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Fast Singular Value Shrinkage With Chebyshev Polynomial Approximation Based on Signal Sparsity

Masaki Onuki, Shunsuke Ono, Keiichiro Shirai, Yuichi Tanaka
2017 IEEE Transactions on Signal Processing  

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2017 pre-print arXiv:1705.07112v1 fatcat:6lqvrhaa3bgpjadi4l5dh7i3hu
We propose an approximation method for thresholding of singular values using Chebyshev polynomial approximation (CPA).  ...  Experimental results suggest the effectiveness of our method through several image processing applications based on matrix rank minimization with nuclear norm relaxation in terms of computation time and  ...  SINGULAR VALUE SHRINKAGE USING CHEBYSHEV POLYNOMIAL APPROXIMATION BY EXPLOITING SPARSITY We discuss singular value shrinkage using CPA.  ... 
doi:10.1109/tsp.2017.2745444 fatcat:fl3mmwqoenf5beqmj6nxfmvqc4
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Masaki Onuki, Shunsuke Ono, Keiichiro Shirai, Yuichi Tanaka. "Fast Singular Value Shrinkage With Chebyshev Polynomial Approximation Based on Signal Sparsity." IEEE Transactions on Signal Processing 65.22 (2017) 6083-6096

Using $$\ell _1$$ ℓ 1 Regularization to Improve Numerical Partial Differential Equation Solvers

Theresa Scarnati, Anne Gelb, Rodrigo B. Platte
2017 Journal of Scientific Computing  

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We present our results on one and two dimensional examples using both finite difference and spectral methods as underlying PDE solvers.  ...  In this paper we investigate the use of 1 regularization to promote sparsity in the shock locations of hyperbolic PDEs.  ...  With this technique, the spatial scheme is updated based on the given spatial location and the dynamics of the system at a given time.  ... 
doi:10.1007/s10915-017-0530-8 fatcat:le75xjkpwjeffaonyxce46xc2a
Citation

Theresa Scarnati, Anne Gelb, Rodrigo B. Platte. "Using $$\ell _1$$ ℓ 1 Regularization to Improve Numerical Partial Differential Equation Solvers." Journal of Scientific Computing 75.1 (2017) 225-252

Hybrid hyperinterpolation over general regions [article]

Congpei An, Jia-Shu Ran, Alvise Sommariva
2023 arXiv   pre-print

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2023 pre-print arXiv:2305.05863v2 fatcat:yhe2yu3qnbfyffb7jjb3z45b34

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2023 pre-print
arXiv:2305.05863v1 fatcat:43ttz2jvazbfrc6emy35zx626m
of coefficients ranges from one to large values.  ...  Hybrid hyperinterpolation, using a soft thresholding operator and a filter function to shrink the Fourier coefficients approximated by a high-order quadrature rule of a given continuous function with respect  ...  This research has been accomplished within the RITA "Research ITalian network on Approximation", the SIMAI Activity Group ANA&A, and the UMI Group TAA "Approximation Theory and Applications" (A.  ... 
arXiv:2305.05863v3 fatcat:aveuqksurjgmpe3oswwyuewave
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Congpei An, Jia-Shu Ran, Alvise Sommariva. "Hybrid hyperinterpolation over general regions." arXiv (2023)

Polynomial Preconditioners for Regularized Linear Inverse Problems [article]

Siddharth Srinivasan Iyer, Frank Ong, Xiaozhi Cao, Congyu Liao, Luca Daniel, Jonathan I. Tamir, Kawin Setsompop
2022 arXiv   pre-print

