外文翻譯--同時(shí)保持邊緣信息的圖像去噪新方法

1、<p>　　1700單詞，9100英文字符，3000漢字</p><p>　　出處：Liu W. New Method for Image Denoising while Keeping Edge Information[C]// International Congress on Image and Signal Processing. IEEE, 2009:1-5.</p><p

2、>　　New method for image denoising while</p><p>　　keeping edge information</p><p><b>　　W Liu</b></p><p>　　Edge information is the most important high- frequency inform

3、ation 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 o

4、n 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 th

5、e 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 to the

6、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

7、effect of 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. According to

8、 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 tryin

9、g 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 detectio

10、n. 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 inf

11、ormation. 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 the proposed denoising me

12、thod 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. </p><p>　　This paper discusses how

13、 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 t

14、he image’s edges 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 edg

15、e 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, Pr

16、ewitt edge </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 c

17、orresponding 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 d

18、iminish 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 u

19、sed 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&

20、gt;<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 r

21、edundant 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

22、chitz 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.Appl

23、yingstage1,2,3, 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 t

24、o the 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

25、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 pixel score sponding to the wavelet coefficients in the chain are con

26、sidered 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 dif

27、ficult 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

28、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 girl’s pupils, are detected; at </

29、p><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

30、 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

31、 time, 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

32、 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 var

33、iances, without worrying about damaging the image’s edges. In our experiment, we choose the VisuShink threshold，The proce</p><p>　　1.Detect the wavelet coefficients corresponding to the image’s edges by the

34、method of wavelet edge detection. </p><p>　　2.Preserve the coefficients corresponding to the edges. </p><p>　　3.Apply wavelet transform to the original noise-corrupted image. </p><p&g

35、t;　　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 al

36、so 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. </p><p&g

37、t;　　5.By applying the reverse wavelet transformation, we can get the denoised image. </p><p>　　We applied three denoising methods to images that had been corrupted by white Gaussian noise with a zero mean an

38、d 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 he experimental result

39、s. 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 th</p><p>　　In the denoising method which

40、 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 denoising. The detected wavelet coefficients will then be protecte

41、d from denoising, and we can therefore set the denoising thresholds based only on the noise variances and without damaging the image’s edges. The theoretical analysis and experimental results presented in this paper show

42、 that, compared with the common</p><p>　　Image denoising via wavelet transform is one success of wavelet applications. Because of its simple algorithm and small computation quantity, denoising by thresholdin

43、g 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 wi

44、th denoising, we can overcome the shortcoming of commonly-used denoising methods and do denoising without notably </p><p>　　Furthermore, there are many denoising and edge detection methods now in use. Differ

45、ent 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 ima

46、ges and the nature of the noise. </p><p>　　同時(shí)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(gè)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(gè)像素我們都需要用3個(gè)取值范圍之間

47、的整數(shù)值來分別表示紅、綠、藍(lán)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(gè)取值范圍的整型數(shù)據(jù)，需要占用8bit 空間，三個(gè)R, G, B這樣的整型數(shù)據(jù)就需要用24bit 來存儲(chǔ)，所以，我們常把一幅真彩色位圖稱為24 位位圖。</p><p>　　邊緣信息的圖像是最重要的高頻信息，所以我們應(yīng)該在去噪的時(shí)候盡量保持更多的邊緣信息。為了保持圖像細(xì)節(jié)以及消除圖像噪聲，我們提出了一種新

48、的圖像去噪方法：基于邊緣檢測的圖像去噪。在去噪之前，首先檢測圖像的邊緣，降噪后的圖像被劃分成兩個(gè)部分：邊緣部分和平滑部分。因此，我們可以設(shè)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(shí)驗(yàn)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(hào)噪聲比。</p><p>　　在小波域去噪算法的門檻上過濾器被廣泛使用，因?yàn)樗潜容^高效，易于實(shí)現(xiàn)的。我們可以選

49、擇所述閾值的圖像的特征，修改所有的離散細(xì)節(jié)系數(shù)，以減少噪聲。不過，很難確定準(zhǔn)確的閾值。因?yàn)樵谕粫r(shí)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(gè)特點(diǎn)之一是可以強(qiáng)烈打動(dòng)視覺系統(tǒng)。因此,我們在去噪過程首先應(yīng)該關(guān)心的是試圖保留邊緣信息。因此，去噪處理時(shí)，我們應(yīng)該關(guān)心的第一件事就是試圖保留邊緣信息。</p>&

50、lt;p>　　本文提出了一種新的方法，能同時(shí)保持邊緣信息的圖像去噪。我們首先運(yùn)用小波變換處理被噪聲污染的圖像，然后進(jìn)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(shè)置高去噪閾值，給邊緣部分設(shè)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(shí)驗(yàn)結(jié)果表明，與常用的小波閾值去噪方法相比，此去噪方法更有效，同時(shí)也證明了邊緣檢測與去噪相結(jié)合的想法是可行的。</p><p>　

