外文翻譯中英文：同時保持邊緣信息的圖像去噪新方法

1、<p><b>　　外 文 文 獻</b></p><p>　　New method for image denoising while</p><p>　　keeping edge information</p><p>　　Edge information is the most important high- frequency

2、 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

3、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 par

4、t of the i</p><p>　　In the wavelet domain, the denoising algorithm based on the threshold filter is widely used, because it’s comparatively efficient and easy to realize. We can select a threshold according

5、to the characteristic of the image, modifying all of thediscrete 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 b

6、ettereffectof denoising will be, and, at the same time, the blurrier the edge will be. </p><p>　　The edges of an image mostly reflect the information of the image, and contain its basic character. Accordin

7、g to research on human eyes, thecharacteristic 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 tr

8、ying to retain edge information. </p><p>　　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 detec

9、tion. 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 hreshold to edge part in order to retain more edge

10、information. The theoretic analysis and experimental results presented in this paper shows that, compared with commo</p><p>　　The rest of this paper is organized as follows. We present theproposeddenoisingme

11、thod in Section .2. Experimental results to demonstrate the performance of theproposed method are given in Section 3 , and conclusions and comments are given in Section 4. </p><p>　　This paper discusses how

12、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. </p><p>　　The denoising method we present needs to detect th

13、e image’sedges before denoising, so as to protect the image’s 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

14、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, Prew

15、itt edge o</p><p>　　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 co

16、rresponding to noise from those corresponding to the potential edges. We know that the Lipschitz exponent values of AWGN are always egative, so the value of its corresponding local maximum of the gradient modulus will di

17、minish at higher scales. This is different from the edges of the image, which always have pos</p><p>　　In practice, we should pay attention to the following：</p><p>　　The length of the filter us

18、ed in DWT should not be too long; otherwise, it will affect the effect of edge detection. </p><p>　　The boundary should be treated properly. In our experiment, we use a mirror-symmetrical extension. </p&g

19、t;<p>　　The edge detecting procedure is composed of the following stages:</p><p>　　1. he image, using the average filter and denoting the resulting image f (x,y).</p><p>　　2. apply the re

20、dundant wavelet transformation to each row .</p><p>　　3. Find the local maximum coefficient so every row.Record these coefficients f (x, y). </p><p>　　4. Remove the coefficients with low Lips ch

21、itz exponent values from the recorded coefficients,because hey score spond to noise.Thus,we can get the coefficient score spond in to the potential edges of each rowat different scales. </p><p>　　5.Applyings

22、tage1,2,3, and 4 to every column, we can get the coefficien score sponding to the potential edges of each column at different scales. </p><p>　　6. Note that the wavelet coefficients in fact correspond to the

23、 gradient of the smoothed version off at the scale. The edge magnitudes and orientation can be calculated from the image gradient as follows: </p><p>　　7. Join the recorded coefficients of similar edge magni

24、tudes along the edge orientation in a chain. Those isolated coefficients are wiped off. When the length of the chain reaches the threshold T, the pixel score sponding to the wavelet coefficients in the chain are conside

25、red to be edge pixels. </p><p>　　We applied our edge detecting technique to a 256*256 Lena image corrupted by AWGN.</p><p>　　A Lena image is an image with relatively complex edges. It is difficu

26、lt 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 tran

27、sformation, 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 girl’s pupils, are detected; at </p>

28、;<p>　　After wavelet transformation, most energy of signal is supposed to be clustered in a few wavelet coefficients, whereas noises are not. The the resholding, or shrinkage on the wavelet coefficients with a p

29、roper 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 tim

30、e, the blurrier the edge will be. </p><p>　　Our denoising method is focused on solving this problem. Before denoising, those wavelet coefficients of an image that correspond to an image’s edges are first det

31、ected 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</p><p>　　thresholds based solel

