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Recovery of Discontinuous Signals Using Group Sparse Higher Degree Total Variation

Greg Ongie, Mathews Jacob
2015 IEEE Signal Processing Letters  
We also propose an extension to 2-D, which can be viewed as a group sparse version of higher degree total variation, and illustrate its effectiveness in denoising experiments.  ...  We introduce an efficient alternating minimization algorithm to solve linear inverse problems regularized with the proposed penalties.  ...  (f) Denoised with TgV regularization (SNR=26.8dB), (g) convex HDTV (SNR=26.7dB), (h) non-convex Co-HDTV (SNR=26.9dB), and (j) non-convex GS-HDTV (SNR=27.2dB).  ... 
doi:10.1109/lsp.2015.2407321 fatcat:xq7ddezw4rc73a36xtgihlllju

Convex 1-D Total Variation Denoising with Non-convex Regularization

Ivan W. Selesnick, Ankit Parekh, Ilker Bayram
2015 IEEE Signal Processing Letters  
A non-convex regularizer can promote sparsity more strongly, but generally leads to a non-convex optimization problem with non-optimal local minima.  ...  Conditions for a non-convex regularizer are given that ensure the total TV denoising objective function is convex. An efficient algorithm is given for the resulting problem.  ...  Example 1 Total variation denoising with convex and non-convex regularization is illustrated in Fig. 1 .  ... 
doi:10.1109/lsp.2014.2349356 fatcat:dhjn75rqlngflbkzwgopevctnu

Wavelet Shrinkage With Consistent Cycle Spinning Generalizes Total Variation Denoising

Ulugbek Kamilov, Emrah Bostan, Michael Unser
2012 IEEE Signal Processing Letters  
We introduce a new wavelet-based method for the implementation of Total-Variation-type denoising. The data term is least-squares, while the regularization term is gradient-based.  ...  We illustrate the performance of our method for image denoising and for the statistical estimation of sparse stochastic processes.  ...  By replacing the soft-thresholding function by another scalar function or by a precomputed lookup table, we can efficiently extend our algorithm beyond traditional regularizers to general, possibly non-convex  ... 
doi:10.1109/lsp.2012.2185929 fatcat:4yyfzzmxmvedjeknki4m7qmb3m

A novel denoising algorithm for medical images based on the non‐convex non‐local similar adaptive regularization

Lin Tian, Jiaqing Miao, Xiaobing Zhou, Chao Wang
2021 IET Image Processing  
This model is more efficient and accurate, Compared with K-means singular value decomposition (KSVD) algorithm, a generalized K-means clustering method, total variation of population sparsity (GSTV) algorithm  ...  Second, the sparse representation of an image introduces non-convex non-local self-similarity as the regularization term.  ...  Therefore, we hope to find a more efficient algorithm by using the high correlation between sparse coefficient and non-convex optimization.  ... 
doi:10.1049/ipr2.12138 fatcat:7vwnvsmy6vdazoowllty76uns4

Artifact-Free Wavelet Denoising: Non-convex Sparse Regularization, Convex Optimization

Yin Ding, Ivan W. Selesnick
2015 IEEE Signal Processing Letters  
Algorithms for signal denoising that combine wavelet-domain sparsity and total variation (TV) regularization are relatively free of artifacts, such as pseudo-Gibbs oscillations, normally introduced by  ...  At the same time, in order to draw on the advantages of convex optimization (unique minimum, reliable algorithms, simplified regularization parameter selection), the non-convex penalties are chosen so  ...  Powerful proximal algorithms have been developed for signal restoration with general hybrid regularization (including wavelet-TV) allowing constraints and non-Gaussian noise [32] .  ... 
doi:10.1109/lsp.2015.2406314 fatcat:mzjf5eq3sjeibij3a2rxjj5ff4

Simultaneous Low-Pass Filtering and Total Variation Denoising

Ivan W. Selesnick, Harry L. Graber, Douglas S. Pfeil, Randall L. Barbour
2014 IEEE Transactions on Signal Processing  
LTI filtering is most suitable for signals restricted to a known frequency band, while sparsity-based denoising is suitable for signals admitting a sparse representation with respect to a known transform  ...  A convex optimization approach is presented and two algorithms derived: one based on majorization-minimization (MM), and the other based on the alternating direction method of multipliers (ADMM).  ...  Weston (Oak Ridge Institute for Science and Education, TN) for providing experimental data used in LPF/TVD Example 2 and LPF/CSD Example 3.  ... 
doi:10.1109/tsp.2014.2298836 fatcat:eozfjm23w5h2heaaqnbmv3x5vu

Moreau-Enhanced Total Variation and Subspace Factorization for Hyperspectral Denoising

Yanhong Yang, Shengyong Chen, Jianwei Zheng
2020 Remote Sensing  
Recently, various prior knowledge has attracted much attention in HSI denoising, e.g., total variation (TV), low-rank, sparse representation, and so on.  ...  In this paper, we fully take advantage of the global spectral correlation of HSI and design a unified framework named subspace-based Moreau-enhanced total variation and sparse factorization (SMTVSF) for  ...  image denoising based on low-rank and sparse representations (FastHyDe) [46] , global matrix factorization and to local tensor factorizations method (GLF) [41] , spatial-spectral total variation regularized  ... 
doi:10.3390/rs12020212 fatcat:leauxhvv6behdksmyd4ep3vfba

