#### DMCA

## Nonlocal Spectral Prior Model for Low-level Vision

Citations: | 1 - 1 self |

### Citations

1314 | An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision,”
- Boykov, Kolmogorov
- 2004
(Show Context)
Citation Context ...es. As in [3], we set wi,j = exp(− 1 ρ 2 ‖xi − xj‖ 2 2) where ρ is a constant to control the decay rate w.r.t. the distance between xi and xj. Eq. (4) is a standard MRF-MAP framework and many methods =-=[26]-=- can be used to effectively solve it. ] (4) 3 The same for λi8 Shenlong Wang, Lei Zhang, Yan Liang 3.3 Image Restoration with Nonlocal Spectral Prior The image degradation process can be generally mo... |

1056 | A fast iterative shrinkage-thresholding algorithm for linear inverse problems
- Beck, Teboulle
- 2009
(Show Context)
Citation Context ...age is obtained by downsampling the blurred high-resolution (HR) image. We compare our proposed NSP based method with some well-known super-resolution methods, including Softcut [28], TV-based method =-=[29]-=-, Sparsity based method [15] and CSR(centralized sparse representation) [17]. In our experiments, 8 commonly used images in literature are selected as the testing image. The LR images are Fig. 6. Exam... |

598 |
Image denoising via sparse and redundant representations over learned dictionaries
- Elad, Aharon
- 2006
(Show Context)
Citation Context ...based denoising algorithm with the trained NSP model, the balancing parameter τ is the only parameter to set. In our experiment, we set τ as 5 for all noise level. We compare our algorithm with K-SVD =-=[5]-=- and the benchmark BM3D [19] as well as three representative algorithms with image prior model: FoE [4], NLR-MRF [24] and EPPL [13]. Among them BM3D is the state-of-the-art in terms of accuracy. In or... |

555 | A singular value thresholding algorithm for matrix completion
- Cai, Candes, et al.
- 2008
(Show Context)
Citation Context ...oss spatial-temporal domain to form a low-rank matrix, and then presented a powerful nonlocal-based video denoising algorithm by using the recently developed low-rank matrix recovery (LRMR) technique =-=[22]-=-. Schaeffer et al. [23] implemented cartoon-texture separation by interpreting texture in low-rank patches. Taking advantage of lowrank interpretation, their method can effectively separated noise fro... |

438 | A non-local algorithm for image denoising
- Buades, Coll, et al.
(Show Context)
Citation Context ...s can be sparsely represented, restoration can be effectively conducted. Nonlocal self-similarity (NSS) has been successfully used for image restoration problems. In their pioneer work, Buades et al. =-=[3]-=- regularized each image patch as the weighted average of its nonlocal neighboring patches. Dabov et al. [19] made use of NSS to construct 3D cubes of similar patches and conduct collaborative filterin... |

422 | Image denoising by sparse 3D transform-domain collaborative filtering
- Dabov, Foi, et al.
- 2007
(Show Context)
Citation Context ... been successfully used for image restoration problems. In their pioneer work, Buades et al. [3] regularized each image patch as the weighted average of its nonlocal neighboring patches. Dabov et al. =-=[19]-=- made use of NSS to construct 3D cubes of similar patches and conduct collaborative filtering on them to remove random noise. The so-called BM3D algorithm has been one benchmark for image denoising. I... |

348 | Example-based superresolution
- Freeman, Jones, et al.
- 2002
(Show Context)
Citation Context ...t recovering the lowrank matrix X from its noisy observation matrix Y. Cai et al. proposed to solve this nonconvex problem by convex relaxation with the nuclear norm: minX ‖X‖∗, s.t.‖X − Y‖ 2 F ≤ η 2 =-=(1)-=- where ‖ · ‖∗ means the nuclear norm and η is the noise standard derivation. Eq. 1 is a convex relaxation of low-rank minimization. In [21] and some similar works [23], it is assumed that the matrix c... |

