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159 nips-2012-Image Denoising and Inpainting with Deep Neural Networks

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Author: Junyuan Xie, Linli Xu, Enhong Chen

Abstract: We present a novel approach to low-level vision problems that combines sparse coding and deep networks pre-trained with denoising auto-encoder (DA). We propose an alternative training scheme that successfully adapts DA, originally designed for unsupervised feature learning, to the tasks of image denoising and blind inpainting. Our method’s performance in the image denoising task is comparable to that of KSVD which is a widely used sparse coding technique. More importantly, in blind image inpainting task, the proposed method provides solutions to some complex problems that have not been tackled before. Speciﬁcally, we can automatically remove complex patterns like superimposed text from an image, rather than simple patterns like pixels missing at random. Moreover, the proposed method does not need the information regarding the region that requires inpainting to be given a priori. Experimental results demonstrate the effectiveness of the proposed method in the tasks of image denoising and blind inpainting. We also show that our new training scheme for DA is more effective and can improve the performance of unsupervised feature learning. 1

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 cn Abstract We present a novel approach to low-level vision problems that combines sparse coding and deep networks pre-trained with denoising auto-encoder (DA). [sent-8, score-0.797]

2 We propose an alternative training scheme that successfully adapts DA, originally designed for unsupervised feature learning, to the tasks of image denoising and blind inpainting. [sent-9, score-1.058]

3 Our method’s performance in the image denoising task is comparable to that of KSVD which is a widely used sparse coding technique. [sent-10, score-0.877]

4 More importantly, in blind image inpainting task, the proposed method provides solutions to some complex problems that have not been tackled before. [sent-11, score-0.913]

5 Speciﬁcally, we can automatically remove complex patterns like superimposed text from an image, rather than simple patterns like pixels missing at random. [sent-12, score-0.246]

6 Moreover, the proposed method does not need the information regarding the region that requires inpainting to be given a priori. [sent-13, score-0.541]

7 Experimental results demonstrate the effectiveness of the proposed method in the tasks of image denoising and blind inpainting. [sent-14, score-0.95]

8 1 Introduction Observed image signals are often corrupted by acquisition channel or artiﬁcial editing. [sent-16, score-0.323]

9 The goal of image restoration techniques is to restore the original image from a noisy observation of it. [sent-17, score-0.498]

10 Image denoising and inpainting are common image restoration problems that are both useful by themselves and important preprocessing steps of many other applications. [sent-18, score-1.337]

11 This paper focuses on image denoising and blind inpainting. [sent-20, score-0.917]

12 One approach is to transfer image signals to an alternative domain where they can be more easily separated from the noise [1, 2, 3]. [sent-22, score-0.324]

13 Another approach is to capture image statistics directly in the image domain. [sent-24, score-0.384]

14 Following this strategy, A family of models exploiting the (linear) sparse coding technique have drawn increasing attention recently [4, 5, 6, 7, 8, 9]. [sent-25, score-0.122]

15 Sparse coding methods reconstruct images from a sparse linear combination of an over-complete dictionary. [sent-26, score-0.214]

16 This learning step improves the performance of sparse coding signiﬁcantly. [sent-28, score-0.122]

17 1 Image inpainting methods can be divided into two categories: non-blind inpainting and blind inpainting. [sent-31, score-1.262]

18 In non-blind inpainting, the regions that need to be ﬁlled in are provided to the algorithm a priori, whereas in blind inpainting, no information about the locations of the corrupted pixels is given and the algorithm must automatically identify the pixels that require inpainting. [sent-32, score-0.35]

19 The stateof-the-art non-blind inpainting algorithms can perform very well on removing text, doodle, or even very large objects [10, 11, 12]. [sent-33, score-0.541]

20 Some image denoising methods, after modiﬁcation, can also be applied to non-blind image inpainting with state-of-the-art results [7]. [sent-34, score-1.47]

21 Recent research suggests, however, that non-linear, deep models can achieve superior performance in various real world problems. [sent-41, score-0.128]

