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## Nonlocally Centralized Sparse Representation for Image Restoration (2011)

Citations: | 25 - 8 self |

### Citations

3592 | Compressed sensing - Donoho |

2704 | Atomic decomposition by basis pursuit - Chen, Donoho, et al. - 1998 |

2602 | Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
- Candès, Romberg, et al.
(Show Context)
Citation Context ...x, image deblurring when H is a blurring operator, image superresolution when H is a composite operator of blurring and down-sampling, and compressive sensing when H is a random projection matrix [1]–=-=[3]-=-. In the past decades, extensive studies have been conducted on developing various IR approaches [4]–[23], [28]. Due to the ill-posed nature of IR, the regularization-based techniques have been widely... |

2265 | Nonlinear total variation based noise removal algorithms
- Rudin, Osher, et al.
- 1992
(Show Context)
Citation Context ...ave been conducted on developing various IR approaches [4]–[23], [28]. Due to the ill-posed nature of IR, the regularization-based techniques have been widely used by regularizing the solution spaces =-=[5]-=-–[9], [12], [22]. In order for an effective regularizer, it is of great importance to find and model the appropriate prior knowledge of natural images, and various image prior models have been develop... |

1497 | Practical signal recovery from random projections
- Candès, Romberg
- 2005
(Show Context)
Citation Context ...atrix, image deblurring when H is a blurring operator, image superresolution when H is a composite operator of blurring and down-sampling, and compressive sensing when H is a random projection matrix =-=[1]-=-–[3]. In the past decades, extensive studies have been conducted on developing various IR approaches [4]–[23], [28]. Due to the ill-posed nature of IR, the regularization-based techniques have been wi... |

928 | K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation
- Aharon, Elad, et al.
- 2006
(Show Context)
Citation Context ...ithms [24], [25]. In addition, compared with the 1057–7149/$31.00 © 2012 IEEE DONG et al.: NCSR FOR IMAGE RESTORATION 1621 (a) (b) Fig. 1. Examples of the sparse coding coefficients by using the KSVD =-=[26]-=- approach. (a) Some natural images. (b) Corresponding distributions of the sparse coding coefficients (associated with the 3rd atom of the dictionary in KSVD) of the patches extracted at each pixel. N... |

742 | An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
- Daubechies, Defrise, et al.
- 2004
(Show Context)
Citation Context ...been conducted on developing various IR approaches [4]–[23], [28]. Due to the ill-posed nature of IR, the regularization-based techniques have been widely used by regularizing the solution spaces [5]–=-=[9]-=-, [12], [22]. In order for an effective regularizer, it is of great importance to find and model the appropriate prior knowledge of natural images, and various image prior models have been developed [... |

598 | 2006 Image denoising via sparse and redundant representations over learned dictionaries - Elad, Aharon |

507 | A review of image denoising algorithms, with a new one. Multiscale Modeling and Simulation
- Buades, Coll, et al.
(Show Context)
Citation Context ...s, as shown in Fig. 1, allows us to learn the estimate β from the input data. Based on the fact that natural images often contain repetitive structures, i.e., the rich amount of nonlocal redundancies =-=[30]-=-, we search the nonlocal similar patches to the given patch i in a large window centered at pixel i . For higher performance, the search of similar patches can also be carried out across different sca... |

506 | Signal recovery by proximal forwardbackward splitting.” - Combettes, Wajs - 2005 |

422 | Image denoising by sparse 3D transform-domain collaborative filtering
- Dabov, Foi, et al.
- 2007
(Show Context)
Citation Context ...In order for an effective regularizer, it is of great importance to find and model the appropriate prior knowledge of natural images, and various image prior models have been developed [5]–[8], [14], =-=[17]-=-, [18], [22]. The classic regularization models, such as the quadratic Tikhonov regularization [8] and the TV regularization [5]–[7] are effective in removing the noise artifacts but tend to oversmoot... |

421 | From sparse solutions of systems of equations to sparse modeling of signals and images
- Bruckstein, Donoho, et al.
(Show Context)
Citation Context ...[22]. In order for an effective regularizer, it is of great importance to find and model the appropriate prior knowledge of natural images, and various image prior models have been developed [5]–[8], =-=[14]-=-, [17], [18], [22]. The classic regularization models, such as the quadratic Tikhonov regularization [8] and the TV regularization [5]–[7] are effective in removing the noise artifacts but tend to ove... |

243 | Enhancing sparsity by reweighted l1 minimization - Candes, Wakin, et al. - 2008 |

