cvpr cvpr2013 cvpr2013-427 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Wangmeng Zuo, Lei Zhang, Chunwei Song, David Zhang
Abstract: Image denoising is a classical yet fundamental problem in low level vision, as well as an ideal test bed to evaluate various statistical image modeling methods. One of the most challenging problems in image denoising is how to preserve the fine scale texture structures while removing noise. Various natural image priors, such as gradient based prior, nonlocal self-similarity prior, and sparsity prior, have been extensively exploited for noise removal. The denoising algorithms based on these priors, however, tend to smooth the detailed image textures, degrading the image visual quality. To address this problem, in this paper we propose a texture enhanced image denoising (TEID) method by enforcing the gradient distribution of the denoised image to be close to the estimated gradient distribution of the original image. A novel gradient histogram preservation (GHP) algorithm is developed to enhance the texture structures while removing noise. Our experimental results demonstrate that theproposed GHP based TEID can well preserve the texture features of the denoised images, making them look more natural.
Reference: text
sentIndex sentText sentNum sentScore
1 hk Abstract Image denoising is a classical yet fundamental problem in low level vision, as well as an ideal test bed to evaluate various statistical image modeling methods. [sent-5, score-0.403]
2 One of the most challenging problems in image denoising is how to preserve the fine scale texture structures while removing noise. [sent-6, score-0.588]
3 Various natural image priors, such as gradient based prior, nonlocal self-similarity prior, and sparsity prior, have been extensively exploited for noise removal. [sent-7, score-0.439]
4 The denoising algorithms based on these priors, however, tend to smooth the detailed image textures, degrading the image visual quality. [sent-8, score-0.393]
5 To address this problem, in this paper we propose a texture enhanced image denoising (TEID) method by enforcing the gradient distribution of the denoised image to be close to the estimated gradient distribution of the original image. [sent-9, score-1.113]
6 A novel gradient histogram preservation (GHP) algorithm is developed to enhance the texture structures while removing noise. [sent-10, score-0.596]
7 Our experimental results demonstrate that theproposed GHP based TEID can well preserve the texture features of the denoised images, making them look more natural. [sent-11, score-0.372]
8 Introduction The goal of image denoising is to estimate the latent clean image x from its noisy observation y. [sent-13, score-0.462]
9 Image denoising is a classical yet still active topic in image processing and low level vision, while it is an ideal test bed to evaluate various statistical image modeling methods. [sent-15, score-0.403]
10 In general, we hope that the denoised image should look like a natural image, and therefore the statistical modeling of natural image priors is crucial to the success of image denoising. [sent-16, score-0.413]
11 Based on the fact that natural image gradients exhibit heavy-tailed distributions, gradient-based priors are widely used in image denoising [10, 17, 18]. [sent-17, score-0.499]
12 By observing that natural images can be sparsely coded over a redundant dictionary, the sparsity prior has proved to be effective in image denoising via l0-norm or l1-norm minimization [8, 9]. [sent-19, score-0.563]
13 Another popular prior is the nonlocal self-similarity (NSS) prior [2, 16]; that is, in natural images there are often many similar patches (i. [sent-20, score-0.279]
14 The joint use of sparsity prior and NSS prior has led to state-of-the-art image denoising results [7, 21]. [sent-23, score-0.488]
15 However, the many denoising algorithms based on the above priors can still fail to preserve the image fine scale texture structures, which have certain overlap with noise in the frequency domain. [sent-24, score-0.656]
16 The over-smoothing of those detailed texture structures makes the denoised image look less natural, degrading much the visual quality (please refer to Fig. [sent-25, score-0.395]
17 On one hand, more fine texture features of the object and scene will be captured; on the other hand, the captured high resolution image is more prone to noise because the smaller size of each pixel makes the exposure less sufficient. [sent-28, score-0.19]
18 Considering the fact that texture regions in an image are homogeneous and are usually composed of similar patterns, statistical descriptors such as histogram are more effective to represent them. [sent-31, score-0.277]