Wasserstein Loss for Image Synthesis and Restoration

Guillaume Tartavel, Gabriel Peyré, Yann Gousseau
2016 SIAM Journal of Imaging Sciences  
This paper presents a novel variational approach to impose statistical constraints to the output of both image generation (to perform typically texture synthesis) and image restoration (for instance to  ...  achieve denoising and super-resolution) methods.  ...  We will see that such a framework is efficient to prevent some defaults of the total variation.  ... 
doi:10.1137/16m1067494 fatcat:vrbtvkvbxfdrplr42sk632ob5i

An Overview on Dictionary and Sparse Representation in Image Denoising

Mrs.S Subha, Mr. I Jesudass, Mrs.S Jeyasree
2014 IOSR Journal of Electronics and Communication Engineering  
A most applicable and expected property of an image denoising is that it should totally remove the noise as well as its preserve edges.  ...  This paper represents the review of parameter and algorithms available for image denoising.  ...  Total variation denoising In signal processing, total variation denoising, also known as ‗total variation regularization' is a process, most often used in digital image processing, that has applications  ... 
doi:10.9790/2834-09616570 fatcat:f2ztteyrxvfdxkspmpywh2h4rq

Hyperspectral Unmixing in the Presence of Mixed Noise Using Joint-Sparsity and Total Variation

Hemant Kumar Aggarwal, Angshul Majumdar
2016 IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing  
A total-variation based regularization has also been utilized for modeling smoothness of abundance maps.  ...  The unmixing model explicitly takes into account both Gaussian noise and sparse noise. The unmixing problem has been formulated to exploit joint-sparsity of abundance maps.  ...  Simultaneous utilization of both total-variation regularization and joint-sparse regularization is not redundant as both achieve different goals.  ... 
doi:10.1109/jstars.2016.2521898 fatcat:dsygey4jp5d5ro5fpru55kzaqu

Generalized Total Variation: Tying the Knots

Ivan W. Selesnick
2015 IEEE Signal Processing Letters  
This paper formulates a convex generalized total variation functional for the estimation of discontinuous piecewise linear signals from corrupted data.  ...  The proposed method refines the recent approach by Ongie and Jacob.  ...  Algorithms based on total variation (TV) regularization assume the signal of interest is piecewise constant; i.e., its derivative is sparse [30] .  ... 
doi:10.1109/lsp.2015.2449297 fatcat:4f5fivar6ndg5kiai6j2k26ngy

Guest editorial

Mario Bertero, Valeria Ruggiero, Luca Zanni
2013 Computational optimization and applications  
In the paper by Lenzen, Becker, Lellmann, Petra and Schnörr, the focus is a class of adaptive non-smooth convex variational problems for image denoising.  ...  total variation models.  ... 
doi:10.1007/s10589-013-9536-9 fatcat:wskd2oeyqvgxbog6lwigxky25e

Compressed sensing MRI with Bayesian dictionary learning

Xinghao Ding, John Paisley, Yue Huang, Xianbo Chen, Feng Huang, Xiao-ping Zhang
2013 2013 IEEE International Conference on Image Processing  
The proposed method incorporates spatial finite differences (total variation) and patch-wise sparsity through in situ dictionary learning.  ...  In addition, we employ an efficient numerical algorithm based on the alternating direction method of multipliers (ADMM). We present empirical results on two MR images.  ...  The regularization function h g (x) is the total variation of the image.  ... 
doi:10.1109/icip.2013.6738478 dblp:conf/icip/DingPHCHZ13 fatcat:3zktiferlzahvnzmoaytjicnee

Estimating Sparse Signals with Smooth Support via Convex Programming and Block Sparsity [article]

Sohil Shah, Tom Goldstein, Christoph Studer
2016 arXiv   pre-print
Conventional algorithms for sparse signal recovery and sparse representation rely on l_1-norm regularized variational methods.  ...  By exploiting the convexity of our regularizers, we develop new computationally-efficient recovery algorithms that guarantee global optimality.  ...  Shah and T. Goldstein  ... 
arXiv:1605.01813v1 fatcat:uvf37wr6lvhpjmnqgyakjixbjm

A Flexible Framework for Designing Trainable Priors with Adaptive Smoothing and Game Encoding [article]

Bruno Lecouat, Jean Ponce, Julien Mairal
2020 arXiv   pre-print
The priors used in this presentation include variants of total variation, Laplacian regularization, bilateral filtering, sparse coding on learned dictionaries, and non-local self similarities.  ...  We introduce a general framework for designing and training neural network layers whose forward passes can be interpreted as solving non-smooth convex optimization problems, and whose architectures are  ...  In the past, total variation has been widely used for MRI [30] , often in combination with sparse regularization in the wavelet domain. • Patch encoding on a dictionary with sparse coding: we solve a  ... 
arXiv:2006.14859v2 fatcat:nj7puapunnbu5eqenovg2sgitm
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