224 | Motion analysis for image enhancement: resolution, occlusion and transparency,” JVCIP,
- Irani, Peleg
- 1993
(Show Context)
Citation Context ...76 29.16 23.14 40.00 15.99 26.61 15.15 Input PSNR 22.23 22.16 20.76 24.62 23.36 29.82 25.61 25.46 24.11 28.06 27.81 29.98 TVMM [7] 7.41 5.17 8.54 2.57 3.36 1.30 7.98 6.57 10.39 4.12 4.54 2.44 L0-Spar =-=[37]-=- 7.70 5.55 9.10 2.93 3.49 1.77 8.40 7.12 11.06 4.55 4.80 2.15 IDD-BM3D [42] 8.85 7.12 10.45 3.98 4.31 4.89 9.95 8.55 12.89 5.79 5.74 7.13 NCSR 8.78 6.69 10.33 3.78 4.60 4.50 9.96 8.48 13.12 5.81 5.67 ... |

219 | Sparse representation for color image restoration
- Mairal, Elad, et al.
- 2008
(Show Context)
Citation Context ...es due to the piecewise constant assumption. As an alternative, in recent years the sparsity-based regularization [9]–[23] has led to promising results for various image restoration problems [1]–[3], =-=[16]-=-–[23]. Mathematically, the sparse representation model assumes that a signal x ∈ N can be represented as x ≈ α, where ∈ n×M (N < M) is an over-complete dictionary, and most entries of the coding ... |

206 | Bivariate shrinkage functions for waveletbased denoising exploiting interscale dependency
- Sendur, Selesnick
- 2002
(Show Context)
Citation Context ...rring and down-sampling, and compressive sensing when H is a random projection matrix [1]–[3]. In the past decades, extensive studies have been conducted on developing various IR approaches [4]–[23], =-=[28]-=-. Due to the ill-posed nature of IR, the regularization-based techniques have been widely used by regularizing the solution spaces [5]–[9], [12], [22]. In order for an effective regularizer, it is of ... |

194 |
Non-local sparse models for image restoration
- Mairal, Bach, et al.
- 2009
(Show Context)
Citation Context ...er for an effective regularizer, it is of great importance to find and model the appropriate prior knowledge of natural images, and various image prior models have been developed [5]–[8], [14], [17], =-=[18]-=-, [22]. The classic regularization models, such as the quadratic Tikhonov regularization [8] and the TV regularization [5]–[7] are effective in removing the noise artifacts but tend to oversmooth the ... |

194 | Image super-resolution via sparse representation.
- Yang, Wright, et al.
- 2010
(Show Context)
Citation Context ...of blurring and down-sampling, and compressive sensing when H is a random projection matrix [1]–[3]. In the past decades, extensive studies have been conducted on developing various IR approaches [4]–=-=[23]-=-, [28]. Due to the ill-posed nature of IR, the regularization-based techniques have been widely used by regularizing the solution spaces [5]–[9], [12], [22]. In order for an effective regularizer, it ... |

182 | A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoratin - Bioucas-Dias, Figueiredo |

168 | Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems
- Beck, Teboulle
(Show Context)
Citation Context ...deblurring operation to the luminance component. We compared the NCSR deblurring method with four stateof-the-art deblurring methods, including the constrained TV deblurring (denoted by FISTA) method =-=[35]-=-, the l0-sparsity based deblurring (denoted by l0-SPAR) method [36], the 1626 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 22, NO. 4, APRIL 2013 TABLE I PSNR (dB) RESULTS BY DIFFERENT DENOISING METHODS... |

167 | Computational methods for sparse solution of linear inverse problems
- Tropp, Wright
(Show Context)
Citation Context ...conducted on developing various IR approaches [4]–[23], [28]. Due to the ill-posed nature of IR, the regularization-based techniques have been widely used by regularizing the solution spaces [5]–[9], =-=[12]-=-, [22]. In order for an effective regularizer, it is of great importance to find and model the appropriate prior knowledge of natural images, and various image prior models have been developed [5]–[8]... |

140 |
Enhancing sparsity by reweighted `1 minimization
- Candes, Wakin
(Show Context)
Citation Context ... Since we update the regularization parameter λi, j and {β i } in every J0 iterations after solving a sub-optimization problem, Algorithm 1 is empirically convergent in general, as those presented in =-=[38]-=-. IV. EXPERIMENTAL RESULTS To verify the IR performance of the proposed NCSR algorithm we conduct extensive experiments on image denoising, deblurring and super-resolution. The basic parameter setting... |

