图像去噪 英文文献及翻译(10页).doc

-图像去噪 英文文献及翻译-第 页New Method for Image Denoising while Keeping Edge InformationEdge information is the most important high- frequency information of an image, so we should try to maintain more edge information while denoising. In order to preserve image details as well as canceling image noise, we present a new image denoising method: image denoising based on edge detection. Before denoising, image's edges are first detected, and then the noised image is divided into two parts: edge part and smooth part. We can therefore set high denoising threshold to smooth part of the image and low denoising threshold to edge part. The theoretical analyses and experimental results presented in this paper show that, compared to commonly-used wavelet threshold denoising methods, the proposed algorithm could not only keep edge information of an image, but also could improve signal-to-noise ratio of the denoised image.In the wavelet domain, the denoising algorithm based on the threshold filter is widely used, because its comparatively efficient and easy to realize. We can select a threshold according to the characteristic of the image, modifying all of the discrete detail coefficients so as to reduce the noise. However, we are in the dilemma of determining the level of the threshold. The higher the threshold is, the better effect of denoising will be, and, at the same time, the blurrier the edge will be.The edges of an image mostly reflect the information of the image, and contain its basic character. According to research on human eyes, the characteristic of the edges is one of several characteristics that can strongly impress the visual system . Thus, when we process denoising, the first thing that we should care about is trying to retain edge information.This paper presents a new method for image denoising while keeping edge information. We first apply wavelet transform to a noised image, and then process edge detection. The wavelet coefficients are divided into two parts: edge part and smooth part. We can therefore set high denoising threshold to the smooth part and low denoising threshold to edge part in order to retain more edge information. The theoretic analysis and experimental results presented in this paper shows that, compared with commonly-used wavelet threshold denoising methods, the proposed denoising method is more effective. The idea of combining edge detection with denoising is doable.The rest of this paper is organized as follows. We present the proposed denoising method in Section 2. Experimental results to demonstrate the performance of the proposed method are given in Section 3 , and conclusions and comments are given in Section 4.This paper discusses how to remove the additive white Gaussian noise (AWGN) with a zero mean. For other kinds of noise modeling, the idea of this paper is also applicable.The denoising method we present needs to detect the images edges before denoising, so as to protect the images edge information from damage in the following denoising process. In our method, finding out the precise location of the edges is pivotal. Many classical edge detectors are already available. Edges can be determined from the image by processing directly in the spatial domain or by transformation to a different domain. In the spatial domain, there are Sobel edge operators, Prewitt edge operators, Kirsch edge operators, and so on. In the transforming field, wavelet transformation is adapted to the wildly-changed edges better than with the normal Fourier transformation. Wavelet transformation, which is called the “mathematical