메뉴 건너뛰기




Volumn 62, Issue 9, 2014, Pages 2317-2329

L1/2 regularization: Convergence of iterative half thresholding algorithm

Author keywords

Convergence; iterative half thresholding algorithm; nonconvex regularization

Indexed keywords

ALGORITHMS;

EID: 84898680921     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2014.2309076     Document Type: Article
Times cited : (162)

References (53)
  • 1
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol.52, no. 4, pp. 1289-1306, 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.4 , pp. 1289-1306
    • Donoho, D.L.1
  • 2
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • DOI 10.1109/TIT.2005.862083
    • E. J. Candès, J. Romberg, and T. Tao, "Robust uncertainty principles:Exact signal reconstruction from highly incomplete frequency information,"IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 489-509, 2006. (Pubitemid 43174093)
    • (2006) IEEE Transactions on Information Theory , vol.52 , Issue.2 , pp. 489-509
    • Candes, E.J.1    Romberg, J.2    Tao, T.3
  • 3
    • 29144439194 scopus 로고    scopus 로고
    • Decoding by linear programming
    • DOI 10.1109/TIT.2005.858979
    • E. J. Candès and T. Tao, "Decoding by linear programming," IEEETrans. Inf. Theory, vol. 51, no. 12, pp. 4203-4215, 2005. (Pubitemid 41800353)
    • (2005) IEEE Transactions on Information Theory , vol.51 , Issue.12 , pp. 4203-4215
    • Candes, E.J.1    Tao, T.2
  • 6
    • 80051736221 scopus 로고    scopus 로고
    • Structured compressed sensing: Fromtheory to applications
    • M. F. Duarte and Y. C. Eldar, "Structured compressed sensing: Fromtheory to applications," IEEE Trans. Signal Process., vol. 59, no. 9, pp.4053-4085, 2011.
    • (2011) IEEE Trans. Signal Process. , vol.59 , Issue.9 , pp. 4053-4085
    • Duarte, M.F.1    Eldar, Y.C.2
  • 7
    • 84864319384 scopus 로고    scopus 로고
    • Sparse microwave imaging:Principles and applications
    • B. C. Zhang, W. Hong, and Y. R. Wu, "Sparse microwave imaging:Principles and applications," Sci. China Inf. Sci., vol. 55, pp.1722-1754, 2012.
    • (2012) Sci. China Inf. Sci. , vol.55 , pp. 1722-1754
    • Zhang, B.C.1    Hong, W.2    Wu, Y.R.3
  • 8
    • 0029291966 scopus 로고
    • Sparse approximate solutions to linear systems,"
    • B. K. Natarajan, "Sparse approximate solutions to linear systems,"SIAM J. Comput., vol. 24, pp. 227-234, 1995.
    • (1995) SIAM J. Comput. , vol.24 , pp. 227-234
    • Natarajan, B.K.1
  • 9
    • 85194972808 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the lasso
    • R. Tibshirani, "Regression shrinkage and selection via the lasso," J.Roy. Statist. Soc, Series B (Methodolog.), vol. 58, no. 1, pp. 267-288,1996.
    • (1996) J.Roy. Statist. Soc, Series B (Methodolog.) , vol.58 , Issue.1 , pp. 267-288
    • Tibshirani, R.1
  • 11
    • 33646479497 scopus 로고    scopus 로고
    • High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension
    • DOI 10.1007/s00454-005-1220-0
    • D. L. Donoho, "High-dimensional centrally symmetric polytopes withneighborliness proportional to dimension," Discrete Comput. Geometry,vol. 35, no. 4, pp. 617-652, 2006. (Pubitemid 43701356)
    • (2006) Discrete and Computational Geometry , vol.35 , Issue.4 , pp. 617-652