292 | Field of experts: A framework for learning image priors.
- Roth, Black
- 2005
(Show Context)
Citation Context ...ge deconvolution. Krishnan and Fergus [12] used hyper-Laplacian priors by minimizing the nonconvex lq-norm (q < 1). Filter-bank based prior models are also powerful for image restoration. Roth et al. =-=[4]-=- extended the Markov random field (MRF) framework by modeling marginal distribution of well-learnt filter response. It is actually an extension of gradient based methods by formulating the responses o... |

278 | Image and depth from a conventional camera with a coded aperture”
- Levin, Durand, et al.
- 2007
(Show Context)
Citation Context ...e restoration. The past decade has witnessed the rapid development on image prior modeling [1–14], and these prior models can be categorized into several categories: gradient (derivative, edge) based =-=[2, 7, 8, 12, 14]-=-, filter-bank based [4, 9–11, 13], transform based [5, 15–17], etc. Gradient-based image prior modeling is based on the fact that natural images usually contain only a small part of edge/texture regio... |

194 |
Non-local sparse models for image restoration
- Mairal, Bach, et al.
- 2009
(Show Context)
Citation Context ...ade use of NSS to construct 3D cubes of similar patches and conduct collaborative filtering on them to remove random noise. The so-called BM3D algorithm has been one benchmark for image denoising. In =-=[16]-=-, Mairal et al. exploited NSS by using an lp,q-norm simultaneous sparse coding model. Dong et al. [17] proposed a centralized sparse representation model to exploit NSS in sparse domain. Zontak and Ir... |

170 |
Understanding and evaluating blind deconvolution algorithms”,
- Levin, Weiss, et al.
- 2009
(Show Context)
Citation Context ...lidate more comprehensively the effectiveness of NSP, we conduct deblurring with real motion blur kernels. The dataset we adopted is a standard testing dataset for motion deblurring from Levin et al. =-=[31]-=-. In this dataset, there are 4 images in total with 8 real-world motion blur kernels. For each blurred image y, its corresponding original image x and blur kernel k are provided. We use two state-of-t... |

135 | Image super-resolution as sparse representation of raw image patches
- Yang, Wright, et al.
- 2008
(Show Context)
Citation Context ...ing the blurred high-resolution (HR) image. We compare our proposed NSP based method with some well-known super-resolution methods, including Softcut [28], TV-based method [29], Sparsity based method =-=[15]-=- and CSR(centralized sparse representation) [17]. In our experiments, 8 commonly used images in literature are selected as the testing image. The LR images are Fig. 6. Example of super-resolution resu... |

128 |
Using contours to detect and localize junctions in natural images.
- Maire, Arbelaez, et al.
- 2008
(Show Context)
Citation Context ...ural images. In Fig. 2 (bottom right) we plot the distribution of the estimated parameters λ and γ from 20,000 different image pieces (size: 256×256) collected from the Internet and BSDS 500 database =-=[25]-=-. The patch size is set as 5×5 and the 49 most similar patches to a given patch are collected to form a 25 × 50 nonlocal matrix. We can see that the estimated λ and γ are mostly located within [2, 8],... |

109 | Fast image deconvolution using hyper-laplacian priors,”
- Krishnan, Fergus
- 2009
(Show Context)
Citation Context ...e restoration. The past decade has witnessed the rapid development on image prior modeling [1–14], and these prior models can be categorized into several categories: gradient (derivative, edge) based =-=[2, 7, 8, 12, 14]-=-, filter-bank based [4, 9–11, 13], transform based [5, 15–17], etc. Gradient-based image prior modeling is based on the fact that natural images usually contain only a small part of edge/texture regio... |

92 | What makes a good model of natural images
- Weiss, Freeman
- 2007
(Show Context)
Citation Context ...hood proposed by Zoran et al. [13], we solve Eq. (9) by using alternating optimization as follows: 1. Solve auxiliary variables {Xi} by: ˆXi = arg minXi{ 1 η 2 ‖Pix − Xi‖ 2 2 + ∑ n i=1 λi‖σ(Xi)‖ γi } =-=(10)-=-Nonlocal Spectral Prior Model for Low-level Vision 9 2. Reconstruct x by { ˆ Xi} and perform gradient descent: x = x − ζ∇x(‖h(x ⊗ k) − y‖ 2 F ) where Pi is the linear operator to extract nonlocal mat... |

