#### DMCA

## Image deblurring and superresolution by adaptive sparse domain selection and adaptive regularization (2011)

Venue: | IEEE Trans. Image Process |

Citations: | 59 - 11 self |

### Citations

3771 |
Introduction to Statistical Pattern Recognition. Computer Science and Scientific Computing
- Fukunaga
- 1990
(Show Context)
Citation Context ...). ThePCA) is a good solution to this end. PCA is a classical signal de-correlation and dimensionality reduction technique that is widely used in pattern recognition and statistical signal processing =-=[37]-=-. In [38] and [39], PCA has been successfully used in spatially adaptive image denoising by computing the local PCA transform of each image patch. In this paper, we apply PCA to each subdataset to com... |

3592 | Compressed sensing
- Donoho
(Show Context)
Citation Context ...re identities, the IR problem becomes denoising; when is identity and is a blurring operator, IR becomes deblurring; when is identity and is a set of random projections, IR becomes compressed sensing =-=[2]-=-–[4]; when is a downsampling operator and is a blurring operator, IR becomes (single-image) super-resolution. As a fundamental problem in image processing, IR has been extensively studied in the past ... |

2704 | Atomic decomposition by basis pursuit
- Chen, Donoho, et al.
- 1998
(Show Context)
Citation Context ...he target signal to be coded, and is a given dictionary of atoms (i.e., code set). The sparse coding of over is to find a sparse vector (i.e., most of the coefficients in are close to zero) such that =-=[49]-=-. If the sparsity is measured as the -norm of , which counts the nonzero coefficients in , the sparse coding problem becomes s.t. , where is a scalar controlling the sparsity [55]. Alternatively, the ... |

2602 | Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
- Candès, Romberg, et al.
(Show Context)
Citation Context ...dentities, the IR problem becomes denoising; when is identity and is a blurring operator, IR becomes deblurring; when is identity and is a set of random projections, IR becomes compressed sensing [2]–=-=[4]-=-; when is a downsampling operator and is a blurring operator, IR becomes (single-image) super-resolution. As a fundamental problem in image processing, IR has been extensively studied in the past thre... |

2265 | Nonlinear total variation based noise removal algorithms
- Rudin, Osher, et al.
- 1992
(Show Context)
Citation Context ...ot unique. To find a better solution, prior knowledge of natural images can be used to regularize the IR problem. One of the most commonly used regularization models is the total variation (TV) model =-=[6]-=-, [7]: , where is the -norm of the first-order derivative of and is a constant. Since the TV model favors the piecewise constant image structures, it tends to smooth out the fine details of an image. ... |

1664 | Matching pursuits with time-frequency dictionaries - Mallat, Zhang - 1993 |

1497 | Practical signal recovery from random projections
- Candès, Romberg
- 2005
(Show Context)
Citation Context ...arse vector can also be found by (2) where is a constant. Since the -norm is nonconvex, it is often replaced by either the standard -norm or the weighted -norm to make the optimization problem convex =-=[3]-=-, [57], [59], [60]. An important issue of the sparse representation modeling is the choice of dictionary . Much effort has been made in learning a redundant dictionary from a set of example image patc... |

1430 | An introduction to compressive sampling
- Candès, Wakin
- 2008
(Show Context)
Citation Context ...vector can also be found by (2) where is a constant. Since the -norm is nonconvex, it is often replaced by either the standard -norm or the weighted -norm to make the optimization problem convex [3], =-=[57]-=-, [59], [60]. An important issue of the sparse representation modeling is the choice of dictionary . Much effort has been made in learning a redundant dictionary from a set of example image patches [1... |

1302 |
Emergence of simple-cell receptive field properties by learning a sparse representation
- Olshausen, Field
- 1996
(Show Context)
Citation Context ...n found that natural images can be generally coded by structural primitives, e.g., edges and line segments [61], and these primitives are qualitatively similar in form to simple cell receptive fields =-=[62]-=-. In [63], Olshausen et al. proposed to represent a natural image using a small number of basis functions chosen out of an over-complete code set. In recent years, such a sparse coding or sparse repre... |

1278 | Denoising by soft-thresholding
- Donoho
- 1995
(Show Context)
Citation Context ... to improve the TV models [17]–[19], [42], [45], [47]. The success of TV regularization validates the importance of good image prior models in solving the IR problems. In waveletbased image denoising =-=[21]-=-, researchers have found that the sparsity of wavelet coefficients can serve as good prior. This reveals the fact that many types of signals, e.g., natural images, can be sparsely represented (or code... |

