cvpr cvpr2013 cvpr2013-17 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Christian J. Schuler, Harold Christopher Burger, Stefan Harmeling, Bernhard Schölkopf
Abstract: Image deconvolution is the ill-posed problem of recovering a sharp image, given a blurry one generated by a convolution. In this work, we deal with space-invariant non- blind deconvolution. Currently, the most successful meth- ods involve a regularized inversion of the blur in Fourier domain as a first step. This step amplifies and colors the noise, and corrupts the image information. In a second (and arguably more difficult) step, one then needs to remove the colored noise, typically using a cleverly engineered algorithm. However, the methods based on this two-step ap- proach do not properly address the fact that the image information has been corrupted. In this work, we also rely on a two-step procedure, but learn the second step on a large dataset of natural images, using a neural network. We will show that this approach outperforms the current state-ofthe-art on a large dataset of artificially blurred images. We demonstrate the practical applicability of our method in a real-world example with photographic out-of-focus blur.
Reference: text
sentIndex sentText sentNum sentScore
1 A machine learning approach for non-blind image deconvolution Christian J. [sent-1, score-0.233]
2 Abstract Image deconvolution is the ill-posed problem of recovering a sharp image, given a blurry one generated by a convolution. [sent-10, score-0.388]
3 Currently, the most successful meth- ods involve a regularized inversion of the blur in Fourier domain as a first step. [sent-12, score-0.373]
4 A blurry image y is given by y = x ∗ v + n, where x is the tAru bel underlying (non-blurry) image, v i+s nth,e w point spread function (PSF) describing the blur and n is noise, usually assumed to be additive, white and Gaussian (AWG) noise. [sent-24, score-0.4]
5 The inversion of the blurring process is called image deconvolution and is ill-posed in the presence of noise. [sent-25, score-0.332]
6 While most methods are well-engineered algorithms, we ask the question: Is it possible to automatically learn an image deconvolution procedure? [sent-30, score-0.233]
7 Contributions: We present an image deconvolution procedure that is learned on a large dataset of natural images with a multi-layer perceptron (MLP). [sent-32, score-0.259]
8 We compare our approach to other methods on a large dataset of synthetically blurred images, and obtain state-of-the-art results for all tested blur kernels. [sent-33, score-0.259]
9 Related Work Image deconvolution methods can be broadly separated into two classes. [sent-38, score-0.233]
10 , and EPLL seek a maximum a posteriori (MAP) estimate of the clean image x, given a blurry (and noisy) version y and the PSF v. [sent-45, score-0.197]
11 The second category of methods apply a regularized inversion of the blur, followed by a denoising procedure. [sent-55, score-0.302]
12 In Fourier domain, the inversion of the blur can be seen as a pointwise division by the blur kernel. [sent-56, score-0.574]
13 Hence, these methods address deconvolution as a denoising problem. [sent-58, score-0.387]
14 Unfortunately, most denoising methods are designed to remove AWG noise [23, 12, 9]. [sent-59, score-0.319]
15 Deconvolution via denoising requires the denoising algorithm to be able to remove colored noise (non-flat power spectrum of the noise, not to be confused with color noise of RGB images). [sent-60, score-0.649]
16 [14]) have been shown to achieve good deconvolution results. [sent-63, score-0.233]
17 Some approaches to denoising rely on learning, where learning can involve learning a probabilistic model of natural images [24], or of smaller natural image patches [3 1]. [sent-65, score-0.232]
18 In that case, denoising can be achieved using a maximum a pos- teriori method. [sent-66, score-0.182]
19 In [16], it is shown that convolutional neural networks can achieve good image denoising results for AWG noise. [sent-68, score-0.31]
20 More recently, it was shown that a type ofneural network based on stacked denoising auto-encoders [29] can achieve good results in image denoising for AWG noise as well as for “blind” image inpainting (when the positions of the pixels to be inpainted are unknown) [30]. [sent-69, score-0.455]
21 Also recently, plain neural networks achieved state-ofthe-art results in image denoising for AWG noise, provided the neural nets have enough capacity and that sufficient training data is provided [3, 4]. [sent-70, score-0.439]
22 It was also shown that plain neural networks can achieve good results on other types of noise, such as noise resembling stripes, salt-and-pepper noise, JPEG-artifacts and mixed Poisson-Gaussian noise. [sent-71, score-0.315]
23 Differences and similarities to our work: We address the deconvolution problem as a denoising problem and therefore take an approach that is in line with [10, 11, 14], but different from [18]. [sent-72, score-0.387]
24 Method The most direct way to deconvolve images with neural networks is to train them directly on blurry/clean patch pairs. [sent-78, score-0.214]
25 Instead, our method relies on two steps: (i) a regularized inversion of the blur in Fourier domain and (ii) a denoising step using a neural network. [sent-80, score-0.607]
26 Direct deconvolution The goal of this step is to make the blurry image sharper. [sent-84, score-0.388]
27 In our model, the underlying true (sharp) image x is blurred with a PSF v and corrupted with AWG noise n with standard deviation σ: y = v ∗ x + n. [sent-86, score-0.236]