19 Actually, in literature of texture representation and classification [13, 27, 28], global histogram of some local features is dominantly used as the final feature descriptor for matching. [sent-32, score-0.259]
20 All these motivate us to use the histogram of image gradient to design new image denoising models. [sent-34, score-0.686]
21 With the above consideration, in this paper we propose a novel method for texture enhanced image denoising (TEID) via gradient histogram preservation (GHP). [sent-35, score-0.934]
22 From the given noisy image y, we will estimate the gradient histogram of 11111222220000013311 Figure 1. [sent-36, score-0.383]
23 (a) A cropped image with hair textures; (b) denoised image by the SAPCA-BM3D method [16]; (c) denoised image by the proposed texture enhanced image denoising via gradient histogram preservation (GHP); (d) the gradient histograms of the denoised images. [sent-38, score-1.767]
24 We can see that the proposed GHP method leads to better texture preservation and visual perception, and the gradient histogram of the denoised image by GHP is also closer to the reference gradient histogram estimated from the noisy image. [sent-39, score-1.15]
25 , the gradient histogram of the denoised image should be close to hr. [sent-43, score-0.546]
26 1, the proposed TEID method can well enhance the image texture regions, which are often over-smoothed by other denoising methods. [sent-45, score-0.489]
27 The major contributions of this paper are as follows: (1) A novel image denoising framework, i. [sent-46, score-0.365]
28 , TEID, is proposed, which preserves the gradient distribution of the original image. [sent-48, score-0.187]
29 The existing image priors can be easily incorporated into the proposed frameworkto improve the quality of denoised image. [sent-49, score-0.297]
30 (2) A histogram specification operator is developed to ensure the gradient histogram of denoised image being close to the reference histogram, resulting in a simple yet effective GHP based TEID algorithm. [sent-50, score-0.917]
31 Related work Generally, image denoising methods can be grouped in two categories: model-based methods and learning-based methods. [sent-53, score-0.365]
32 Most denoising methods reconstruct the clean image by exploiting some image and noise prior models, and they belong to the first category. [sent-54, score-0.485]
33 Numerous image denoising algorithms have been proposed, and here we only review those model-based denoising methods related to our work from a viewpoint of natural image priors. [sent-56, score-0.768]
34 One representative class of image priors is the gradient priors based on the observation that natural images generally have a heavytailed distribution of gradients. [sent-60, score-0.369]
35 The use of gradient prior can be traced back to 1990s, when Rudin et al. [sent-61, score-0.195]
36 Another well-known prior model, the mixture of Gaussians (GMM), can also be used to approximate the distribution of gradient magnitude [10, 19]. [sent-63, score-0.224]
37 The image gradient prior is basically a kind of sparsity prior, i. [sent-65, score-0.244]
38 More gener- ally, the sparsity prior has been well applied to filter responses, wavelet/curvelet transform coefficients, or the coding coefficients over a redundant dictionary. [sent-68, score-0.194]
39 , K-SVD [9], task driven DL [20], and ASDS [8]) have been proposed and applied to image denoising and other restoration tasks. [sent-73, score-0.462]
40 The seminal work of nonlocal means denoising in [2] has motivated a wide range of studies on NSS, and has led to a flurry of NSS based state-of-the-art denoising methods, e. [sent-77, score-0.876]
41 Different image priors characterize different and complementary aspects of natural image statistics, and thus it is possible to combine multiple priors to improve the denoising performance. [sent-80, score-0.567]
42 [7] unified both image local sparsity and nonlocal similarity priors via clustering-based sparse representation. [sent-82, score-0.293]
43 However, many existing image denoising algorithms, including those sparsity and NSS priors based ones, tend to wipe out the image detailed textures while removing noise. [sent-85, score-0.584]
44 As we discussed in the Introduction section, considering the randomness and homogeneousness of image texture regions, we propose to use the histogram of gradient to describe the image texture and design new image denoising algorithm with gradient histogram preservation. [sent-86, score-1.222]