955 | Sparse coding with an overcomplete basis set: A strategy employed by V1
- Olshausen, Field
- 1997
(Show Context)
Citation Context ...hat natural images can be generally coded by structural primitives, e.g., edges and line segments [61], and these primitives are qualitatively similar in form to simple cell receptive fields [62]. In =-=[63]-=-, Olshausen et al. proposed to represent a natural image using a small number of basis functions chosen out of an over-complete code set. In recent years, such a sparse coding or sparse representation... |

928 | K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation - Aharon, Elad, et al. - 2006 |

742 | An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
- Daubechies, Defrise, et al.
- 2004
(Show Context)
Citation Context ...and, we need to have an initial estimation of it. The initial estimation of can be accomplished by taking wavelet bases as the dictionary and then solving (6) with the iterated shrinkage algorithm in =-=[10]-=-. Denote by the estimate of and denote by a local patch of . Recall that we have the centroid of each cluster available, and hence we could select the best fitted subdictionary to by comparing the hig... |

598 |
2006 Image denoising via sparse and redundant representations over learned dictionaries
- Elad, Aharon
(Show Context)
Citation Context ...ary is selected for it. Then, can be approximated as , , via sparse coding. The whole image can be reconstructed by averaging all of the reconstructed patches , which can be mathematically written as =-=[22]-=- (4) In (4), the matrix to be inverted is a diagonal matrix, and hence the calculation of (4) can be done in a pixel-by-pixel manner [22]. Obviously, the image patches can be overlapped to better supp... |

507 | A review of image denoising algorithms, with a new one. Multiscale Modeling and Simulation
- Buades, Coll, et al.
(Show Context)
Citation Context ...m high-quality training images, to increase the AR modeling accuracy. In recent years, the nonlocal (NL) methods have led to promising results in various IR tasks, especially in image denoising [15], =-=[36]-=-, [39]. The mathematical framework of NL means filtering was well established by Buades et al. [36]. The idea of NL methods is very simple: the patches that have similar patterns can be spatially far ... |

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

490 |
What is the goal of sensory coding
- Field, J
- 1994
(Show Context)
Citation Context ...sents experimental results, and Section VII concludes the paper. II. RELATED WORKS It has been found that natural images can be generally coded by structural primitives, e.g., edges and line segments =-=[61]-=-, and these primitives are qualitatively similar in form to simple cell receptive fields [62]. In [63], Olshausen et al. proposed to represent a natural image using a small number of basis functions c... |

421 | From sparse solutions of systems of equations to sparse modeling of signals and images
- Bruckstein, Donoho, et al.
(Show Context)
Citation Context ...ges of fast implementation; however, they lack the adaptivity to image local structures. Recently, there has been much effort in learning dictionaries from example image patches [13]–[15], [26]–[31], =-=[55]-=-, leading to state-of-the-art results in image denoising and reconstruction. Many dictionary learning (DL) methods aim at learning a universal and over-complete dictionary to represent various image s... |

348 | Example-based super-resolution
- Freeman, Jones, et al.
- 2002
(Show Context)
Citation Context ...g into account the pixel intensities and helps to increase the accuracy of clustering. The high-pass filtering is often used in low-level statistical learning tasks to enhance the meaningful features =-=[50]-=-. Denote by the high-pass filtered dataset of . We adopt the -means algorithm to partition into clusters and denote by the centroid of cluster . Once is partitioned, dataset can then be clustered into... |

259 |
Digital image restoration
- Banham, Katsaggelos
- 1997
(Show Context)
Citation Context ...a downsampling operator and is a blurring operator, IR becomes (single-image) super-resolution. As a fundamental problem in image processing, IR has been extensively studied in the past three decades =-=[5]-=-–[20]. In this paper, we focus on deblurring and single-image super-resolution. Due to the ill-posed nature of IR, the solution to (1) with an -norm fidelity constraint, i.e., , is generally not uniqu... |

244 | New edge-directed interpolation
- Li, Orchard
- 2001
(Show Context)
Citation Context ...izing the local image structures and often generate over-smoothed results. As a classic method, the autoregressive (AR) modeling has been successfully used in image compression [33] and interpolation =-=[34]-=-, 1840 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 20, NO. 7, JULY 2011 [35]. Recently, the AR model was used for adaptive regularization in compressive image recovery [40]: s.t. , where is the vector... |