28 asurement of the blur kernel is corrupted by AWG, a further term β? [sent-96, score-0.301]
29 Illustration of the effect of the regularized blur inversion. [sent-116, score-0.274]
30 The result z of the regularized inversion is the sum of a corrupted image xcorrupted and colored noise ncolored. [sent-118, score-0.448]
31 Other methods [10, 11, 14] attempt to remove ncolored but ignore the noise in xcorrupted, whereas our method learns to denoise z and therefore addresses both problems. [sent-119, score-0.225]
32 Using the regularized inverse R, we can estimate the Fourier transform of the true image by the so-called direct deconvolution (following [15]) Z = R ? [sent-123, score-0.338]
33 ve Hrseen cise given by the sum of the colored noise image R ? [sent-133, score-0.176]
34 We therefore see that methods trying to remove the colored noise component R ? [sent-140, score-0.215]
35 t W Re propose as step (aici)t a procedure that removes the colored noise and additional ×× image artifacts. [sent-142, score-0.176]
36 Artifact removal by MLPs A multi-layer perceptron (MLP) is a neural network that processes multivariate input via several hidden layers and outputs multivariate output. [sent-147, score-0.269]
37 (392, 2047, 2047, 2047, 2047, 132) describes an MLP with four hidden layers (each having 2047 nodes) and patches of size 39 39 as input, and of size 13 13 as output. [sent-151, score-0.164]
38 Training procedure: Our goal is to learn an MLP that maps corrupted input patches to clean output patches. [sent-156, score-0.238]
39 2, the clean image x is blurred by the PSF v and additionally corrupted by noise n. [sent-160, score-0.278]
40 In this case φ is equivalent to the linear blur model in Equation (1). [sent-161, score-0.225]
41 We apply the direct deconvolution to φ(x) to obtain the image z = F−1(R ? [sent-164, score-0.289]
42 The free parameters of the MLP are learned on such pairs of corrupted and clean image patches from z and x, using stochastic gradient descent [19]. [sent-168, score-0.196]
43 The resulting image (showing characteristic artifacts) is then chopped into overlapping patches and each patch is processed separately by the trained MLP. [sent-174, score-0.165]
44 If the regularization in the direct deconvolution is weak, strong artifacts are created, leading to bad results. [sent-186, score-0.354]
45 Figure 4 shows that the results tend to improve with longer training times, but that the choice of the MLP’s architecture as well as of the regularization strength α during direct deconvolution is important. [sent-194, score-0.343]
46 In our experiments, we use α = 20 for the direct deconvolution and (392 , 4 2047, 132) for the architecture. [sent-198, score-0.289]
47 (d) Square blur (box blur) with size 19 19 and AWG noise Swqiutha σ b=l u0r. [sent-218, score-0.351]
48 (e) Motion blur from [21] and AWG noise with σ = 0. [sent-220, score-0.351]
49 Scenario (e) uses a motion blur recorded in [21], which is easier to deblur. [sent-227, score-0.225]
50 Since only the methods using an image prior would be able to treat the boundary conditions correctly, we use circular convolution in all methods but exclude the borders of the images in the evaluation (we cropped by half the size of the blur kernel). [sent-241, score-0.225]
51 In Figure 5 we see that in smooth areas, IDD-BM3D [11] and DEB-BM3D [10] produce artifacts resembling the PSF (square blur), whereas our method does 1 1 10 0 06 67 80 8 ]B (a) Gaussian blur σ=1 . [sent-245, score-0.335]
52 0 (d) Square blur 19x19 (e) Motion blur d[ AWG noise σ=0. [sent-248, score-0.576]
53 look “grainy” and the results achieved by EPLL [3 1] look more blurry than those achieved by our method. [sent-258, score-0.277]
54 Table 1 summarizes the results achieved on 11 standard test images for denoising [9], downsampled to 128 128 pixels. [sent-301, score-0.182]
55 The other methods rank differently depending on noise and blur strength. [sent-304, score-0.351]
56 In the supplementary material we demonstrate that the MLP is optimal only for the noise level it was trained on, but still achieves good results if used at the wrong noise level. [sent-306, score-0.307]
57 Poisson noise For scenario (c) we also consider Poisson noise with equivalent average variance. [sent-307, score-0.252]
58 Poisson noise is approximately equivalent to additive Gaussian noise, where the variance of the noise depends on the intensity of the underlying pixel. [sent-308, score-0.279]
59 Averaged over the 500 images in the Berkeley dataset, the results achieved with an MLP trained on this type of noise are slightly better (0. [sent-310, score-0.209]
60 The fact that our results become somewhat better is consistent with the finding that equivalent Poisson noise is slightly easier to remove [22]. [sent-313, score-0.165]
61 We note that even though the improvement is slight, this result shows that MLPs are able to automatically adapt to a new noise type, whereas methods that are not based on learning would ideally have to be engineered to cope with a new noise type (e. [sent-314, score-0.325]
62 Qualitative results on a real photograph To test the performance of our method in a real-world setting, we remove defocus blur from a photograph. [sent-319, score-0.322]
63 In order to make the defocus blur approximately constant over the image plane, the lens is stopped down to f/5. [sent-322, score-0.311]
64 The randomness in the size of the pillbox PSF expresses that we don’t know the exact blur and a pillbox is only an approximation. [sent-330, score-0.353]
