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154
Fast and Robust Multi-Frame Super-Resolution
- IEEE Transactions on Image ProcessinG
, 2003
"... In the last two decades, many papers have been published, proposing a variety of methods for multi- frame resolution enhancement. These methods are usually very sensitive to their assumed model of data and noise, which limits their utility. This paper reviews some of these methods and addresses th ..."
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Cited by 272 (37 self)
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In the last two decades, many papers have been published, proposing a variety of methods for multi- frame resolution enhancement. These methods are usually very sensitive to their assumed model of data and noise, which limits their utility. This paper reviews some of these methods and addresses their shortcomings. We propose an alternate approach using L norm minimization and robust regularization based on a bilateral prior to deal with different data and noise models. This computationally inexpensive method is robust to errors in motion and blur estimation, and results in images with sharp edges.
Mathematical Models for Local Nontexture Inpaintings
- SIAM J. Appl. Math
, 2002
"... Inspired by the recent work of Bertalmio et al. on digital inpaintings [SIGGRAPH 2000], we develop general mathematical models for local inpaintings of nontexture images. On smooth regions, inpaintings are connected to the harmonic and biharmonic extensions, and inpainting orders are analyzed. For i ..."
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Cited by 214 (29 self)
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Inspired by the recent work of Bertalmio et al. on digital inpaintings [SIGGRAPH 2000], we develop general mathematical models for local inpaintings of nontexture images. On smooth regions, inpaintings are connected to the harmonic and biharmonic extensions, and inpainting orders are analyzed. For inpaintings involving the recovery of edges, we study a variational model that is closely connected to the classical total variation (TV) denoising model of Rudin, Osher, and Fatemi [PhSG D, 60 (1992), pp. 259--268]. Other models are also discussed based on the Mumford--Shah regularity [Comm. Pure Appl. Mathq XLII (1989), pp. 577--685] and curvature driven di#usions (CDD) of Chan and Shen [J. Visual Comm. Image Rep., 12 (2001)]. The broad applications of the inpainting models are demonstrated through restoring scratched old photos, disocclusion in vision analysis, text removal, digital zooming, and edge-based image coding.
Kernel regression for image processing and reconstruction
- IEEE TRANSACTIONS ON IMAGE PROCESSING
, 2007
"... In this paper, we make contact with the field of nonparametric statistics and present a development and generalization of tools and results for use in image processing and reconstruction. In particular, we adapt and expand kernel regression ideas for use in image denoising, upscaling, interpolation, ..."
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Cited by 172 (53 self)
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In this paper, we make contact with the field of nonparametric statistics and present a development and generalization of tools and results for use in image processing and reconstruction. In particular, we adapt and expand kernel regression ideas for use in image denoising, upscaling, interpolation, fusion, and more. Furthermore, we establish key relationships with some popular existing methods and show how several of these algorithms, including the recently popularized bilateral filter, are special cases of the proposed framework. The resulting algorithms and analyses are amply illustrated with practical examples.
Variational Restoration Of Nonflat Image Features: Models And Algorithms
, 2000
"... We develop both mathematical models and computational algorithms for variational denoising and restoration of nonflat image features. Nonflat image features are those that live on Riemannian manifolds, instead of on the Euclidean spaces. Familiar examples include the orientation feature (from optica ..."
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Cited by 89 (13 self)
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We develop both mathematical models and computational algorithms for variational denoising and restoration of nonflat image features. Nonflat image features are those that live on Riemannian manifolds, instead of on the Euclidean spaces. Familiar examples include the orientation feature (from optical flows or gradient flows) that lives on the unit circle S¹, the alignment feature (from fingerprint waves or certain texture images) that lives on the real projective line RP¹ and the chromaticity feature (from color images) that lives on the unit sphere S². In this paper, we apply the variational method to denoise and restore general nonflat image features. Mathematical models for both continuous image domains and discrete domains (or graphs) are constructed. Riemannian objects such as metric, distance and Levi-Civita connection play important roles in the models. Computational algorithms are also developed for the resulting nonlinear equations. The mathematical framework can be applied to restoring general nonflat data outside the scope of image processing and computer vision.
A Common Framework for Nonlinear Diffusion, Adaptive Smoothing, Bilateral Filtering and Mean Shift
, 2004
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Local adaptivity to variable smoothness for exemplar-based image denoising and representation
, 2005
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Multi-frame demosaicing and super-resolution of color images
- IEEE Trans. on Image Processing
, 2006
"... In the last two decades, two related categories of problems have been studied independently in the image restoration literature: super-resolution and demosaicing. A closer look at these problems reveals the relation between them, and as conventional color digital cameras suffer from both low-spatial ..."
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Cited by 53 (8 self)
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In the last two decades, two related categories of problems have been studied independently in the image restoration literature: super-resolution and demosaicing. A closer look at these problems reveals the relation between them, and as conventional color digital cameras suffer from both low-spatial resolution and color-filtering, it is reasonable to address them in a unified context. In this paper, we propose a fast and robust hybrid method of super-resolution and demosaicing, based on a MAP estimation technique by minimizing a multi-term cost function. The L 1 norm is used for measuring the difference between the projected estimate of the high-resolution image and each low-resolution image, removing outliers in the data and errors due to possibly inaccurate motion estimation. Bilateral regularization is used for spatially regularizing the luminance component, resulting in sharp edges and forcing interpolation along the edges and not across them. Simultaneously, Tikhonov regularization is used to smooth the chrominance components. Finally, an additional regularization term is used to force similar edge location and orientation in different color channels. We show that the minimization of the total cost function is relatively easy and fast. Experimental results on synthetic and real data sets confirm the effectiveness of
Augmented Lagrangian method, dual methods, and split Bregman iteration for ROF, vectorial TV, and high order models
- SIAM Journal on Imaging Sciences
"... E. Fatemi, Physica D, 60(1992), pp. 259–268] based on total variation (TV) minimization has proven to be very useful. A lot of efforts have been devoted to obtain fast numerical schemes and overcome the non-differentiability of the model. Methods considered to be particularly efficient for the ROF m ..."
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Cited by 51 (10 self)
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E. Fatemi, Physica D, 60(1992), pp. 259–268] based on total variation (TV) minimization has proven to be very useful. A lot of efforts have been devoted to obtain fast numerical schemes and overcome the non-differentiability of the model. Methods considered to be particularly efficient for the ROF model include the dual methods of Chan-Golub-Mulet (CGM) [T.F. Chan, G.H. Golub, and P. Mulet, SIAM J. Sci. Comput., 20(1999), pp. 1964–1977] and Chambolle [A. Chambolle, J. Math. Imaging
Signal Restoration with Overcomplete Wavelet Transforms: Comparison of Analysis and Synthesis Priors
"... The variational approach to signal restoration calls for the minimization of a cost function that is the sum of a data fidelity term and a regularization term, the latter term constituting a ‘prior’. A synthesis prior represents the sought signal as a weighted sum of ‘atoms’. On the other hand, an a ..."
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Cited by 47 (5 self)
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The variational approach to signal restoration calls for the minimization of a cost function that is the sum of a data fidelity term and a regularization term, the latter term constituting a ‘prior’. A synthesis prior represents the sought signal as a weighted sum of ‘atoms’. On the other hand, an analysis prior models the coefficients obtained by applying the forward transform to the signal. For orthonormal transforms, the synthesis prior and analysis prior are equivalent; however, for overcomplete transforms the two formulations are different. We compare analysis and synthesis ℓ1-norm regularization with overcomplete transforms for denoising and deconvolution.