224 | Motion analysis for image enhancement: resolution, occlusion and transparency,” JVCIP,
- Irani, Peleg
- 1993
(Show Context)
Citation Context ...ts method [43], and the sparse representation based method [25].1 Since the method in [25] does not handle the blurring of LR images, for fair comparisons we used the iterative back-projection method =-=[16]-=- to deblur the HR images produced by [25]. In the proposed ASDS-AReg based super-resolution, the parameters are set as follows. For the noiseless LR images, we empirically set , and , where is the est... |

219 | Sparse representation for color image restoration
- Mairal, Elad, et al.
- 2008
(Show Context)
Citation Context ... . To make it tractable, approximation approaches, including MOD [56] and K-SVD [26], have been proposed to alternatively optimizing and , leading to many state-of-the-art results in image processing =-=[14]-=-, [15], [31]. Various extensions and variants of the K-SVD algorithm [27], [29]–[31] have been proposed to learn a universal and overcomplete dictionary. However, the image contents can vary significa... |

194 |
Non-local sparse models for image restoration
- Mairal, Bach, et al.
- 2009
(Show Context)
Citation Context ...share the advantages of fast implementation; however, they lack the adaptivity to image local structures. Recently, there has been much effort in learning dictionaries from example image patches [13]–=-=[15]-=-, [26]–[31], [55], leading to state-of-the-art results in image denoising and reconstruction. Many dictionary learning (DL) methods aim at learning a universal and over-complete dictionary to represen... |

193 | Supervised dictionary learning
- Mairal, Ponce, et al.
- 2009
(Show Context)
Citation Context ... [26], have been proposed to alternatively optimizing and , leading to many state-of-the-art results in image processing [14], [15], [31]. Various extensions and variants of the K-SVD algorithm [27], =-=[29]-=-–[31] have been proposed to learn a universal and overcomplete dictionary. However, the image contents can vary significantly across images. One may argue that a well-learned over-complete dictionary ... |

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 ...ewise constant image structures, it tends to smooth out the fine details of an image. To better preserve the image edges, many algorithms have been later developed to improve the TV models [17]–[19], =-=[42]-=-, [45], [47]. The success of TV regularization validates the importance of good image prior models in solving the IR problems. In waveletbased image denoising [21], researchers have found that the spa... |

167 | Computational methods for sparse solution of linear inverse problems
- Tropp, Wright
(Show Context)
Citation Context ... number of nonzero coefficients in vector . Once is obtained, can then be estimated as . The -minimization is an NP-hard combinatorial search problem, and is usually solved by greedy algorithms [48], =-=[60]-=-. The -minimization, as the closest convex function to -minimization, is then widely used as an alternative approach to solving the sparse coding problem: [60]. In addition, recent studies showed that... |

155 | Image quality assessment: From error measurement to structural similarity,” - Wang, Bovik, et al. - 2004 |

135 | Image super-resolution as sparse representation of raw image patches
- Yang, Wright, et al.
- 2008
(Show Context)
Citation Context ...ly reweighting the -norm sparsity regularization term can lead to better IR results [59]. Sparse representation has been successfully used in various image processing applications [2]–[4], [13], [21]–=-=[25]-=-, [32]. 1057-7149/$26.00 © 2011 IEEE DONG et al.: IMAGE DEBLURRING AND SUPER-RESOLUTION BY ASDS AND ADAPTIVE REGULARIZATION 1839 A critical issue in sparse representation modeling is the determination... |

107 | Dictionaries for Sparse Representation Modeling
- Rubinstein, Bruckstein, et al.
(Show Context)
Citation Context ...dvantages of fast implementation; however, they lack the adaptivity to image local structures. Recently, there has been much effort in learning dictionaries from example image patches [13]–[15], [26]–=-=[31]-=-, [55], leading to state-of-the-art results in image denoising and reconstruction. Many dictionary learning (DL) methods aim at learning a universal and over-complete dictionary to represent various i... |

103 | Learning multiscale sparse representations for image and video restoration”,
- Mairal, Sapiro, et al.
- 2008
(Show Context)
Citation Context ... K-SVD [26], have been proposed to alternatively optimizing and , leading to many state-of-the-art results in image processing [14], [15], [31]. Various extensions and variants of the K-SVD algorithm =-=[27]-=-, [29]–[31] have been proposed to learn a universal and overcomplete dictionary. However, the image contents can vary significantly across images. One may argue that a well-learned over-complete dicti... |