65 The variance of readout noise is independent of the expected illumination, but photon shot noise scales linearly with the mean, and pixel non-uniformity causes a quadratic increase in variance [1]. [sent-334, score-0.252]
66 To generate the input to the MLP we pre-process each of the four channels generated by the Bayer pattern via direct deconvolution using a pillbox of the corresponding size at this resolution (radius 9. [sent-339, score-0.376]
67 Following [5], we call weights connecting the input to the first hidden layer feature detectors and weights connecting the last layer to the output feature generators, both of which can be represented as patches. [sent-353, score-0.281]
68 Finding an input pattern maximizing the activation of a specific hidden unit can be performed using activation maximization [13]. [sent-355, score-0.273]
69 The first MLP is trained on patches tha,t4 are pre-processed with direct deconvolution, whereas the second MLP is trained on the blurry image patches themselves (i. [sent-357, score-0.505]
70 Eight feature detectors of an MLP trained to remove a square blur. [sent-361, score-0.195]
71 The MLP was trained on patches pre-processed with direct deconvolution. [sent-362, score-0.189]
72 A potential explanation for this surprising observation is that these feature detectors focus on artifacts created by the regularized inversion of the blur. [sent-372, score-0.267]
73 We perform the same analysis on the MLP trained on blurry patches, see Figure 7. [sent-373, score-0.21]
74 The shape ofthe blur is evident 1 1 10 0 07 7 702 0 Figure 7. [sent-374, score-0.225]
75 Eight feature detectors of an MLP trained to remove a square blur. [sent-375, score-0.195]
76 The MLP was trained on the blurry patches themselves (i. [sent-376, score-0.288]
77 In some feature detectors, the shape of the blur is not evident (the three rightmost). [sent-381, score-0.253]
78 We also observe that all features are large compared to the size of the output patch (the output patches are three times smaller than the input patches). [sent-382, score-0.171]
79 This was not the case for the MLP trained with pre-processing (Figure 6) and is explained by the fact that in the blurry inputs, information is very spread out. [sent-383, score-0.23]
80 We clearly see that the direct deconvolution has the effect of making the information more local. [sent-384, score-0.289]
81 Analysis of the feature generators: We now analyze the feature generators learned by the MLPs. [sent-385, score-0.28]
82 We will compare the feature generators to the input patterns maximizing the activation of their corresponding unit. [sent-386, score-0.367]
83 feature generators (bottom row) in an MLP trained on pre-processed patches. [sent-390, score-0.307]
84 Figure 8 shows eight feature generators (bottom row) along with their corresponding input features (top row) maximizing the activation of the same hidden unit. [sent-394, score-0.451]
85 We repeat the analysis for the MLP trained on blurry patches (i. [sent-398, score-0.288]
86 Figure 9 shows eight feature generators (middle row) along with their corresponding input features (top row). [sent-401, score-0.304]
87 This time, the features found with activation maximization look different from their corresponding feature generators. [sent-402, score-0.164]
88 However, the feature detectors look remarkably similar to the feature generators convolved with the PSF (bottom row). [sent-403, score-0.39]
89 We interpret this observation as follows: If the MLP detects a blurry version of a certain feature in the input, it copies the (non-blurry) feature into the output. [sent-404, score-0.232]
90 feature generators (middle row) in an MLP trained on blurry patches (i. [sent-407, score-0.54]
91 The input patterns look like the feature generators convolved with the PSF (bottom row). [sent-410, score-0.339]
92 This was possible by looking at the weights connecting the input to the first hidden layer and the weights connecting the last hidden layer to the output, as well as through the use of activation maximization [13]. [sent-414, score-0.318]
93 We have seen that the MLP trained on blurry patches has to learn large feature detectors, because the information in the input is very spread-out. [sent-415, score-0.339]
94 For both MLPs, the feature generators look similar: Many resemble Gabor filters or blobs. [sent-417, score-0.306]
95 We were also able to answer the question: Which inputs cause the individual feature generators to activate? [sent-419, score-0.298]
96 Roughly speaking, in the case of the MLP trained on pre-processed patches, the inputs have to look like the feature generators themselves, whereas in the case of the MLP trained on blurry patches, the inputs have to look like the feature generators convolved with the PSF. [sent-420, score-0.94]
97 Finally, by directly learning the mapping from corrupted patches to clean patches, we handle both types of artifacts introduced by the direct deconvolution, instead of being limited to removing colored noise. [sent-427, score-0.347]
98 A limitation of our approach is that each MLP has to be trained on only one blur kernel: Results achieved with MLPs trained on several blur kernels are inferior to those achieved with MLPs trained on a single blur kernel. [sent-430, score-0.896]
99 However, in this case the deblurring quality is currently more limited by errors in the blur estimation than in the non-blind deconvolution step. [sent-432, score-0.485]
100 Stacked denoising autoencoders: Learning useful representations in a deep network with a local denoising criterion. [sent-669, score-0.352]
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