22 In this paper, we propose to combine the advantageous “sparse” and “deep” principles of sparse coding and deep networks to solve the image denoising and blind inpainting problems. [sent-45, score-1.71]

23 The sparse variants of deep neural network are expected to perform especially well in vision problems because they have a similar structure to human visual cortex [17]. [sent-46, score-0.224]

24 Deep neural networks with many hidden layers were generally considered hard to train before a new training scheme was proposed which is to adopt greedy layer-wise pre-training to give better initialization of network parameters before traditional back-propagation training [18, 19]. [sent-47, score-0.277]

25 We employ DA to perform pre-training in our method because it naturally lends itself to denoising and inpainting tasks. [sent-49, score-1.086]

26 DA is a two-layer neural network that tries to reconstruct the original input from a noisy version of it. [sent-50, score-0.159]

27 A series of DAs can be stacked to form a deep network called Stacked Denoising Auto-encoders (SDA) by using the hidden layer activation of the previous layer as input of the next layer. [sent-53, score-0.524]

28 In these settings, only the clean data is provided while the noisy version of it is generated during training by adding random Gaussian or Salt-and-Pepper noise to the clean data. [sent-55, score-0.511]

29 After training of one layer, only the clean data is passed on to the network to produce the clean training data for the next layer while the noisy data is discarded. [sent-56, score-0.569]

30 The noisy training data for the next layer is similarly constructed by randomly corrupting the generated clean training data. [sent-57, score-0.471]

31 For the image denoising and inpainting tasks, however, the choices of clean and noisy input are natural: they are set to be the desired image after denoising or inpainting and the observed noisy image respectively. [sent-58, score-3.049]

32 Therefore, we propose a new training scheme that trains the DA to reconstruct the clean image from the corresponding noisy observation. [sent-59, score-0.509]

33 After training of the ﬁrst layer, the hidden layer activations of both the noisy input and the clean input are calculated to serve as the training data of the second layer. [sent-60, score-0.493]

34 Our experiments on the image denoising and inpainting tasks demonstrate that SDA is able to learn features that adapt to speciﬁc noises from white Gaussian noise to superimposed text. [sent-61, score-1.506]

35 Inspired by SDA’s ability to learn noise speciﬁc features in denoising tasks, we argue that in unsupervised feature learning problems the type of noise used can also affect the performance. [sent-62, score-0.805]

36 Speciﬁcally, instead of corrupting the input with arbitrarily chosen noise, more sophisticated corruption process that agrees to the true noise distribution in the data can improve the quality of the learned features. [sent-63, score-0.293]

37 For example, when learning audio features, the variations of noise on different frequencies are usually different and sometimes correlated. [sent-64, score-0.14]

38 Hence instead of corrupting the training data with simple i. [sent-65, score-0.124]

39 2 (a) Denoising auto-encoder (DA) architecture (b) Stacked sparse denoising auto-encoder architecture Figure 1: Model architectures. [sent-71, score-0.598]

40 1 Problem Formulation Assuming x is the observed noisy image and y is the original noise free image, we can formulate the image corruption process as: x = η(y). [sent-73, score-0.6]

41 Then, the denoising task’s learning objective becomes: f = argmin Ey f (x) − y 2 (2) 2 f From this formulation, we can see that the task here is to ﬁnd a function f that best approximates η −1 . [sent-75, score-0.545]

42 We can now treat the image denoising and inpainting problems in a uniﬁed framework by choosing appropriate η in different situations. [sent-76, score-1.278]

43 , N and xi be the corrupted version of corresponding yi . [sent-81, score-0.158]

44 1a: h(xi ) = σ(Wxi + b) (3) y(xi ) = σ(W h(xi ) + b ) ˆ (4) where σ(x) = (1 + exp(−x))−1 is the sigmoid activation function which is applied element-wise to vectors, hi is the hidden layer activation, y(xi ) is an approximation of yi and Θ = {W, b, W , b } ˆ represents the weights and biases. [sent-83, score-0.226]