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2022 pre-print
arXiv:2204.10252v1 fatcat:m6s2hirbpjct5pdbs6lbgr2ryy
2022 pre-print
arXiv:2204.10252v2 fatcat:wlhn5doeqras3bq5o2gig5dgum
This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal operator derived from the linear operator.  ...  The preconditioner does not assume any explicit structure on the linear function and thus can be deployed in diverse applications of interest.  ...  However, defining r(z) = 1 − q(z)z, and using Chebyshev polynomials to determine r yields a polynomial with r(z) = 1 for multiple values of z ∈ [0, 1] due to the constraint r(0) = 1, which implies the  ... 
arXiv:2204.10252v3 fatcat:dvnqc4ma3naehasqyoyvfoneam
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Siddharth Srinivasan Iyer, Frank Ong, Xiaozhi Cao, Congyu Liao, Luca Daniel, Jonathan I. Tamir, Kawin Setsompop. "Polynomial Preconditioners for Regularized Linear Inverse Problems." arXiv (2022)

Graph Spectral Image Processing [article]

Gene Cheung, Enrico Magli, Yuichi Tanaka, Michael Ng
2018 arXiv   pre-print

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2018 pre-print
arXiv:1801.04749v1 fatcat:jt65xdbzwjdfbor2rhu6eb63iy
one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain.  ...  Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then  ...  Finally, fast implementation of graph filters using Chebyshev polynomial approximation is discussed.  ... 
arXiv:1801.04749v2 fatcat:emorqmvkinf2tnaccvup3ot4fi
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Gene Cheung, Enrico Magli, Yuichi Tanaka, Michael Ng. "Graph Spectral Image Processing." arXiv (2018)

A unified approach to sparse signal processing

Farokh Marvasti, Arash Amini, Farzan Haddadi, Mehdi Soltanolkotabi, Babak Khalaj, Akram Aldroubi, Saeid Sanei, Jonathon Chambers
2012 EURASIP Journal on Advances in Signal Processing  

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The methods of Prony, Pisarenko, and MUltiple SIgnal Classification (MUSIC) are next shown to be targeted at analyzing signals with sparse frequency domain representations.  ...  A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited.  ...  Sampling of signals with finite rate of innovation (row 7) is related to piecewise smooth (polynomial based) signals.  ... 
doi:10.1186/preaccept-1686979482577015 fatcat:7zjru2zjpne3rceluc5empoanq
DOAJ
Citation

Farokh Marvasti, Arash Amini, Farzan Haddadi, Mehdi Soltanolkotabi, Babak Khalaj, Akram Aldroubi, Saeid Sanei, Jonathon Chambers. "A unified approach to sparse signal processing." EURASIP Journal on Advances in Signal Processing (2012) 44

A unified approach to sparse signal processing

Farokh Marvasti, Arash Amini, Farzan Haddadi, Mahdi Soltanolkotabi, Babak Hossein Khalaj, Akram Aldroubi, Saeid Sanei, Janathon Chambers
2012 EURASIP Journal on Advances in Signal Processing  

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The methods of Prony, Pisarenko, and MUltiple SIgnal Classification (MUSIC) are next shown to be targeted at analyzing signals with sparse frequency domain representations.  ...  A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited.  ...  Sampling of signals with finite rate of innovation (row 7) is related to piecewise smooth (polynomial based) signals.  ... 
doi:10.1186/1687-6180-2012-44 fatcat:sbby5qh65bh5jd57i567br7el4
DOAJ
Citation

Farokh Marvasti, Arash Amini, Farzan Haddadi, Mahdi Soltanolkotabi, Babak Hossein Khalaj, Akram Aldroubi, Saeid Sanei, Janathon Chambers. "A unified approach to sparse signal processing." EURASIP Journal on Advances in Signal Processing 2012.1 (2012)

The Reconstruction of Magnetic Particle Imaging: Current Approaches Based on the System Matrix

Xiaojun Chen, Zhenqi Jiang, Xiao Han, Xiaolin Wang, Xiaoying Tang
2021 Diagnostics  

