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L 0-Norm and Total Variation for Wavelet Inpainting [chapter]

Andy C. Yau, Xue-Cheng Tai, Michael K. Ng
2009 Lecture Notes in Computer Science  
We propose a wavelet inpainting model by using L0-norm and the total variation (TV) minimization. Traditionally, L0-norm is replaced by L1-norm or L2-norm due to numerical difficulties.  ...  In this paper, we suggest an algorithm to recover an image whose wavelet coefficients are partially lost.  ...  Chan and Shen [6] proposed a total variation (TV) inpainting model which uses variational methods in inpainting.  ... 
doi:10.1007/978-3-642-02256-2_45 fatcat:6swfpwvfevcu3f3wphlx6p562m

Low Dimensional Manifold Regularization Based Blind Image Inpainting and Non-uniform Impulse Noise Recovery

Mei Gao, Baosheng Kang, Xiangchu Feng, Lixia Cao, Wenjuan Zhang
2020 IEEE Access  
Zuoqiang Shi for providing us with the original matlab code of his paper, which is convenient for our experiment .  ...  proposed the total variation (TV) model [14] . As a further improvement of the TV method, the curvaturedriven diffusions (CDD) inpainting model was developed by Chan et al. [15] .  ...  [30] proposed a method by which the 1 l norm of wavelet frame coefficients of images were used as the regularization term.  ... 
doi:10.1109/access.2020.3035532 fatcat:vxcgqqu3gnazzjdlzixgqwde2i

An Efficient Algorithm for ℓ 0 Minimization in Wavelet Frame Based Image Restoration

Bin Dong, Yong Zhang
2012 Journal of Scientific Computing  
This study reassures the feasibility of using the ℓ0 "norm" for image restoration problems.  ...  Recently in [10] , the authors propose to penalize the ℓ0 "norm" of the wavelet frame coefficients instead, and they have demonstrated significant improvements of their method over some commonly used ℓ1  ...  The trend of variational methods for image processing started with the refined Rudin-Osher-Fatemi (ROF) model [12] which penalizes the total variation (TV) of u.  ... 
doi:10.1007/s10915-012-9597-4 fatcat:5xv6pni5jjgfhd3hlfplus5mam

3-D Sparse Representations [chapter]

Francois Lanusse, Jean-Luc Starck, Arnaud Woiselle, M.Jalal Fadili
2014 Advances in Imaging and Electron Physics  
In particular, we describe 3D wavelets, ridgelets, beamlets and curvelets.  ...  Illustrative examples are provided for the different transforms.  ...  Inpainting has received considerable interest and excitement and has been attacked using diffusion and transport PDE/Variational principles, non-local exemplar region fill-in and sparsity-based regularization  ... 
doi:10.1016/b978-0-12-800265-0.00003-5 fatcat:fudih7tionatjctv5aqbb2orkq

Sampling theorems and compressive sensing on the sphere

J. D. McEwen, G. Puy, J.-Ph. Thiran, P. Vandergheynst, D. Van De Ville, Y. Wiaux
2011 arXiv   pre-print
A reduction in the number of samples required to represent a band-limited signal on the sphere has important implications for compressive sensing, both in terms of the dimensionality and sparsity of signals  ...  We illustrate the impact of this property with an inpainting problem on the sphere, where we show superior reconstruction performance when adopting the new sampling theorem.  ...  shown to improve the quality of compressive sampling reconstruction. 7 We review this very recent work, discussing the impact of efficient sampling on the sphere in the context of a total variation  ... 
arXiv:1110.6297v1 fatcat:gi2y5wngfvegddlktp4a3z6hh4

Group-Based Sparse Representation for Image Restoration

Jian Zhang, Debin Zhao, Wen Gao
2014 IEEE Transactions on Image Processing  
Extensive experiments on image inpainting, image deblurring and image compressive sensing recovery manifest that the proposed GSR modeling outperforms many current state-of-the-art schemes in both PSNR  ...  To make GSR tractable and robust, a split Bregman based technique is developed to solve the proposed GSR-driven 0 minimization problem for image restoration efficiently.  ...  GSR is compared with four representative CS recovery methods in literature, i.e., wavelet method (DWT), total variation (TV) method [41] , multi-hypothesis (MH) method [40] , collaborative sparsity (  ... 
doi:10.1109/tip.2014.2323127 pmid:24835225 fatcat:eteqjl354rc2baxoipue5vahai

Support Driven Wavelet Frame-based Image Deblurring [article]

Liangtian He, Yilun Wang, Zhaoyin Xiang
2016 arXiv   pre-print
The wavelet frame systems have been playing an active role in image restoration and many other image processing fields over the past decades, owing to the good capability of sparsely approximating piece-wise  ...  In this paper, we propose a novel wavelet frame based sparse recovery model called Support Driven Sparse Regularization (SDSR) for image deblurring, where the partial support information of frame coefficients  ...  The connection of wavelet frame based methods with variational and PDE based approaches is studied in [5] , [9] .  ... 
arXiv:1603.08108v1 fatcat:n6mlnf4kybe3bf4bbejkjrro7i

Group-based Sparse Representation for Image Restoration [article]

Jian Zhang, Debin Zhao, Wen Gao
2014 arXiv   pre-print
Extensive experiments on image inpainting, image deblurring and image compressive sensing recovery manifest that the proposed GSR modeling outperforms many current state-of-the-art schemes in both PSNR  ...  To make GSR tractable and robust, a split Bregman based technique is developed to solve the proposed GSR-driven minimization problem for image restoration efficiently.  ...  GSR is compared with four representative CS recovery methods in literature, i.e., wavelet method (DWT), total variation (TV) method [41] , multi-hypothesis (MH) method [40] , collaborative sparsity (  ... 
arXiv:1405.3351v1 fatcat:q6xz5rw5xrdjjiydojmnl6nsxy