45 used hyper-Laplacian to model gradient, and proposed a content-aware prior for image deblurring by setting different shape parameters of gradient distribution in different image regions. [sent-88, score-0.266]
46 By matching the gradient distribution prior, Cho et al. [sent-89, score-0.187]
47 However, in [4, 5] the estimation of desired gradient distribution is rather heuristic, and the gradient histogram matching algorithm is very complex. [sent-91, score-0.508]
48 The denoising model Given a clean image x, the noisy observation y of x is usually modeled as y = x + v, (1) where v is the additive white Gaussian noise (AWGN) with zero mean and standard deviation σ. [sent-96, score-0.532]
49 The goal of image denoising is to estimate the desired image x from y. [sent-97, score-0.383]
50 One popular approach to image denoising is the variational method, in which the denoised image is obtained by xˆ = +μ where R(x) denotes some regulariz? [sent-98, score-0.59]
51 One common problem of image denoising methods is that the image fine scale details such as texture structures will be over-smoothed. [sent-103, score-0.531]
52 Intuitively, a good estimation of x without smoothing too much the textures should have a similar gradient distribution to that of x. [sent-105, score-0.257]
53 With this motivation, we propose a gradient histogram preservation (GHP) model for texture enhanced image denoising (TEID). [sent-106, score-0.934]
54 Our intuitive idea is to integrate the gradient histogram prior with the other image priors to further improve the denoising performance. [sent-107, score-0.795]
55 Suppose that we have an estimation ofthe gradient histogram ofx, denoted by hr (the estimation method will be discussed in Section 4). [sent-108, score-0.401]
56 In order to make the gradient histogram of denoised image ˆx nearly the same as argminx? [sent-109, score-0.546]
57 , , the reference histogram hr, we propose the following GHP based image denoising model: xˆ = argminx,F? [sent-113, score-0.572]
58 hF = hr (2) where F denotes an odd function which is monotonically non-descending in (0, +∞), hF denotes the histogram of the tnroann-sdfeosrmceendd gradient image h|F (∇x)|, and ∇ denotes the gradtriaennstf operator. [sent-121, score-0.401]
59 Given F, we can fix ∇x0 = F(∇x), and use the conventional denoising mcaenth foixds ∇ txo update x. [sent-123, score-0.421]
60 aGndive uns x, we can update d Fe simply by the histogram operator introduced in Section 3. [sent-124, score-0.249]
61 Thus, with the introduction of F, we can easily incorporate gradient histogram prior with any existing image priors R(x). [sent-126, score-0.43]
62 Specifically, we adopt the sparse nonlocal regularization term proposed in the centralized sparse representation (CSR) model [7], resulting in the following denoising model: xˆ = argminx,F? [sent-128, score-0.623]
63 hr where λ is the regularization parameter, D is the dictionary and α is the coding coefficients of x over D. [sent-141, score-0.257]
64 Each xi is coded over the dictionary D, and the coding coefficients is αi. [sent-148, score-0.173]
65 (4) is that we use xˆi = Dαi to reconstruct each patch xi, and then put all reconstructed patches together as the denoised image ˆx (the overlapped pixels between neighboring patches are averaged). [sent-156, score-0.305]
66 (3), βi is the nonlocal means of αi in the sparse coding domain. [sent-158, score-0.222]
67 Next, we will see that there is an efficient iterative histogram specification algorithm to solve the model in Eq. [sent-200, score-0.317]
68 (7) To get the solution to the above sub-problem, we first use a gradient descent method to update x: x(k+1/2) = x(k) + δ? [sent-228, score-0.214]
69 (11) To solve this sub-problem, we let d0 = |∇x|, and use the standard histogram specification operator |[∇1x2]| ,t aon odb utasine tthhee monotonic non-parametric mapping function F so that the histogram of |F (∇x)| is the same as hr. [sent-245, score-0.49]
70 Finally, we Fs (u∇mxm)|a isriz the our proposed iterative histogram specification based GHP algorithm in Algorithm 1. [sent-246, score-0.317]
71 It should be noted that, for any gradient based image denoising model, we can easily incorporate the proposed GHP in it by simply modifying the gradient term and adding an extra histogram specification operation. [sent-247, score-0.978]
72 Update the coding coeff+icμi∇ents(g o −f ∇eaxch patch: αi(k+1/2) = DTRix(k+1/2) Update the nonlocal mean of coding vector αi: βi ? [sent-264, score-0.246]
73 Update x x(k+1) = D ◦ α(k+1) Update F= =v iDa histogram specification by Eq. [sent-270, score-0.297]