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on the improved methods, SM-based MPI reconstruction methods to subtract the background signal, SM-based MPI reconstruction approaches to expand the spatial coverage, and matrix transformations to accelerate  ...  In this review, we compared and grouped different studies on the above issues, including SM-based MPI reconstruction based on the state-of-the-art Tikhonov regularization, SM-based MPI reconstruction based  ...  In 2009, Rahmer studied the structure and properties of the SF used for image reconstruction and proposed to replace the SF based on calibration or measurement with an SF based on Chebyshev polynomial  ... 
doi:10.3390/diagnostics11050773 pmid:33925830 fatcat:onbi5slykbcb3jyyglkkfiflim
DOAJ
Citation

Xiaojun Chen, Zhenqi Jiang, Xiao Han, Xiaolin Wang, Xiaoying Tang. "The Reconstruction of Magnetic Particle Imaging: Current Approaches Based on the System Matrix." Diagnostics 11.5 (2021)

Coherent-Like Integration for PD Radar Target Detection Based on Short-Time Fourier Transform

Xiao-wei Zhang, Lei Zuo, Dongdong Yang, Jian-Xin Guo
2019 IET radar, sonar & navigation  

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Furthermore, the experiments based on raw data are conducted to illustrate the performance of the proposed detector.  ...  be compared with the detection threshold.  ...  Finally, SVD can be achieved by using the fast singular value shrinkage with Chebyshev polynomial approximation and its computation complexity is represented as O Fig. 3 3 Frame of the experiments 5.1.1  ... 
doi:10.1049/iet-rsn.2019.0190 fatcat:5hakrlonsjbohah47bhv2k3eyy
DOAJ
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Xiao-wei Zhang, Lei Zuo, Dongdong Yang, Jian-Xin Guo. "Coherent-Like Integration for PD Radar Target Detection Based on Short-Time Fourier Transform." IET radar, sonar & navigation 14.1 (2019)

Patch-based models and algorithms for image denoising: a comparative review between patch-based images denoising methods for additive noise reduction

Monagi H. Alkinani, Mahmoud R. El-Sakka
2017 EURASIP Journal on Image and Video Processing  

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We first explain the type of noise in digital images and discuss various image denoising approaches, with a focus on patch-based denoising methods.  ...  Fast patch similarity measurements produce fast patch-based image denoising methods. Patch-based image denoising approaches can effectively reduce noise and enhance images.  ...  They proposed using iterative filtering with Chebyshev polynomial approximation (CPA) in order to collect the patches from the whole noisy image.  ... 
doi:10.1186/s13640-017-0203-4 pmid:32010201 pmcid:PMC6961526 fatcat:pvqyzmj36bejfle4dsz5fqqnii
DOAJ
Citation

Monagi H. Alkinani, Mahmoud R. El-Sakka. "Patch-based models and algorithms for image denoising: a comparative review between patch-based images denoising methods for additive noise reduction." EURASIP Journal on Image and Video Processing 2017.1 (2017) 58

A Survey of Sparse Representation: Algorithms and Applications

Zheng Zhang, Yong Xu, Jian Yang, Xuelong Li, David Zhang
2015 IEEE Access  

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2016 pre-print
arXiv:1602.07017v1 fatcat:zprmkmgmc5et3f7kektoagfsza
The available sparse representation algorithms can also be empirically categorized into four groups: greedy strategy approximation, constrained optimization, proximity algorithm-based optimization, and  ...  For example, in terms of different norm minimizations used in sparsity constraints, the methods can be roughly categorized into five groups: sparse representation with l_0-norm minimization, sparse representation  ...  FAST ITERATIVE SHRINKAGE THRESHOLDING ALGORITHM (FISTA) The fast iterative shrinkage thresholding algorithm (FISTA) is an improvement of ISTA.  ... 
doi:10.1109/access.2015.2430359 fatcat:fdi57s5xxfc3jekrgbgxigkt2q
DOAJ Multiple Versions
Citation

Zheng Zhang, Yong Xu, Jian Yang, Xuelong Li, David Zhang. "A Survey of Sparse Representation: Algorithms and Applications." IEEE Access (2015) 490-530