77 |
Image upsampling via imposed edge statistics.
- Fattal
- 2007
(Show Context)
Citation Context ... them alternately. In this work, we assume that k is known. The most popular approach for image restoration is to conduct maximum-a-posterior (MAP) estimation of x: p(x|y, k, h, η) ∝ p(y|x, k, η)p(x) =-=(6)-=- where η is the standard deviation of noise n and the likelihood function is standard Gaussian distribution: p(y|x, k, h, η) ∝ exp(−‖y − h(x ⊗ k)‖ 2 2/η 2 ) (7) Therefore, in order to estimate the unk... |

77 | From learning models of natural image patches to whole image restoration,”
- Zoran, Weiss
- 2011
(Show Context)
Citation Context ... log p(x|y, k, h, η) = arg minx − log p(y|x, k, h, η)p(x) = arg minx{ 1 η2 ‖y − h(x ⊗ k)‖2 2 + ∑n i=1 λi‖σ(xi)‖γi } (9) 3.4 Optimization Similar to the patch-based likelihood proposed by Zoran et al. =-=[13]-=-, we solve Eq. (9) by using alternating optimization as follows: 1. Solve auxiliary variables {Xi} by: ˆXi = arg minXi{ 1 η 2 ‖Pix − Xi‖ 2 2 + ∑ n i=1 λi‖σ(Xi)‖ γi } (10)Nonlocal Spectral Prior Model... |

74 | Pointwise shape-adaptive DCT for high-quality denoising and deblocking of grayscale and color images.
- Foi, Katkovnik, et al.
- 2007
(Show Context)
Citation Context ...2 and 2). We choose τ as 6 and gradient descent step length ζ as 0.6 in the deblurring experiment. We compare our method with several state-of-the-art deblurring methods, including FISTA [29], SA-DCT =-=[30]-=-, BM3D [19] and CSR [17]. Note that the recently developed CSR has shown very strong deblurring capability. Three images are used in this experiment, and the PSNR results are listed in Table 3. We can... |

70 | Image super-resolution using gradient profile prior", in
- Sun, Sun, et al.
- 2008
(Show Context)
Citation Context ... by those works, we propose the following iteratively reweighted singular vector thresholding algorithm. Considering the following optimization problem: (q − Nuclear) minX τ||σ(X)||q + 1 2 ‖X − Y‖2 F =-=(11)-=- where q < 1. The 1 st order Taylor expansion of ‖σ(X)‖q in terms of σ is: ‖σ(X)‖q = ‖σ0‖q + (σ(X) − σ0)/σ 1−q 0 (12) Since each entry of σ(X) is nonnegative, we can use the following updating strateg... |

57 | Blind motion deblurring using image statistics,”
- Levin
- 2006
(Show Context)
Citation Context ...e restoration. The past decade has witnessed the rapid development on image prior modeling [1–14], and these prior models can be categorized into several categories: gradient (derivative, edge) based =-=[2, 7, 8, 12, 14]-=-, filter-bank based [4, 9–11, 13], transform based [5, 15–17], etc. Gradient-based image prior modeling is based on the fact that natural images usually contain only a small part of edge/texture regio... |

52 | Exploiting the sparse derivative prior for super-resolution and image demosaicing. SCTV,
- Tappen, Russell, et al.
- 2003
(Show Context)
Citation Context |

45 | A generative perspective on mrfs in low-level vision - Schmidt, Gao, et al. - 2010 |

43 | Robust video denoising using Low rank matrix completion,”
- Ji, Liu, et al.
- 2010
(Show Context)
Citation Context ...epresentation model to exploit NSS in sparse domain. Zontak and Irani [20] proposed an ‘internal parametric prior’ to evaluate the patch recurrence of images for super-resolution. Recently, Ji et al. =-=[21]-=- grouped the similar patches across spatial-temporal domain to form a low-rank matrix, and then presented a powerful nonlocal-based video denoising algorithm by using the recently developed low-rank m... |