32、y on the noise variances, without worrying about damaging the image’s edges. In our experiment, we choose the VisuShink threshold，The procedure is composed of the following six stages: </p><p>　　1.Detect the

33、 wavelet coefficients corresponding to the image’s edges by the method of wavelet edge detection. </p><p>　　2.Preserve the coefficients corresponding to the edges. </p><p>　　3.Apply wavelet tran

34、sform to the original noise-corrupted image. </p><p>　　4.Do the normal wavelet image threshold noising process. In the equation, T presents VisuShink threshold Here，Replace the coefficients corresponding to

35、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

36、 in order to maintain more edge information. </p><p>　　5.By applying the reverse wavelet transformation, we can get the denoised image. </p><p>　　We applied three denoising methods to images tha

37、t 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 wa

38、velet threshold denoising, Table II shows he 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

39、 value of th</p><p>　　In the denoising method which we present, those Wavelet coefficients of an image that correspond to an image’s edges are first detected by the method of wavelet edge detection before de

40、noising. 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 image’s edges. The theoretica

41、l analysis and experimental results presented in this paper show that, compared with the common</p><p>　　Image denoising via wavelet transform is one success of wavelet applications. Because of its simple al

42、gorithm and smallcomputation 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 inevi

43、table 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 b</p><p>　　Furthermore, there

44、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

45、 and edge detection methods, according to the content of the images and the nature of the noise. </p><p>　　同時保持邊緣信息的圖像去噪新方法</p><p>　　由于是數(shù)字圖像，那么對于一幅黑白圖像來說，只要把各個像素賦值為0或1即可，我們用1 表示白色，用0 表示黑色，于是我們把一

46、幅黑白圖像稱為二值圖像，彩色圖像或其它圖像轉(zhuǎn)化為黑白圖像的過程叫做二值化。對于一幅彩色圖像，每個像素我們都需要用3個取值范圍之間的整數(shù)值來分別表示紅、綠、藍三原色分量，且這些分量都是用整型數(shù)據(jù)表示，稱之為像素顏色的R, G, B值。表示一個取值范圍的整型數(shù)據(jù)，需要占用8bit 空間，三個R, G, B這樣的整型數(shù)據(jù)就需要用24bit 來存儲，所以，我們常把一幅真彩色位圖稱為24 位位圖。</p><p>　　邊緣

47、信息的圖像是最重要的高頻信息，所以我們應該在去噪的時候盡量保持更多的邊緣信息。為了保持圖像細節(jié)以及消除圖像噪聲，我們提出了一種新的圖像去噪方法：基于邊緣檢測的圖像去噪。在去噪之前，首先先檢測圖像的邊緣，降噪后的圖像被劃分成兩個部分：邊緣部分和平滑部分。因此，我們可以設置給平滑部分比較高的去噪閾值，邊緣部分低的去噪閾值。本文提出的理論分析和實驗結(jié)果，常用的小波閾值去噪方法相比，該算法不僅能保持圖像邊緣信息，而且還可以提高去噪圖像信號噪聲比

48、。</p><p>　　在小波域去噪算法的門檻上過濾器被廣泛使用，因為它是比較高效，易于實現(xiàn)的。我們可以選擇所述閾值的圖像的特征，修改所有的離散細節(jié)系數(shù)，以減少噪聲。不過，很難確定準確的閾值。因為在同一時間，閾值越高，去噪效果越好，邊緣越模糊。</p><p>　　圖像的邊緣主要反映了圖像的信息,包含它的基本特征。根據(jù)對人類眼睛的研究，邊緣的幾個特點之一是可以強烈打動視覺系統(tǒng)。因此,我們在