Sparse Modeling in Quantum Many-Body Problems [article]

Junya Otsuki, Masayuki Ohzeki, Hiroshi Shinaoka, Kazuyoshi Yoshimi
2019 arXiv   pre-print

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https://web.archive.org/web/20200824050630/https://arxiv.org/pdf/1911.04116v1.pdf

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Because the singular values decay exponentially with l, one may not need basis functions that correspond to small singular values below S α l /S α 0 < δ to express Green's function in practical calculations  ...  The standard method for approximately solving this optimization problem is K-SVD (SVD stands for singular value decomposition).  ... 
arXiv:1911.04116v1 fatcat:ci5xzw24czg4nlsh4bumc6loty
Citation

Junya Otsuki, Masayuki Ohzeki, Hiroshi Shinaoka, Kazuyoshi Yoshimi. "Sparse Modeling in Quantum Many-Body Problems." arXiv (2019)

Learning to solve TV regularized problems with unrolled algorithms [article]

Hamza Cherkaoui and Jeremias Sulam and Thomas Moreau
2020 arXiv   pre-print

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We validate those findings with experiments on synthetic and real data.  ...  Total Variation (TV) is a popular regularization strategy that promotes piece-wise constant signals by constraining the ℓ_1-norm of the first order derivative of the estimated signal.  ...  Acknowledgement We gratefully acknowledge discussions with Pierre Ablin, whose suggestions helped us completing some parts of the proofs. H. Cherkaoui is supported by a CEA PhD scholarship. J.  ... 
arXiv:2010.09545v1 fatcat:uhj5dfxuzfbede3j3mybhxixym
Citation

Hamza Cherkaoui and Jeremias Sulam and Thomas Moreau. "Learning to solve TV regularized problems with unrolled algorithms." arXiv (2020)

Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark [article]

Nora Lüthen, Stefano Marelli, Bruno Sudret
2021 arXiv   pre-print

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2021 pre-print
arXiv:2002.01290v2 fatcat:eidf4j6ri5f37etlljnumokb2u
2021 accepted
arXiv:2002.01290v4 fatcat:w6ajotfxe5gqvl3i5gdhlpsima
2020 pre-print
arXiv:2002.01290v1 fatcat:b7pt7vd2o5crrfkjg3dflb6mci
sparse regression solvers to approximate computer models with many input parameters, relying on only few model evaluations.  ...  Sparse polynomial chaos expansions are a popular surrogate modelling method that takes advantage of the properties of polynomial chaos expansions (PCE), the sparsity-of-effects principle, and powerful  ...  On one hand, A should include enough candidate polynomials to facilitate a good approximation.  ... 
arXiv:2002.01290v3 fatcat:bawss37oarczvdg5btxlmy2ng4
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Citation

Nora Lüthen, Stefano Marelli, Bruno Sudret. "Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark." arXiv (2021)

Sparse Modeling in Quantum Many-Body Problems

Junya Otsuki, Masayuki Ohzeki, Hiroshi Shinaoka, Kazuyoshi Yoshimi
2020 Journal of the Physical Society of Japan  

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(Color online) Graphical solution for L 1 -norm minimization, Eq. (4), with ðN; MÞ ¼ ð2; 1Þ.  ...  Because the singular values decay exponentially with l, one may not need basis functions that correspond to small singular values below S l =S 0 < to express Green's function in practical calculations  ...  0 (if the ranges of τ and ω are scaled properly). 85) Similarly to classical orthogonal polynomials such as Legendre and Chebyshev polynomials, all the available numerical data indicate that U l ðÞ and  ... 
doi:10.7566/jpsj.89.012001 fatcat:dw2v6sjvy5eyhoo4rca3um42bm
Citation

Junya Otsuki, Masayuki Ohzeki, Hiroshi Shinaoka, Kazuyoshi Yoshimi. "Sparse Modeling in Quantum Many-Body Problems." Journal of the Physical Society of Japan 89.1 (2020) 012001

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