ShearLab 3D

Gitta Kutyniok, Wang-Q Lim, Rafael Reisenhofer
2016 ACM Transactions on Mathematical Software  
Wavelets and their associated transforms are highly efficient when approximating and analyzing one-dimensional signals.  ...  , for instance, detecting their direction.  ...  Frobenius norm.  ... 
doi:10.1145/2740960 fatcat:t44mrn5ydbbtbgyrrplm55hh6i

Denoising Fast X-Ray Fluorescence Raster Scans of Paintings [article]

Henry Chopp, Alicia McGeachy, Matthias Alfeld, Oliver Cossairt, Marc Walton, Aggelos Katsaggelos
2022 arXiv   pre-print
Macro x-ray fluorescence (XRF) imaging of cultural heritage objects, while a popular non-invasive technique for providing elemental distribution maps, is a slow acquisition process in acquiring high signal-to-noise  ...  In an effort to reduce the scan times without sacrificing elemental map and XRF volume quality, we propose using dictionary learning with a Poisson noise model as well as a color image-based prior to restore  ...  Define a total variation (TV) regularizer that adapts to the RGB gradient by: TV Ã = H−1 h=1 W w=1 C c=1 Ω H h,w t 2 Ãh+1,w,c − Ãh,w,c 2 + H h=1 W −1 w=1 C c=1 Ω W h,w t 2 Ãh,w+1,c − Ãh,w,c 2 (4) where  ... 
arXiv:2206.01740v1 fatcat:vdsuqc7dtrg4zne4zcjiape7oi

Edge-Aware Gradient Domain Optimization Framework for Image Filtering by Local Propagation

Miao Hua, Xiaohui Bie, Minying Zhang, Wencheng Wang
2014 2014 IEEE Conference on Computer Vision and Pattern Recognition  
In this paper, we present new constraints explicitly to better preserve edges for general gradient domain image filtering and theoretically analyse why these constraints are edge-aware.  ...  Gradient domain methods are popular for image processing. However, these methods even the edge-preserving ones cannot preserve edges well in some cases.  ...  We present edge-aware constraints for improving the general gradient domain optimization framework and attest the superiority over existing methods in edge preserving.  ... 
doi:10.1109/cvpr.2014.363 dblp:conf/cvpr/HuaBZW14 fatcat:brrpud6dobcdzimueq63zfn4my

Dictionary learning approach for image deconvolution with variance estimation

Hang Yang, Ming Zhu, Xiaotian Wu, Zhongbo Zhang, Heyan Huang
2014 Applied Optics  
In this paper, we propose a new dictionary learning approach for image deconvolution, which effectively integrates the Fourier regularization and dictionary learning technique into the deconvolution framework  ...  In the denoising step, we propose an approach to update the estimation of noise variance for dictionary learning.  ...  (TVMM), and [6] total variation shrinkage (TVS).  ... 
doi:10.1364/ao.53.005677 pmid:25321363 fatcat:l5675tndirazbmnzdar3zct7cq

MPTV: Matching Pursuit-Based Total Variation Minimization for Image Deconvolution

Dong Gong, Mingkui Tan, Qinfeng Shi, Anton van den Hengel, Yanning Zhang
2019 IEEE Transactions on Image Processing  
Total variation (TV) regularization has proven effective for a range of computer vision tasks through its preferential weighting of sharp image edges.  ...  Relying on this new model, we propose a matching pursuit based total variation minimization method (MPTV), specifically for image deconvolution.  ...  Many kinds of regularizer Ω(·), such as the total variation (TV) norm [1] , wavelet frame-based sparse priors [2] and Gaussian mixture models [3] , have been proposed to handle different image restoration  ... 
doi:10.1109/tip.2018.2875352 pmid:30307866 fatcat:2bovgckgefclngpcxbjjh6hdvq

Tensor Least Angle Regression for Sparse Representations of Multidimensional Signals

Ishan Wickramasingha, Ahmed Elrewainy, Michael Sobhy, Sherif S. Sherif
2020 Neural Computation  
However, all of these methods are not suitable for solving large multidimensional sparse least-squares problems, as they would require extensive computational power and memory.  ...  However, its memory usage and computation time increase quickly with the number of problem dimensions and iterations.  ...  , and 𝜱𝜱 (4) to be a wavelet dictionary to obtain a time-frequency representation of temporal variations in video frames.  ... 
doi:10.1162/neco_a_01304 pmid:32687768 fatcat:3waxqaoghnafjlydao6zqlbjom

Compressive Sensing of Color Images Using Nonlocal Higher Order Dictionary [article]

Khanh Quoc Dinh, Thuong Nguyen Canh, Byeungwoo Jeon
2017 arXiv   pre-print
vector-based approach of the state-of-the-art methods, we exploit the nonlocal similarities inherently existing in images by treating each patch of a color image as a 3D tensor consisting of not only horizontal and  ...  A group of nonlocal similar patches form a 4D tensor for which a nonlocal higher order dictionary is learned via higher order singular value decomposition.  ...  (gradient, ℓ1 norm) [11] , FPD (trained dictionary, ℓ1 norm) [29] , GSR (nonlocal dictionary, ℓ0 norm) [15] , and NLR (nonlocal dictionary, log norm) [14] .  ... 
arXiv:1711.09375v1 fatcat:nm5ihsao4fa77l53miwenqy6yu
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