138 | M.: Super-resolution from a single image
- Glasner, Bagon, et al.
- 2009
(Show Context)
Citation Context ...large window centered at pixel i . For higher performance, the search of similar patches can also be carried out across different scales at the expense of higher computational complexity, as shown in =-=[31]-=-. Then a good estimation of αi , i.e., β i , can be computed as the weighted average of those sparse codes associated with the nonlocal similar patches (including patch i) to patch i . For each patch ... |

107 | Dictionaries for Sparse Representation Modeling - Rubinstein, Bruckstein, et al. |

102 |
Introduction to Inverse Problems in Imaging
- Bertero, Boccacci
- 1998
(Show Context)
Citation Context ...tor of blurring and down-sampling, and compressive sensing when H is a random projection matrix [1]–[3]. In the past decades, extensive studies have been conducted on developing various IR approaches =-=[4]-=-–[23], [28]. Due to the ill-posed nature of IR, the regularization-based techniques have been widely used by regularizing the solution spaces [5]–[9], [12], [22]. In order for an effective regularizer... |

88 | Bregmanized nonlocal regularization for deconvolution and sparse reconstruction - Zhang, Burger, et al. - 2010 |

77 | On the role of sparse and redundant representations in image processing - Elad, Figueiredo, et al. |

77 | FSIM: A feature similarity index for image quality assessment
- Zhang, Zhang, et al.
- 2011
(Show Context)
Citation Context ...= 3; for image deblurring and super-resolution, δ = 2.4, L = 5, and J = 160. To evaluate the quality of the restored images, the PSNR and the recently proposed powerful perceptual quality metric FSIM =-=[32]-=- are calculated. Due to the limited page space, we only show part of the results in this paper, and all the experimental results can be downloaded on the website: http://www.comp.polyu.edu.hk/∼cslzhan... |

77 | From learning models of natural image patches to whole image restoration,”
- Zoran, Weiss
- 2011
(Show Context)
Citation Context ...rruption. From left to right and top to bottom: original image, noisy image (σ = 20), and denoised images by SAPCA-BM3D [39] (PSNR=30.91 dB; FSIM=0.9404), LSSC [18] (PSNR=30.58 dB; FSIM=0.9310), EPLL =-=[33]-=- (PSNR=30.48 dB; FSIM=0.9330), and NCSR (PSNR=30.69 dB; FSIM=0.9316). The proposed NCSR based IR algorithm is summarized in Algorithm 1. In Algorithm 1, for fixed parameters λi, j and {βi } the object... |

70 | Recent developments in total variation image restoration - Chan, Esedoglu, et al. - 2005 |

65 | Image restoration by sparse 3d transformdomain collaborative filtering
- Dabov, Foi, et al.
(Show Context)
Citation Context ...3D deblurring method [41], and the adaptive sparse domain selection method (denoted by ASDS-Reg) [21]. Note that the recently proposed IDD-BM3D method is an improved version of BM3D deblurring method =-=[20]-=-, and ASDS-Reg is a very competitive sparsity-based deblurring method with adaptive sparse domain selection. The PSNR and FSIM results on a set of 10 photographic images are reported in Table II. From... |

63 |
Tikhonov, Solutions of incorrectly formulated problems and the regularization method,
- N
- 1963
(Show Context)
Citation Context ...12], [22]. In order for an effective regularizer, it is of great importance to find and model the appropriate prior knowledge of natural images, and various image prior models have been developed [5]–=-=[8]-=-, [14], [17], [18], [22]. The classic regularization models, such as the quadratic Tikhonov regularization [8] and the TV regularization [5]–[7] are effective in removing the noise artifacts but tend ... |

59 | Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization,”
- Dong, Zhang, et al.
- 2011
(Show Context)
Citation Context ...t various image local structures. However, it has been shown that sparse coding with an overcomplete dictionary is unstable [42], especially in the scenario of image restoration. In our previous work =-=[21]-=-, we cluster the training patches extracted from a set of example images into K clusters, and learn a PCA sub-dictionary for each cluster. Then for a given patch, one compact PCA sub-dictionary is ada... |

53 | From local kernel to nonlocal multiple-model image denoising,”
- Katkovnik, Foi, et al.
- 2010
(Show Context)
Citation Context ...image denoising, deblurring and super-resolution, demonstrate that the proposed NCSR based IR method can achieve highly competitive performance to state-of-the-art denoising methods (e.g., BM3D [17], =-=[39]-=-–[41], LSSC [18]), and outperforms state-of-the-art image deblurring and super-resolution methods. The rest of this paper is organized as follows. Section II presents the modeling of NCSR. Section III... |