36 | Soft edge smoothness prior for alpha channel super resolution,” in CVPR,
- Dai, Han, et al.
- 2007
(Show Context)
Citation Context ...low-resolution (LR) image is obtained by downsampling the blurred high-resolution (HR) image. We compare our proposed NSP based method with some well-known super-resolution methods, including Softcut =-=[28]-=-, TV-based method [29], Sparsity based method [15] and CSR(centralized sparse representation) [17]. In our experiments, 8 commonly used images in literature are selected as the testing image. The LR i... |

35 | Internal statistics of a single natural image.
- Zontak, Irani
- 2011
(Show Context)
Citation Context ...the proposed NSP algorithm is verified on the Kodak PhotoCD dataset (http://r0k.us/graphics/kodak), which contains 24 images of size 512 × 768. Gaussian white noise of 5 different standard deviations =-=(10, 15, 20, 25, 50)-=- are added to the original images to simulate the noisy images. In our NSP based denoising algorithm with the trained NSP model, the balancing parameter τ is the only parameter to set. In our experime... |

26 | Reweighted nuclear norm minimization with application to system identification
- Mohan, Fazel
- 2010
(Show Context)
Citation Context ...race function. When γ < 1, Eq. (10) is a non-convex optimization problem. In this case, convex optimization approach cannot ensure to find the global optimum. However, iterative reweighted approaches =-=[27]-=- can be adopted to tackle this problem by solving a series of weighted l1-minimization problem. Motivated by those works, we propose the following iteratively reweighted singular vector thresholding a... |

22 |
Steerable random fields
- Roth, Black
- 2007
(Show Context)
Citation Context ... image x can be obtained by minimizing the log-posterior as follows: ˆx = arg minx − log p(x|y, k, h, η) = arg minx − log p(y|x, k, h, η)p(x) = arg minx{ 1 η2 ‖y − h(x ⊗ k)‖2 2 + ∑n i=1 λi‖σ(xi)‖γi } =-=(9)-=- 3.4 Optimization Similar to the patch-based likelihood proposed by Zoran et al. [13], we solve Eq. (9) by using alternating optimization as follows: 1. Solve auxiliary variables {Xi} by: ˆXi = arg mi... |

21 | A content-aware image prior
- Cho, Joshi, et al.
- 2010
(Show Context)
Citation Context |

18 | Centralized sparse representation for image restoration
- Dong, Zhang, et al.
- 2011
(Show Context)
Citation Context ... remove random noise. The so-called BM3D algorithm has been one benchmark for image denoising. In [16], Mairal et al. exploited NSS by using an lp,q-norm simultaneous sparse coding model. Dong et al. =-=[17]-=- proposed a centralized sparse representation model to exploit NSS in sparse domain. Zontak and Irani [20] proposed an ‘internal parametric prior’ to evaluate the patch recurrence of images for super-... |

6 |
A low patch-rank interpretation of texture
- Schaeffer, Osher
(Show Context)
Citation Context ...main to form a low-rank matrix, and then presented a powerful nonlocal-based video denoising algorithm by using the recently developed low-rank matrix recovery (LRMR) technique [22]. Schaeffer et al. =-=[23]-=- implemented cartoon-texture separation by interpreting texture in low-rank patches. Taking advantage of lowrank interpretation, their method can effectively separated noise from texture. The joint us... |

4 | Learning non-local range Markov random field for image restoration
- Sun, Tappen
- 2011
(Show Context)
Citation Context ... experiment, we set τ as 5 for all noise level. We compare our algorithm with K-SVD [5] and the benchmark BM3D [19] as well as three representative algorithms with image prior model: FoE [4], NLR-MRF =-=[24]-=- and EPPL [13]. Among them BM3D is the state-of-the-art in terms of accuracy. In order to prove the effectiveness of the proposed GGD model, we have also conducted a comparison experiments with the fi... |