microscope,” has a resolution in both the time field and the frequency field. It can focus onto any detail of the analyzed object by taking more and more fine steps of the space field. owing to these characteristics, wavelet transform is very suitable for use in edge detection. In this part we present an image edge detection method based on wavelet transformation.When images are corrupted by AWGN, due to noise, some pixels of the homogeneous regions may also have a local maximum of the gradient modulus, so we should distinguish the coefficients corresponding to noise from those corresponding to the potential edges. We know that the Lipschitz exponent values of AWGN are always negative, so the value of its corresponding local maximum of the gradient modulus will diminish at higher scales. This is different from the edges of the image, which always have positive Lipschitz exponent values. As a result, we can wipe off some coefficients corresponding to noise by using these different attributions. Furthermore, we can connect the remaining coefficients along the edge orientation, which is vertical to the gradient direction. Those that cannot be connected will be considered as coefficients corresponding to noise, and then will be wiped off.In practice, we should pay attention to the following：The length of the filter used in DWT should not be too long; otherwise, it will affect the effect of edge detection.The boundary should be treated properly. In our experiment, we use a mirror-symmetrical extension.The edge detecting procedure is composed of the following stages:1.apply pretreatment to the image, using the average filter and denoting the resulting image f (x, y)。2. apply the redundant wavelet transformation to each row 3. Find the local maximum coefficients of every row. Record these coefficients f (x, y).4. Remove the coefficients with low Lipschitz exponent values from the recorded coefficients, because they correspond to noise. Thus, we can get the coefficients corresponding to the potential edges of each rowat different scales.5. Applying stage 1,2,3, and 4 to every column, we can get the coefficients corresponding to the potential edges of each column at different scales.6. Note that the wavelet coefficients in fact correspond to the gradient of the smoothed version off at the scale. The edge magnitudes and orientation can be calculated from the image gradient as follows:7. Join the recorded coefficients of similar edge magnitudes along the edge orientation in a chain. Those isolated coefficients are wiped off. When the length of the chain reaches the threshold T, the pixels corresponding to the wavelet coefficients in the chain are considered to be edge pixels.We applied our edge detecting technique to a 256*256 Lena image corrupted by AWGN. A Lena image is an image with relatively complex edges. It is difficult for normal edge detection to completely detect the different types of edges. With a noise-corrupted Lena image, the edge detection task is even more difficult. The method we present uses the advantages of wavelet transformation, which can focus onto any detail of the analyzed object by taking more and more fine steps of the space field. At the low scale, many details of the edges, such as the girls pupils, are detected; at a high scale, smooth longer edges, such as the pole on the left, are seen. The experimental results shown prove that our edge detecting method is effective.After wavelet transformation, most energy of signal is supposed to be clustered in a few wavelet coefficients, whereas noises are not. The thresholding, or