49、去噪過程首先應該關(guān)心的是試圖保留邊緣信息。因此，去噪處理時，我們應該關(guān)心的第一件事就是試圖保留邊緣信息。</p><p>　　本文提出了一種新的方法，能同時保持邊緣信息的圖像去噪。我們首先運用小波變換處理被噪聲污染的圖像，然后進行邊緣檢測。小波系數(shù)被劃分為兩部分：邊緣部分和平滑部分。因此，我們可以給平滑部分設置高去噪閾值，給邊緣部分設置低去噪閾值，以保留更多的邊緣信息。本文提出的理論分析和實驗結(jié)果表明，與常用的小

50、波閾值去噪方法相比，此去噪方法更有效，同時也證明了邊緣檢測與去噪相結(jié)合的想法是可行的。</p><p>　　本文的其余部分安排如下：第2節(jié)中，我們提出去噪方法。在第3節(jié)用實驗結(jié)果證明所提出的方法的性能，第4節(jié)中給出結(jié)論和意見。本文討論如何去掉一個零均值的加性高斯白噪聲（AWGN）。對于其他類型的噪聲模型，本文的想法也同樣適用。</p><p>　　我們提出的去噪方法是去噪前需要檢測圖像的邊

51、緣，從而保護圖像的邊緣信息不會在去噪過程中損壞。在我們的方法中，找出邊緣的精確位置是很重要的。許多經(jīng)典的邊緣探測器已經(jīng)上市，可以從圖像中確定，通過直接在空間處理，或通過轉(zhuǎn)化到一個不同的域。在空間域中，Sobel算子的邊緣算子，Prewitt算子的邊緣算子，Kirsch邊緣運營商等等。在轉(zhuǎn)化的字段中，小波變換比正常的傅里葉變換更好地適應多變的邊緣。小波變換，就是所謂的“數(shù)學顯微鏡”，在時域和頻域都有分辨率。它可以聚焦到任何一個細節(jié)的分析對

52、象，通過采取的步驟空間領(lǐng)域越來越細。由于這些特性，小波變換是非常適合在邊緣檢測中使用。在此，我們提出了基于小波變換的圖像邊緣檢測方法。</p><p>　　當圖像被加性高斯白噪聲損壞時，由于噪聲均勻區(qū)域的一些像素可能也有梯度模數(shù)的局部最大值，所以我們應該區(qū)分潛在在邊緣的噪聲相對應的系數(shù)。我們知道加性高斯白噪聲利普希茨(Lipschitz)指數(shù)值總是負的，所以其相應的本地最大的梯度模量的價值將更大幅度的減少。這不同

53、于圖像的邊緣總是具有正Lipschitz指數(shù)值。因此，我們可以通過使用這些不同的屬性擦去一些系數(shù)對應的噪聲。此外，我們可以連接其余的垂直于梯度方向的沿邊緣方向的系數(shù)。那些不能被連接的系數(shù)將被視為噪聲，然后將被擦去。</p><p>　　在實踐中，我們應注意以下幾點：</p><p>　　1.小波變換使用的濾波器的長度不能太長，否則會影響邊緣檢測的效果。</p><p&g

54、t;　　2.邊界應妥善處理。在實驗中，我們使用了鏡面對稱擴展。</p><p>　　3.找到每一行的最大系數(shù)，記錄這些系數(shù)。</p><p>　　4.在記錄中刪除低李普希茨指數(shù)值的系數(shù),因為它符合噪聲。因此我們可以得到在不同的情況下系數(shù)對應的每一行的潛在邊緣。</p><p>　　5.應用階段1、2、3和4,每一列,我們可以得到對應于潛在的邊緣在不同情況下的每一列的

55、系數(shù)。</p><p>　　6．注意,小波系數(shù)實際上適用于梯度平滑版本的f(x,y)在級數(shù)。大小、邊緣定位可以從圖像梯度計算如下: </p><p>　　沿邊緣鏈中的方向加入記錄的類似的邊緣幅度系數(shù)。這些離散的系數(shù)被擦去。鏈的長度達到閾值T時，對應于鏈中的小波系數(shù)的像素被認為是邊緣像素。</p><p>　　應用我們的邊緣檢測技術(shù)對256 * 256的被加性高斯白噪