45 |
L1-l2 optimization in signal and image processing
- Zibuleusky, Elad
- 2010
(Show Context)
Citation Context ...d the term “sparse coding” refer to this sparse approximation process of x. Many efficient l1minimization techniques have been proposed to solve Eq. (2), such as iterative thresholding algorithms [9]–=-=[11]-=- and Bregman split algorithms [24], [25]. In addition, compared with the 1057–7149/$31.00 © 2012 IEEE DONG et al.: NCSR FOR IMAGE RESTORATION 1621 (a) (b) Fig. 1. Examples of the sparse coding coeffic... |

43 |
Adaptive total variation image deblurring: A majorization-minimization approach.
- Oliveira, Bioucas-Dia, et al.
- 2009
(Show Context)
Citation Context ... and various image prior models have been developed [5]–[8], [14], [17], [18], [22]. The classic regularization models, such as the quadratic Tikhonov regularization [8] and the TV regularization [5]–=-=[7]-=- are effective in removing the noise artifacts but tend to oversmooth the images due to the piecewise constant assumption. As an alternative, in recent years the sparsity-based regularization [9]–[23]... |

30 | A plurality of sparse representations is better than the sparsest one alone
- Elad, Yavneh
- 2009
(Show Context)
Citation Context ... 29.34 28.72 26.42 28.11 28.66 26.30 28.44 [37] 0.8879 0.9094 0.8689 0.9225 0.9262 0.9063 0.8691 0.8951 0.9066 0.8776 0.8970 IDD-BM3D 29.21 31.20 28.56 34.44 31.06 29.70 27.98 29.48 29.62 29.38 30.06 =-=[42]-=- 0.9287 0.9304 0.9007 0.9369 0.9364 0.9197 0.9014 0.9167 0.9200 0.9295 0.9220 ASDS-Reg 28.70 30.80 28.08 34.03 31.22 29.92 27.86 29.72 29.48 28.59 29.84 [21] 0.9053 0.9236 0.8950 0.9337 0.9306 0.9256 ... |

28 | BM3D frames and variational image deblurring
- Danielyan, Katkovnik, et al.
(Show Context)
Citation Context ... denoising, deblurring and super-resolution, demonstrate that the proposed NCSR based IR method can achieve highly competitive performance to state-of-the-art denoising methods (e.g., BM3D [17], [39]–=-=[41]-=-, LSSC [18]), and outperforms state-of-the-art image deblurring and super-resolution methods. The rest of this paper is organized as follows. Section II presents the modeling of NCSR. Section III prov... |

27 |
Image super-resolution by TV-regularization and Bregman iteration
- Marquina, Osher
- 2008
(Show Context)
Citation Context ... sparse approximation process of x. Many efficient l1minimization techniques have been proposed to solve Eq. (2), such as iterative thresholding algorithms [9]–[11] and Bregman split algorithms [24], =-=[25]-=-. In addition, compared with the 1057–7149/$31.00 © 2012 IEEE DONG et al.: NCSR FOR IMAGE RESTORATION 1621 (a) (b) Fig. 1. Examples of the sparse coding coefficients by using the KSVD [26] approach. (... |

24 |
Image restoration through l0 analysis-based sparse optimization in tight frames
- Portilla
- 2009
(Show Context)
Citation Context ... deviation 1.6, are used for simulations. Additive Gaussian noise with noise levels σn = √ 2 is added to the blurred images. In addition, 6 typical non-blind deblurring image experiments presented in =-=[36]-=- and [41] are conducted for further test. For the real motion blurred images, we borrowed the motion blur kernel estimation method from [34] to estimate the blur kernel and then fed the estimated blur... |

23 | Bm3d image denoising with shape-adaptive principal component analysis - Dabov, Foi, et al. - 2009 |

18 | Centralized sparse representation for image restoration - Dong, Zhang, et al. - 2011 |

16 |
Removing camera shake from a single image
- Fergus, Singh, et al.
- 2006
(Show Context)
Citation Context ...typical non-blind deblurring image experiments presented in [36] and [41] are conducted for further test. For the real motion blurred images, we borrowed the motion blur kernel estimation method from =-=[34]-=- to estimate the blur kernel and then fed the estimated blur kernel into the NCSR deblurring method. For color images, we only apply the deblurring operation to the luminance component. We compared th... |

9 | Universal regularizers for robust sparse coding and modeling - Ramirez, Sapiro |

6 | On the Role of Sparse and Redundant - Elad, Figueiredo, et al. - 2010 |