shrinkage on the wavelet coefficients with a proper threshold, can then significantly reduce noise. The key point of wavelet threshold denoising is selecting a proper threshold the higher the threshold is, the better effect of denoising will be, and, at the same time, the blurrier the edge will be.Our denoising method is focused on solving this problem. Before denoising, those wavelet coefficients of an image that correspond to an images edges are first detected by the method of wavelet edge detection. The detected wavelet coefficients will be protected from the ensuing denoising process, and, therefore, we can set the denoising thresholds based solely on the noise variances, without worrying about damaging the images edges. In our experiment, we choose the VisuShink threshold，The procedure is composed of the following six stages:1. Detect the wavelet coefficients corresponding to the images edges by the method of wavelet edge detection.2. Preserve the coefficients corresponding to the edges.3. Apply wavelet transform to the original noise-corrupted image.4. Do the normal wavelet image threshold noising process. In the equation, T presents VisuShink threshold Here，Replace the coefficients corresponding to the edges with the preserved coefficients. The detected edges also contain noise, so they must be denoised too. Here we again use wavelet denoising based on the threshold filter, but a much lower threshold, T, is applied in order to maintain more edge information.5. By applying the reverse wavelet transformation, we can get the denoised image.We applied three denoising methods to images that had been corrupted by white Gaussian noise with a zero mean and different variances (see Fig.2). The three methods are: the method we present, the classical image wavelet threshold denoising, and the classical image wavelet threshold denoising, Table II shows the experimental results. gives the resulting denoising images. From the table and the figures, we can see that, with the classical denoising method, it is difficult to decide the value of the threshold. When we use the VisuShink threshold, the denoised image is smoother, but, at the same time, more edge information is lost, so the edges are notably blurred. When we lower the threshold and multiply it by a factor more edge information is maintained, but the PSNR value is also lowered. Thus, with the classical denoising method, it is a dilemma to determine the level of the threshold. The higher the threshold is, the better effect of denoising will be, and, at the same time, the blurrier the edge will be.In the denoising method which we present, those wavelet coefficients of an image that correspond to an images edges are first detected by the method of wavelet edge detection before denoising. The detected wavelet coefficients will then be protected from denoising, and we can therefore set the denoising thresholds based only on the noise variances and without damaging the images edges. The theoretical analysis and experimental results presented in this paper show that, compared with the commonly-used wavelet threshold denoising methods, our method can keep an images edges from damage and increase the PSNR up to 12dB.Image denoising via wavelet transform is one success of wavelet applications. Because of its simple algorithm and small computation quantity, denoising by thresholding can obtain the widespread application. Both edge and noise information are high-frequency information, so the loss of edge information is evident and inevitable in the denoising process. If we combine edge detection with denoising, we can overcome the shortcoming of commonly-used denoising methods and do denoising without notably blurring the edge.Furthermore, there are many denoising and edge detection methods now in use. Different methods are suitable for different type of images and for different noise models. We can do further research on how to combine these different denoising and edge detection methods, according to the content of the images and the nature of the noise.