102 |
Introduction to Inverse Problems in Imaging
- Bertero, Boccacci
- 1998
(Show Context)
Citation Context ...ion, sparse representation, super-resolution. I. INTRODUCTION I MAGE restoration (IR) aims to reconstruct a high-qualityimage from its degraded measurement . IR is a typical ill-posed inverse problem =-=[1]-=-, and it can be generally modeled as (1) Manuscript received February 12, 2010; revised July 28, 2010 and November 15, 2010; accepted January 03, 2011. Date of publication January 28, 2011; date of cu... |

88 | Bregmanized nonlocal regularization for deconvolution and sparse reconstruction
- Zhang, Burger, et al.
- 2010
(Show Context)
Citation Context ...wnsampling operator and is a blurring operator, IR becomes (single-image) super-resolution. As a fundamental problem in image processing, IR has been extensively studied in the past three decades [5]–=-=[20]-=-. In this paper, we focus on deblurring and single-image super-resolution. Due to the ill-posed nature of IR, the solution to (1) with an -norm fidelity constraint, i.e., , is generally not unique. To... |

86 |
Deblurring and denoising of images by nonlocal functionals
- Kindermann, Osher, et al.
- 2005
(Show Context)
Citation Context ...ple: the patches that have similar patterns can be spatially far from each other, and thus we can collect them in the whole image. This NL self-similarity prior was later employed in image deblurring =-=[8]-=-, [20] and super-resolution [41]. In [15], the NL self-similarity prior was combined with the sparse representation modeling, where the similar image patches are simultaneously coded to improve the ro... |

81 | Generalizing the nonlocal-means to super-resolution reconstruction,”
- Protter, Elad, et al.
- 2009
(Show Context)
Citation Context ...lar patterns can be spatially far from each other, and thus we can collect them in the whole image. This NL self-similarity prior was later employed in image deblurring [8], [20] and super-resolution =-=[41]-=-. In [15], the NL self-similarity prior was combined with the sparse representation modeling, where the similar image patches are simultaneously coded to improve the robustness of inverse reconstructi... |

77 | On the role of sparse and redundant representations in image processing
- Elad, Figueiredo, et al.
(Show Context)
Citation Context ...t iteratively reweighting the -norm sparsity regularization term can lead to better IR results [59]. Sparse representation has been successfully used in various image processing applications [2]–[4], =-=[13]-=-, [21]–[25], [32]. 1057-7149/$26.00 © 2011 IEEE DONG et al.: IMAGE DEBLURRING AND SUPER-RESOLUTION BY ASDS AND ADAPTIVE REGULARIZATION 1839 A critical issue in sparse representation modeling is the de... |

70 | Recent developments in total variation image restoration
- Chan, Esedoglu, et al.
- 2005
(Show Context)
Citation Context ...ique. To find a better solution, prior knowledge of natural images can be used to regularize the IR problem. One of the most commonly used regularization models is the total variation (TV) model [6], =-=[7]-=-: , where is the -norm of the first-order derivative of and is a constant. Since the TV model favors the piecewise constant image structures, it tends to smooth out the fine details of an image. To be... |

65 | Image restoration by sparse 3d transformdomain collaborative filtering
- Dabov, Foi, et al.
(Show Context)
Citation Context ...let shrinkage method [10], the constrained TV deblurring method [42], the spatially weighted TV deblurring method [45], the -norm sparsity based deblurring method [46], and the BM3D deblurring method =-=[58]-=-. In the proposed ASDSAReg Algorithm 1, we empirically set , , and , where is adaptively computed by (15). In the experiments of super-resolution, the degraded LR images were generated by first applyi... |

63 | Double sparsity: Learning sparse dictionaries for sparse signal approximation - Rubinstein, Zibulevsky, et al. |

56 | Eigenface-domain super-resolution for face recognition.
- Gunturk, Batur, et al.
- 2003
(Show Context)
Citation Context ...eighting the -norm sparsity regularization term can lead to better IR results [59]. Sparse representation has been successfully used in various image processing applications [2]–[4], [13], [21]–[25], =-=[32]-=-. 1057-7149/$26.00 © 2011 IEEE DONG et al.: IMAGE DEBLURRING AND SUPER-RESOLUTION BY ASDS AND ADAPTIVE REGULARIZATION 1839 A critical issue in sparse representation modeling is the determination of di... |