56、聲損壞的Lena圖像。</p><p>　　莉娜的圖像為邊緣相對復雜的圖像。正常的邊緣檢測很難完全檢測到不同類型的邊。有噪聲損壞的Lena圖像，邊緣的檢測任務更加困難。我們提出的方法，利用小波變換，它可以集中精力采取在空間領(lǐng)域內(nèi)一步一步地越來越細地分析對象的任何細節(jié)上。在低尺度的邊緣，許多細節(jié)，如女孩的瞳孔可以檢測到;在一個較高的規(guī)模，可以看到光滑的長邊緣，如桿的左側(cè)。在圖3所示的實驗結(jié)果證明，我們的邊緣檢測方法

57、是有效的。</p><p>　　小波變換后的信號的大部分能量應該是集中在少數(shù)的小波系數(shù)，而不是噪聲。閾值，或一個合適閾值的小波系數(shù)，就可以明顯地降低噪音。小波閾值去噪的關(guān)鍵點是選擇一個適當?shù)拈撝担撝翟礁?，去噪效果越佳，并且，在同一時間，將虛化邊緣。</p><p>　　我們的去噪方法是專注于解決這個問題。之前的去噪，那些適用于圖片邊緣的小波系數(shù)是小波邊緣檢測的首選方法。在隨后的去噪過程檢

58、測的小波系數(shù)將被保護，因此，我們可以設置完全基于噪聲方差的去噪閾值，而不用擔損壞圖像的邊緣。在我們的實驗中，我們選擇的VisuShink閾值。</p><p>　　小波邊緣檢測的方法，適用于圖像的邊緣檢測的小波系數(shù)。</p><p>　　更換與保存與系數(shù)的邊緣相對應的系數(shù)。檢測到的邊緣也包含噪聲，因此必須對其進行降噪處理過。在這里，我們再次使用基于小波消噪的門檻濾器，但應用的門檻要低得多，

59、T，以保持更多的邊緣信息：通過施加反向小波變換，我們可以得到去噪圖像。</p><p>　　我們對已被具有零均值和不同的方差的高斯白噪聲損壞的圖像采用三個去噪方法。這三種方法是：我們提出的方法，經(jīng)典圖像小波閾值去噪，和經(jīng)典的圖像小波閾值去噪。顯示了實驗結(jié)果。給出了去噪圖像。從表和圖中，我們可以看到，傳統(tǒng)的降噪方法是很難決定閾值的。當我們使用的VisuShink閾值，去噪圖像是平滑的，但是，在同一時間，更多的邊緣信

60、息丟失，所以也有明顯的模邊緣。當我們降低門檻，它乘以一個系數(shù)p，更多的邊緣信息保持，但也降低PSNR值。因此，傳統(tǒng)的降噪方法是很難決定閾值的高低。在同一時間，閾值越高，去噪效果越好，邊緣越模糊。</p><p>　　在我們提出的去噪方法中，這些圖像的適用于圖像邊緣小波邊緣檢測的方法在噪前圖像小波系數(shù)的被首選。然后，檢測到的小波系數(shù)將被保護的去噪，因此，我們可以設置僅基于噪聲方差，而不損壞圖像的邊緣的去噪閾值。本文

61、的理論分析和實驗結(jié)果，常用的小波閾值去噪方法相比，我們的方法可以保持圖像的邊緣損壞和提高PSNR可達1?2分貝的。</p><p>　　基于小波變換的圖像去噪是小波應用的一個成功。由于其算法簡單，計算量小，去噪閾值可以得到廣泛的應用。邊緣和噪聲信息是高頻信息，所以邊緣信息的損失是明顯的去噪過程中的必然。如果我們結(jié)合邊緣檢測與去噪，我們可以克服的缺點常用的去噪方法，并做去噪無需特別是模糊的邊緣。</p>