同时保持边缘信息的图像去噪新方法由于是数字图像，那么对于一幅黑白图像来说，只要把各个像素赋值为0或1即可，我们用1 表示白色，用 0 表示黑色，于是我们把一幅黑白图像称为二值图像，彩色图像或其它图像转化为黑白图像的过程叫做二值化。对于一幅彩色图像，每个像素我们都需要用3个取值范围为之间的整数值来分别表示红、绿、蓝三原色分量，且这些分量都是用整型数据表示，称之为像素颜色的R, G, B值。表示一个取值范围为的整型数据，需要占用 8bit 空间，三个 R, G, B这样的整型数据就需要用24bit 来存储，所以，我们常把一幅真彩色位图称为 24 位位图。边缘信息的图像是最重要的高频信息，所以我们应该在去噪的时候尽量保持更多的边缘信息。为了保持图像细节以及消除图像噪声，我们提出了一种新的图像去噪方法：基于边缘检测的图像去噪。在去噪之前，首先先检测图像的边缘，降噪后的图像被划分成两个部分：边缘部分和平滑部分。因此，我们可以设置给平滑部分比较高的去噪阈值，边缘部分低的去噪阈值。本文提出的理论分析和实验结果，常用的小波阈值去噪方法相比，该算法不仅能保持图像边缘信息，而且还可以提高去噪图像信号噪声比。在小波域去噪算法的门槛上过滤器被广泛使用，因为它是比较高效，易于实现的。我们可以选择所述阈值的图像的特征，修改所有的离散细节系数，以减少噪声。不过，很难确定准确的阈值。因为在同一时间，阈值越高，去噪效果越好，边缘越模糊。图像的边缘主要反映了图像的信息,包含它的基本特征。根据对人类眼睛的研究，边缘的几个特点之一是可以强烈打动视觉系统。因此,我们在去噪过程首先应该关心的是试图保留边缘信息。因此，去噪处理时，我们应该关心的第一件事就是试图保留边缘信息。本文提出了一种新的方法，能同时保持边缘信息的图像去噪。我们首先运用小波变换处理被噪声污染的图像，然后进行边缘检测。小波系数被划分为两部分：边缘部分和平滑部分。因此，我们可以给平滑部分设置高去噪阈值，给边缘部分设置低去噪阈值，以保留更多的边缘信息。本文提出的理论分析和实验结果表明，与常用的小波阈值去噪方法相比，此去噪方法更有效，同时也证明了边缘检测与去噪相结合的想法是可行的。本文的其余部分安排如下：第2节中，我们提出去噪方法。在第3节用实验结果证明所提出的方法的性能，第4节中给出结论和意见。本文讨论如何去掉一个零均值的加性高斯白噪声（AWGN）。对于其他类型的噪声模型，本文的想法也同样适用。我们提出的去噪方法是去噪前需要检测图像的边缘，从而保护图像的边缘信息不会在去噪过程中损坏。在我们的方法中，找出边缘的精确位置是很重要的。许多经典的边缘探测器已经上市，可以从图像中确定，通过直接在空间域处理，或通过转化到一个不同的域。在空间域中，Sobel算子的边缘算子，Prewitt算子的边缘算子，Kirsch边缘运营商等等。在转化的字段中，小波变换比正常的傅里叶变换能更好地适应多变的边缘。小波变换，就是所谓的“数学显微镜”，在时域和频域都有分辨率。它可以聚焦到任何一个细节的分析对象，通过采取的步骤空间领域越来越细。由于这些特性，小波变换是非常适合在边缘检测中使用。在此，我们提出了基于小波变换的图像边缘检测方法。当图像被加性高斯白噪声损坏时，由于噪声均匀区域的一些像素可能也有梯度模数的局部最大值，所以我们应该区分潜在在边缘的噪声相对应的系数。我们知道加性高斯白噪声利普希茨(Lipschitz)指数值总是负的，所以其相应的本地最大的梯度模量的价值将更大幅度的减少。这不同于图像的边缘总是具有正Lipschitz指数值。因此，我们可以通过使用这些不同的属性擦去一些系数对应的噪声。此外，我们可以连接其余的垂直于梯度方向的沿边缘方向的系数。那些不能被连接的系数将被视为噪声，然后将被擦去。在实践中，我们应注意以下几点：1. 小波变换使用的滤波器的长度不能太长，否则会影响边缘检测的效果。2. 边界应妥善处理。在实验中，我们使用了镜面对称扩展。3. 找到每一行的最大系数，记录这些系数。4. 在记录中删除低李普希茨指数值的系数,因为它符合噪声。因此,我们可以得到在不同的情况下系数对应的每一行的潜在边缘。5. 应用阶段1、2、3和4,每一列,我们可以得到对应于潜在的边缘在不同情况下的每一列的系数。6注意,小波系数实际上适用于梯度平滑版本的f(x,y)在级数。 大小、边缘定位可以从图像梯度计算如下:7沿边缘链中的方向加入记录的类似的边缘幅度系数。这些离散的系数被擦去。链的长度达到阈值T时，对应于链中的小波系数的像素被认为是边缘像素。应用我们的边缘检测技术对256 * 256的被加性高斯白噪声损坏的Lena图像。莉娜的图像为边缘相对复杂的图像。正常的边缘检测很难完全检测到不同类型的边。有噪声损坏的Lena图像，边缘的检测任务更加困难。我们提出的方法，利用小波变换，它可以集中精力采取在空间领域内一步一步地越来越细地分析对象的任何细节上。在低尺度的边缘，许多细节，如女孩的瞳孔可以检测到;在一个较高的规模，可以看到光滑的长边缘，如杆的左侧。在图3所示的实验结果证明，我们的边缘检测方法是有效的。小波变换后的信号的大部分能量应该是集中在少数的小波系数，而不是噪声。阈值，或一个合适阈值的小波系数，就可以明显地降低噪音。小波阈值去噪的关键点是选择一个适当的阈值，阈值越高，去噪效果越佳，并且，在同一时间，将虚化边缘。我们的去噪方法是专注于解决这个问题。之前的去噪，那些适用于图片边缘的小波系数是小波边缘检测的首选方法。在随后的去噪过程检测的小波系数将被保护，因此，我们可以设置完全基于噪声方差的去噪阈值，而不用担心损坏图像的边缘。在我们的实验中，我们选择的VisuShink阈值，该程序是由以下六个阶段：小波边缘检测的方法，适用于图像的边缘检测的小波系数。更换与保存与系数的边缘相对应的系数。检测到的边缘也包含噪声，因此必须对其进行降噪处理过。在这里，我们再次使用基于小波消噪的门槛过滤器，但应用的门槛要低得多，T，以保持更多的边缘信息：通过施加反向小波变换，我们可以得到去噪图像。我们对已被具有零均值和不同的方差的高斯白噪声损坏的图像采用三个去噪方法。这三种方法是：我们提出的方法，经典图像小波阈值去噪，和经典的图像小波阈值去噪。显示了实验结果。给出了去噪图像。从表和图中，我们可以看到，传统的降噪方法是很难决定阈值的。当我们使用的VisuShink阈值，去噪图像是平滑的，但是，在同一时间，更多的边缘信息丢失，所以也有明显的模糊边缘。当我们降低门槛，它乘以一个系数p，更多的边缘信息保持，但也降低PSNR值。因此，传统的降噪方法，是很难决定阈值的高低。在同一时间，阈值越高，去噪效果越好，边缘越模糊。在我们提出的去噪方法中，这些图像的适用于图像边缘小波边缘检测的方法在噪前图像小波系数的被首选。然后，检测到的小波系数将被保护的去噪，因此，我们可以设置仅基于噪声方差，而不损坏图像的边缘的去噪阈值。本文的理论分析和实验结果，常用的小波阈值去噪方法相比，我们的方法可以保持图像的边缘损坏和提高PSNR可达12分贝的。基于小波变换的图像去噪是小波应用的一个成功。由于其算法简单，计算量小，去噪阈值可以得到广泛的应用。边缘和噪声信息是高频信息，所以边缘信息的损失是明显的去噪过程中的必然。如果我们结合边缘检测与去噪，我们可以克服的缺点常用的去噪方法，并做去噪无需特别是模糊的边缘。此外，还有许多去噪和边缘检测的方法，现在在使用。不同的方法适用于不同的图像类型，对于不同的噪声模型。关于如何根据图像的内容和噪声的性质组合这些不同的去噪及边缘检测方法，我们可以做进一步的研究。