里的真实形象的参数估计使用观察或退化图像和一个已知PSF（点扩展函数）。图像盲解卷积是一个比较困难的图像复原图像恢复的地方，很少或根本没有进行降解点扩散函数的先验知识。反卷积的好处是更高的分辨率和更好的质量。本文的结构如下：第2节描述了模糊图像的退化模型。第3节代表Canny边缘检测。第4节介绍了本文的去模糊算法和整体架构。第5节介绍了deblurred图像使用我们所提出的算法的抽样调查结果。第6节描述的结论，比较
43、和今后的工作。2退化模型在退化模型，图像模糊使用过滤器和附加噪声。图像可以被降解利用高斯滤波器和高斯噪声。高斯滤波器代表点扩散函数这是一个模糊的功能。被降职的图像可以被描述为以下公式（1） （公式1）在方程（1），G是退化/模糊图像，H是空间不变函数（IE）的模糊函数，f为原始图像，n为加性噪声。下面的图1代表退化模型的结构。图1 退化模型图像清晰化，可以通过该技术，高斯模糊3。这是与二维高斯函数卷积图像。A） 高斯滤波器：高斯滤波器是用来使用高斯模糊图像的功能。它需要两个均值和方差等参数。这是加权模糊。高斯函数的形式如下 （公式2）其中为方差，x和y是从在原产地和高斯横轴纵轴距离滤波器有一个
44、有效的实施，它允许创建一个非常模糊，模糊在一个相对短的时间内图像。B） 高斯噪声：能够模拟的行为和隔音效果是至关重要的图像复原。高斯噪声是一个恒定的均值和方差的白噪声。均值和方差的默认值是0和0.01。C） 模糊参数：对于模糊图像所需要的参数是涤纶短纤，长度模糊，模糊的角度和噪声类型。点扩展函数是一个模糊的功能。当观测点图像强度在几个像素的蔓延，这就是所谓的点扩散函数。模糊长度的像素数，其中图像退化。这是像素位置的数目从原来的位置转移。模糊角是在哪个角度图像退化。可用类型的噪声是高斯噪声，椒盐噪声，泊松噪声，斑点噪声，是模糊使用。在本文中，我们使用高斯噪声也被称为白噪声。它需要的均值和方差作为
45、参数。D） 退化模型的算法输入：载入输入图像“f”初始化模糊长度1初始化模糊角theta指定的噪音n点扩散函数（点扩展功能），h程序-h=create (f, l, theta) %Creation of PSFBlurred image (g) = f*h + ng= filter (f, h, n,”convolution”)如果g包含“响铃”，然后在其边缘利用边缘删除振铃效应锥度功能其他转到步骤 -结束程序-3 Canny边缘检测和振铃效应离散傅立叶变换所使用的反降晰函数创建高频率落于图像的边缘了。这种高频率落客可以创建一个效果称为边界有关的deblurred图像振铃。为了避免在这个图像
46、边缘振铃效应，我们要检测图像的边缘。有各种边缘检测方法可用来检测图像的边缘4。边缘可以检测有效利用Canny边缘检测方法。它不同于其他的边缘检测比如Sobel,，Prewitt， Roberts， Log，因为它使用了两个不同的阈值探测敌人都强，弱边缘的方法。边缘提供了衍生数（大于阈值的强度更大）估计。边缘可以检测是否存在检查振铃在输入的图像效果。A)Canny边缘检测器Canny边缘检测方法中找到对F的梯度当地最大的（x，y）展望边缘。梯度的计算使用了高斯滤波器的衍生物。该方法使用两个阈值来检测强，弱边缘，只有当包括它们连接到强边输出的弱边缘。因此，这种方法更容易发现真正的弱边缘。涉及的步骤
47、以精明的方法：使用的是平滑指定的标准差高斯滤波器的形象，降低噪音当地的梯度为g（x，y）和边缘方向是在每个点计算的。边缘点确定引起的梯度幅值图像脊。然后，这脊像素的阈值，T1及T2，与T1T2的。与值大于T2是说bestrong边缘的像素岭像素。 T1及T2之间的像素值里奇说是弱边缘的像素。B）Edgetaper振铃效应：振铃效应可避免使用边缘锥度功能。 Edgetaper功能是用来进行预处理，然后将它传递给我们的形象清晰化功能。它消除了高频率下降，在一个图像的模糊整个图像然后代替了该中心关闭像素边缘模糊的图像与原始图像。4 整体构架和去模糊算法下面的图.2代表本文的整体架构。原始图像是利用退化或模糊的退化模型产生的模糊图像。模糊的图像应该是对去模糊算法的输入。不同的算法是清晰化提供。在本文中，我们将使用盲反卷积算法。这种算法的结果产生的图像清晰化，可以用我们的原始图像进行比较5。图2 整体构架一）盲反卷积算法：盲反卷积算法可以有效地加以利用时不会失真信息是众所周知的。它同时恢复图像和PSF。该算法可以实现基于最大似然估计（MLE）6。算法去模糊：输入：模糊图像 g初始化迭代 i初始化点扩散函数 h图像的w的重量像素考虑恢复a=0（默认）数组对应的加性噪