51、　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(shí)驗(yàn)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(gè)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緣，從而保護(hù)圖像的邊緣信息不會(huì)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

52、圖像中確定，通過直接在空間處理，或通過轉(zhuǎn)化到一個(gè)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(yùn)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(yīng)多變的邊緣。小波變換，就是所謂的“數(shù)學(xué)顯微鏡”，在時(shí)域和頻域都有分辨率。它可以聚焦到任何一個(gè)細(xì)節(jié)的分析對象，通過采取的步驟空間領(lǐng)域越來越細(xì)。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

53、法。</p><p>　　當(dāng)圖像被加性高斯白噪聲損壞時(shí)，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(yīng)該區(qū)分潛在在邊緣的噪聲相對應(yīng)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(fù)的，所以其相應(yīng)的本地最大的梯度模量的價(jià)值將更大幅度的減少。這不同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(yīng)的噪聲。此外，我們可以連接其余

54、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(shí)踐中，我們應(yīng)注意以下幾點(diǎn)：</p><p>　　1.小波變換使用的濾波器的長度不能太長，否則會(huì)影響邊緣檢測的效果。</p><p>　　2.邊界應(yīng)妥善處理。在實(shí)驗(yàn)中，我們使用了鏡面對稱擴(kuò)展。</p><p>　　3.找到每一行的最大系

55、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?yàn)樗显肼暋Ｒ虼宋覀兛梢缘玫皆诓煌那闆r下系數(shù)對應(yīng)的每一行的潛在邊緣。</p><p>　　5.應(yīng)用階段1、2、3和4,每一列,我們可以得到對應(yīng)于潛在的邊緣在不同情況下的每一列的系數(shù)。</p><p>　　6．注意,小波系數(shù)實(shí)際上適用于梯度平滑版本的f(x,y)在級(jí)數(shù)。大小、邊緣定位

56、可以從圖像梯度計(jì)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(dá)到閾值T時(shí)，對應(yīng)于鏈中的小波系數(shù)的像素被認(rèn)為是邊緣像素。</p><p>　　應(yīng)用我們的邊緣檢測技術(shù)對256 * 256的被加性高斯白噪聲損壞的Lena圖像。</p><p>　　莉娜的圖像為邊緣相對復(fù)雜的圖像。正常的邊緣檢測很難完全檢測到不

57、同類型的邊。有噪聲損壞的Lena圖像，邊緣的檢測任務(wù)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(xì)地分析對象的任何細(xì)節(jié)上。在低尺度的邊緣，許多細(xì)節(jié)，如女孩的瞳孔可以檢測到;在一個(gè)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(shí)驗(yàn)結(jié)果證明，我們的邊緣檢測方法是有效的。</p><p>　　小波變換后的信號(hào)的大部分能量應(yīng)該是集中在少數(shù)的小波系數(shù)，而不是噪聲。閾值，

58、或一個(gè)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(diǎn)是選擇一個(gè)適當(dāng)?shù)拈撝?，閾值越高，去噪效果越佳，并且，在同一時(shí)間，將虛化邊緣。</p><p>　　我們的去噪方法是專注于解決這個(gè)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測的小波系數(shù)將被保護(hù)，因此，我們可以設(shè)置完全基于噪聲方差的去噪閾值，而不用擔(dān)損壞圖像的邊緣。在我們的實(shí)驗(yàn)中，我們選擇的VisuSh

59、ink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(yīng)的系數(shù)。檢測到的邊緣也包含噪聲，因此必須對其進(jìn)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(yīng)用的門檻要低得多，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

60、值和不同的方差的高斯白噪聲損壞的圖像采用三個(gè)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(shí)驗(yàn)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(dāng)我們使用的VisuShink閾值，去噪圖像是平滑的，但是，在同一時(shí)間，更多的邊緣信息丟失，所以也有明顯的模邊緣。當(dāng)我們降低門檻，它乘以一個(gè)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

61、閾值的高低。在同一時(shí)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(hù)的去噪，因此，我們可以設(shè)置僅基于噪聲方差，而不損壞圖像的邊緣的去噪閾值。本文的理論分析和實(shí)驗(yàn)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(dá)1?2分貝的。</p>

62、<p>　　基于小波變換的圖像去噪是小波應(yīng)用的一個(gè)成功。由于其算法簡單，計(jì)算量小，去噪閾值可以得到廣泛的應(yīng)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(diǎn)常用的去噪方法，并做去噪無需特別是模糊的邊緣。</p><p>　　此外，還有許多去噪和邊緣檢測的方法在使用。不同的方法適用于不同的圖像類型，對于不同的噪聲模型。關(guān)于如何根據(jù)圖