53 | Morphological component analysis: An adaptive thresholding strategy, - Bobin, Starck, et al. - 2007 |

51 | Two-stage image denoising by principal component analysis with local pixel grouping.
- Zhang, Dong, et al.
- 2010
(Show Context)
Citation Context ...-quality training images, to increase the AR modeling accuracy. In recent years, the nonlocal (NL) methods have led to promising results in various IR tasks, especially in image denoising [15], [36], =-=[39]-=-. The mathematical framework of NL means filtering was well established by Buades et al. [36]. The idea of NL methods is very simple: the patches that have similar patterns can be spatially far from e... |

43 | Adaptive total variation image deblurring: A majorization-minimization approach. - Oliveira, Bioucas-Dia, et al. - 2009 |

43 |
Multi-frame compression: Theory and design
- Engan, Aase, et al.
- 2000
(Show Context)
Citation Context ...ormulated by the following minimization problem: (3) where is the Frobenius norm. The above minimization problem is nonconvex even when . To make it tractable, approximation approaches, including MOD =-=[56]-=- and K-SVD [26], have been proposed to alternatively optimizing and , leading to many state-of-the-art results in image processing [14], [15], [31]. Various extensions and variants of the K-SVD algori... |

40 | Iterative image restoration combining total variation minimization and a second-order functional,”
- Lysaker, Tai
- 2006
(Show Context)
Citation Context ...e piecewise constant image structures, it tends to smooth out the fine details of an image. To better preserve the image edges, many algorithms have been later developed to improve the TV models [17]–=-=[19]-=-, [42], [45], [47]. The success of TV regularization validates the importance of good image prior models in solving the IR problems. In waveletbased image denoising [21], researchers have found that t... |

37 | Blind Deconvolution Using a Variational Approach to Parameter, Image, and Blur Estimation, - Molina, Mateos, et al. - 2006 |

36 | Sparse representation-based image deconvolution by iterative thresholding - Fadili, Starck - 2006 |

32 | Sequential subspace optimization method for LargeScale unconstrained problems
- Narkiss, Zibulevsky
- 2005
(Show Context)
Citation Context ... about 2 5 min for image deblurring and super-resolution on an Intel Core2 Duo 2.79G PC under the MATLAB R2010a programming environment. In addition, several accelerating techniques, such as those in =-=[51]-=- and [52], can be used to accelerate the convergence of the proposed algorithm. Hence, the computational cost of the proposed method can be further reduced. VII. CONCLUSION We proposed a novel sparse ... |

30 | A plurality of sparse representations is better than the sparsest one alone
- Elad, Yavneh
- 2009
(Show Context)
Citation Context ...sal and over-complete dictionary to represent various image structures. However, sparse decomposition over a highly redundant dictionary is potentially unstable and tends to generate visual artifacts =-=[53]-=-, [54]. In this paper, we propose an adaptive sparse domain selection (ASDS) scheme for sparse representation. A set of compact subdictionaries is learned from high-quality example image patches. The ... |

27 |
Image super-resolution by TV-regularization and Bregman iteration
- Marquina, Osher
- 2008
(Show Context)
Citation Context ...nt image structures, it tends to smooth out the fine details of an image. To better preserve the image edges, many algorithms have been later developed to improve the TV models [17]–[19], [42], [45], =-=[47]-=-. The success of TV regularization validates the importance of good image prior models in solving the IR problems. In waveletbased image denoising [21], researchers have found that the sparsity of wav... |

23 |
Piecewise 2-D autoregression for predictive image coding
- Wu, Zhang
- 1998
(Show Context)
Citation Context ...xibilities in characterizing the local image structures and often generate over-smoothed results. As a classic method, the autoregressive (AR) modeling has been successfully used in image compression =-=[33]-=- and interpolation [34], 1840 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 20, NO. 7, JULY 2011 [35]. Recently, the AR model was used for adaptive regularization in compressive image recovery [40]: s.t... |

23 |
Teboulle M., A Fast Iterative Shrinkage- Thresholding Algorithm for Linear Inverse Problems
- Beck
- 2009
(Show Context)
Citation Context ...5 min for image deblurring and super-resolution on an Intel Core2 Duo 2.79G PC under the MATLAB R2010a programming environment. In addition, several accelerating techniques, such as those in [51] and =-=[52]-=-, can be used to accelerate the convergence of the proposed algorithm. Hence, the computational cost of the proposed method can be further reduced. VII. CONCLUSION We proposed a novel sparse represent... |