45 ˆ θ = argmin θ (5) i=1 After ﬁnish training a DA, we can move on to training the next layer by using the hidden layer activation of the ﬁrst layer as the input of the next layer. [sent-85, score-0.484]

46 Due to the fact that directly processing the entire image is intractable, we instead draw overlapping patches from the image as our data objects. [sent-89, score-0.413]

47 In the training phase, the model is supplied with both the corrupted noisy image patches xi , for i = 1, 2, . [sent-90, score-0.488]

48 After training, SSDA will be able to reconstruct the corresponding clean image given any noisy observation. [sent-94, score-0.433]

49 We regularize the hidden layer representation to be sparse by choosing small ρ so that the KLdivergence term will encourage the mean activation of hidden units to be small. [sent-122, score-0.289]

50 After training of the ﬁrst DA, we use h(yi ) and h(xi ) as the clean and noisy input respectively for the second DA. [sent-124, score-0.282]

51 We then initialize a deep network with the weights obtained from K stacked DAs. [sent-127, score-0.232]

52 The network has one input layer, one output and 2K − 1 hidden layers as shown in Fig. [sent-128, score-0.134]

53 3 Experiments We narrow our focus down to denoising and inpainting of grey-scale images, but there is no difﬁculty in generalizing to colored images. [sent-133, score-1.11]

54 We use a set of natural images collected from the web1 as our training set and standard testing images2 as the testing set. [sent-134, score-0.166]

55 We create noisy images from clean training and testing images by applying the function (1) to them. [sent-135, score-0.406]

56 Image patches are then extracted from both clean and noisy images to train SSDAs. [sent-136, score-0.312]

57 We employ Peak Signal to Noise Ratio (PSNR) 2 2 to quantify denoising results: 10 log10 (2552 /σe ), where σe is the mean squared error. [sent-137, score-0.545]

58 PSNR is one of the standard indicators used for evaluating image denoising results. [sent-138, score-0.737]

59 1 Denoising White Gaussian Noise We ﬁrst corrupt images with additive white Gaussian noise of various standard deviations. [sent-140, score-0.281]

60 For the proposed method, one SSDA model is trained for each noise level. [sent-141, score-0.144]

61 In the meantime, we try different patch sizes and ﬁnd that higher noise level generally requires larger patch size. [sent-144, score-0.144]

62 2 4 Figure 2: Visual comparison of denoising results. [sent-149, score-0.56]

63 Results of images corrupted by white Gaussian noise with standard deviation σ = 50 are shown. [sent-150, score-0.309]

64 This indicates that although the reconstruction errors averaged over all pixels are the same, SSDA is better at denoising complex regions. [sent-162, score-0.601]

65 2 Image Inpainting Figure 3: Visual comparison of inpainting results. [sent-164, score-0.556]

66 For the image inpainting task, we test our model on the text removal problem. [sent-165, score-0.804]

67 Both the training and testing set compose of images with super-imposed text of various fonts and sizes from 18-pix to 36-pix. [sent-166, score-0.232]

68 Due to the lack of comparable blind inpainting algorithms, We compare our method to the non-blind KSVD inpainting algorithm [7], which signiﬁcantly simpliﬁes the problem by requiring the knowledge of which pixels are corrupted and require inpainting. [sent-167, score-1.412]

69 We ﬁnd that SSDA is able to eliminate text of small fonts completely while text of larger fonts is dimmed. [sent-170, score-0.152]

70 Non-blind inpainting is a well developed technology that works decently on the removal of small objects. [sent-172, score-0.595]

71 SSDA’s capability of blind inpainting of complex patterns is one of this paper’s major contributions. [sent-178, score-0.765]

72 3 Hidden Layer Feature Analysis Traditionally when training denoising auto-encoders, the noisy training data is usually generated with arbitrarily selected simple noise distribution regardless of the characteristics of the speciﬁc training data [21]. [sent-191, score-0.908]