74 Reference gradient histogram estimation To apply the model in Eq. [sent-276, score-0.321]
75 (3), we need to know the reference histogram hr, which is supposed to be the gradient histogram of original image x. [sent-277, score-0.528]
76 In this section, we propose a one dimensional deconvolution model to estimate the histogram hr. [sent-278, score-0.212]
77 (13) (14) If we use the normalized histogram hx and hy to approximate px and py, we can rewrite Eq. [sent-316, score-0.392]
78 Note that hg can wbeh eobreta ⊗in deden by discretizing pg, ann odp hy can N beo computed directly from the noisy observation y. [sent-318, score-0.166]
79 ome regularization term based on the prior information of natural image’s gradient histogram. [sent-328, score-0.264]
80 2 shows an example of reference gradient histogram estimation. [sent-357, score-0.365]
81 Experimental results We first give the parameter setting in our GHP based TEID algorithm, and then conduct experiments to validate its performance in comparison with state-of-the-art denoising algorithms. [sent-360, score-0.365]
82 Some state-of-the-art denoising methods are used for comparison, including shape-adaptive PCA based BM3D (SAPCA-BM3D) [16], the learned simultaneously sparse coding (LSSC) [21] and the CSR [7] methods. [sent-386, score-0.441]
83 Considering the fact when noise is too strong, all methods cannot recover the fine scale texture structures in the image, and in practice the noise is often moderate or be- low, we set the AWGN noise level σ ∈ {20, 25, 30, 35, 40} ilonw wth,e w experiments. [sent-388, score-0.31]
84 Nonetheless, the goal of our GHP method is to preserve and enhance the image texture structures, and let’s compare the visual quality of the denoised images by these methods. [sent-392, score-0.378]
85 Though they have good PSNR and even SSIM indices, the denoised images by them look somewhat unnatural. [sent-397, score-0.247]
86 (a) Real and simulated AWGN gradient histograms (noise level σ = 30); (b) real and simulated gradient histograms of noisy image; and (c) real and estimated gradient histograms of the clean image. [sent-401, score-0.553]
87 σ20S2A5PCA-3B0M3D[136]5402025LSS3C0[21]35402025CS3R0[7]35402025G3H0P3540 preserves much better these fine texture areas, making the denoised image look more natural and visually pleasant. [sent-404, score-0.427]
88 Discussions It is worth noting that, to further enhance the noise removal and texture preservation performance of our method, region-based GHP could be implemented. [sent-409, score-0.271]
89 Since natural images often consist of different regions with different textures, the gradient distributions in these regions will also vary. [sent-410, score-0.196]
90 5(c), GHP leads to very satisfying denoising results in all regions. [sent-420, score-0.365]
91 Conclusion In this paper, we presented a novel gradient histogram preserving (GHP) model for texture-enhanced image denoising (TEID). [sent-423, score-0.686]
92 The GHP model can preserve the gradient distribution by pushing the gradient histogram of the denoised image toward the reference histogram, and thus is promising in enhancing the texture structure while re1 1 12 2 20 0 068 6 moving random noise. [sent-424, score-0.902]
93 To implement the GHP model, we proposed an efficient iterative histogram specification algorithm. [sent-425, score-0.317]
94 Meanwhile, we presented a simple but theoretically solid algorithm to estimate the reference gradient histogram from the noisy image. [sent-426, score-0.427]
95 The proposed GHP has similar PSNR/SSIM measures to state-of-the-art denoising methods such as SAPCA-BM3D, LSSC and CSR; however, it leads to more natural and visually pleasant denoising results by preserving better the image texture areas. [sent-428, score-0.864]
96 A review of image denoising methods, with a new one. [sent-443, score-0.365]
97 Image denoising via sparse and redundant representations over learned dictionaries. [sent-509, score-0.415]
98 Image denoising using a scale mixture of gaussians in the wavelet domain. [sent-619, score-0.408]
99 (a) Noisy image with AWGN of standard deviation 30; (b) SAPCA-BM3D [16] restoration result; (c) LSSC [21] restoration result; (d) CSR [7] restoration result; (e) GHP restoration result; (f) ground truth. [sent-682, score-0.388]
100 (a) Top: noisy image with AWGN of standard deviation 30; bottom: a two-region segmentation of it; (b) SAPCA-BM3D [16] restoration results; (c) GHP restoration results without segmentation; (d) GHP restoration results with segmentation; (e) ground truth. [sent-685, score-0.335]
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