18 | A.: Softcuts: a soft edge smoothness prior for color image super-resolution
- Dai, Han, et al.
(Show Context)
Citation Context ...egularization, and the image quality can be further improved by incorporating the nonlocal similarity regularization. Next we compare the proposed methods with state-of-the-art methods in [10], [25], =-=[43]-=-, [47]. The visual comparisons are shown in Figs. 8 and 9. We see that the reconstructed HR images by the method in [10] have many jaggy and ringing artifacts. 1850 IEEE TRANSACTIONS ON IMAGE PROCESSI... |

18 | Variational Bayesian image restoration with a product of spatially weighted total variation image priors
- Chantas, Galatsanos, et al.
- 2010
(Show Context)
Citation Context ...constant image structures, it tends to smooth out the fine details of an image. To better preserve the image edges, many algorithms have been later developed to improve the TV models [17]–[19], [42], =-=[45]-=-, [47]. The success of TV regularization validates the importance of good image prior models in solving the IR problems. In waveletbased image denoising [21], researchers have found that the sparsity ... |

16 | PCA-based spatially adaptive denoising of CFA images for single-sensor digital cameras
- Zhang, Lukac, et al.
- 2009
(Show Context)
Citation Context ...) is a good solution to this end. PCA is a classical signal de-correlation and dimensionality reduction technique that is widely used in pattern recognition and statistical signal processing [37]. In =-=[38]-=- and [39], PCA has been successfully used in spatially adaptive image denoising by computing the local PCA transform of each image patch. In this paper, we apply PCA to each subdataset to compute the ... |

15 | Closed-form MMSE estimation for signal denoising under sparse representation modeling over a unitary dictionary,”
- Protter, Yavneh, et al.
- 2010
(Show Context)
Citation Context ...d over-complete dictionary to represent various image structures. However, sparse decomposition over a highly redundant dictionary is potentially unstable and tends to generate visual artifacts [53], =-=[54]-=-. In this paper, we propose an adaptive sparse domain selection (ASDS) scheme for sparse representation. A set of compact subdictionaries is learned from high-quality example image patches. The exampl... |

12 | Total variation super resolution using a variational approach
- Babacan, Molina, et al.
- 2008
(Show Context)
Citation Context ...rs the piecewise constant image structures, it tends to smooth out the fine details of an image. To better preserve the image edges, many algorithms have been later developed to improve the TV models =-=[17]-=-–[19], [42], [45], [47]. The success of TV regularization validates the importance of good image prior models in solving the IR problems. In waveletbased image denoising [21], researchers have found t... |

9 |
Model-guided adaptive recovery of compressive sensing
- Wu, Zhang, et al.
(Show Context)
Citation Context ...sion [33] and interpolation [34], 1840 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 20, NO. 7, JULY 2011 [35]. Recently, the AR model was used for adaptive regularization in compressive image recovery =-=[40]-=-: s.t. , where is the vector containing the neighboring pixels of pixel within the support of the AR model, and is the AR parameter vector. In [40], the AR models are locally computed from an initiall... |

5 | Enhancing sparsity by reweighted - Candès, Wakin, et al. - 2007 |

3 | Learning structured dictionaries for image representation - Monaci, Vanderqheynst - 2004 |

2 |
Image interpolation by 2-D autoregressive modeling and soft-decision estimation
- Zhang, Wu
- 2008
(Show Context)
Citation Context ...s a classic method, the autoregressive (AR) modeling has been successfully used in image compression [33] and interpolation [34], 1840 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 20, NO. 7, JULY 2011 =-=[35]-=-. Recently, the AR model was used for adaptive regularization in compressive image recovery [40]: s.t. , where is the vector containing the neighboring pixels of pixel within the support of the AR mod... |

1 |
Image restoration through analysis-based sparse optimization in tight frames
- Portilla
- 2009
(Show Context)
Citation Context ...w: Original, degraded, method [10] ( sdB, s) and the method in [42] ( dB, s). Bottom row: the method in [45] ( dB, s), the method in =-=[46]-=- ( sdB, s), BM3D [58] ( dB, s ) and the proposed method ( dB, s). methods in [42] and [45] are effective in suppressing the noises; how... |