73 In real world problems, the clean training data is in fact usually subject to noise. [sent-193, score-0.189]

74 Hence, if we estimate the distribution of noise and exaggerate it to generate noisy training data, the resulting DA will learn to be more robust to noise in the input data and produce better features. [sent-194, score-0.374]

75 Inspired by SSDA’s ability to learn different features when trained on denoising different noise patterns, we argue that training denoising auto-encoders with noise patterns that ﬁt to speciﬁc situations can also improve the performance of unsupervised feature learning. [sent-195, score-1.477]

76 We train DAs with different types of noise and then apply them to handwritten digits corrupted by the type of noise they are trained on as well as other types of noise. [sent-197, score-0.368]

77 We ﬁnd that the highest classiﬁcation accuracy on each type of noise is achieved by the DA trained to remove that type of noise. [sent-201, score-0.169]

78 This is not surprising since more information is utilized, however it indicates that instead of arbitrarily corrupting input with noise that follows simple distribution and feeding it to DA, more sophisticated methods that corrupt input in more realistic ways can achieve better performance. [sent-202, score-0.323]

79 Learned Structure Unlike models relying on structural priors, our method’s denoising ability comes from learning. [sent-205, score-0.545]

80 Therefore SSDA’s ability to denoise and inpaint images is mostly the result of training. [sent-208, score-0.17]

81 With some modiﬁcations, it is possible to denoise audio signals or complete missing data (as a data preprocessing step) with SSDA. [sent-210, score-0.157]

82 2 Advantages and Limitations Traditionally, for complicated inpainting tasks, an inpainting mask that tells the algorithm which pixels correspond to noise and require inpainting is supplied a priori. [sent-212, score-1.8]

83 This makes our method a suitable choice for fully automatic and noise pattern speciﬁc image processing. [sent-215, score-0.306]

84 Generally speaking, however, SSDA can remove only the noise patterns it has seen in the training data. [sent-218, score-0.236]

85 7 SSDA would only be suitable in circumstances where the scope of denoising tasks is narrow, such as reconstructing images corrupted by a certain procedure. [sent-222, score-0.749]

86 5 Conclusion In this paper, we present a novel approach to image denoising and blind inpainting that combines sparse coding and deep neural networks pre-trained with denoising auto-encoders. [sent-223, score-2.255]

87 We propose a new training scheme for DA that makes it possible to denoise and inpaint images within a uniﬁed framework. [sent-224, score-0.246]

88 In the experiments, our method achieves performance comparable to traditional linear sparse coding algorithm on the simple task of denoising additive white Gaussian noise. [sent-225, score-0.743]

89 Moreover, our non-linear approach successfully tackles the much harder problem of blind inpainting of complex patterns which, to the best of our knowledge, has not been addressed before. [sent-226, score-0.789]

90 We also show that the proposed training scheme is able to improve DA’s performance in the tasks of unsupervised feature learning. [sent-227, score-0.141]

91 In our future work, we would like to explore the possibility of adapting the proposed approach to various other applications such as denoising and inpainting of audio and video, image super-resolution and missing data completion. [sent-228, score-1.343]

92 An adaptive threshold method for image denoising based on wavelet domain. [sent-240, score-0.789]

93 Image denoising using scale mixtures of Gaussians in the wavelet domain. [sent-249, score-0.597]

94 A new SURE approach to image denoising: Interscale orthonormal wavelet thresholding. [sent-255, score-0.244]

95 Image denoising via sparse and redundant representations over learned dictionaries. [sent-280, score-0.618]

96 Region ﬁlling and object removal by exemplar-based e image inpainting. [sent-308, score-0.229]

97 An image inpainting technique based on the fast marching method. [sent-319, score-0.733]

98 Robust locally linear analysis with applications to image denoising and blind inpainting. [sent-334, score-0.917]

99 Restoration of images corrupted by impulse noise using blind inpainting and l0 norm. [sent-338, score-1.028]

100 Stacked denoising autoencoders: Learning useful representations in a deep network with a local denoising criterion. [sent-379, score-1.234]

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