    • Donoho, D.L.1
  • 12
    • 85014561619 scopus 로고    scopus 로고
    • A fast iterative shrinkage-thresholding algorithmfor linear inverse problems
    • A. Beck and M. Teboulle, "A fast iterative shrinkage-thresholding algorithmfor linear inverse problems," SIAM J. Image Sci., vol. 2, no. 1,pp. 183-202, 2009.
    • (2009) SIAM J. Image Sci. , vol.2 , Issue.1 , pp. 183-202
    • Beck, A.1    Teboulle, M.2
  • 14
    • 84880544524 scopus 로고    scopus 로고
    • Sparse methods for biomedical data
    • J. Ye and J. Liu, "Sparse methods for biomedical data," ACM SIGKDDExplorat. Newslett., vol. 14, no. 1, pp. 4-15, 2012.
    • (2012) ACM SIGKDDExplorat. Newslett. , vol.14 , Issue.1 , pp. 4-15
    • Ye, J.1    Liu, J.2
  • 15
    • 57349174008 scopus 로고    scopus 로고
    • Enhancing sparsity byreweighted minimization
    • E. J. Candès, M. B. Wakinm, and S. P. Boyd, "Enhancing sparsity byreweighted minimization," J. Fourier Anal. Appl., vol. 14, no. 5, pp.877-905, 2008.
    • (2008) J. Fourier Anal. Appl. , vol.14 , Issue.5 , pp. 877-905
    • Candès, E.J.1    Wakinm, M.B.2    Boyd, S.P.3
  • 16
    • 77951191949 scopus 로고    scopus 로고
    • Analysis of multi-stage convex relaxation for sparse regularization
    • T. Zhang, "Analysis of multi-stage convex relaxation for sparse regularization,"J. Mach. Learn. Res., vol. 11, pp. 1081-1107, 2010.
    • (2010) J. Mach. Learn. Res. , vol.11 , pp. 1081-1107
    • Zhang, T.1
  • 17
    • 34548724437 scopus 로고    scopus 로고
    • Exact reconstruction of sparse signals via nonconvex minimization
    • DOI 10.1109/LSP.2007.898300
    • R. Chartrand, "Exact reconstruction of sparse signals via nonconvexminimization," IEEE Signal Process. Lett., vol. 14, no. 10, pp.707-710, 2007. (Pubitemid 47434090)
    • (2007) IEEE Signal Processing Letters , vol.14 , Issue.10 , pp. 707-710
    • Chartrand, R.1
  • 18
    • 44449127493 scopus 로고    scopus 로고
    • Restricted isometry properties and nonconvexcompressive sensing
    • R. Chartrand and V. Staneva, "Restricted isometry properties and nonconvexcompressive sensing," Inverse Problems, vol. 24, pp. 1-14,2008.
    • (2008) Inverse Problems , vol.24 , pp. 1-14
    • Chartrand, R.1    Staneva, V.2
  • 20
    • 84871085657 scopus 로고    scopus 로고
    • Regularization:A thresholding representation theory and a fast solver
    • Z. B. Xu, X. Y. Chang, F. M. Xu, and H. Zhang, " regularization:A thresholding representation theory and a fast solver," IEEE Trans.Neural Netw. Learn. Syst., vol. 23, no. 7, pp. 1013-1027, 2012.
    • (2012) IEEE Trans.Neural Netw. Learn. Syst. , vol.23 , Issue.7 , pp. 1013-1027
    • Xu, Z.B.1    Chang, X.Y.2    Xu, F.M.3    Zhang, H.4
  • 21
    • 84865551389 scopus 로고    scopus 로고
    • The representationof regularizer among regularizer: An experimentalstudy based on phase diagram
    • Z. B. Xu, H. L. Guo, Y. Wang, and H. Zhang, "The representationof regularizer among regularizer: An experimentalstudy based on phase diagram," Acta Autom. Sin., vol. 38, pp.1225-1228, 2012.
    • (2012) Acta Autom. Sin. , vol.38 , pp. 1225-1228
    • Xu, Z.B.1    Guo, H.L.2    Wang, Y.3    Zhang, H.4
  • 23
    • 84869878642 scopus 로고    scopus 로고
    • Fast image deconvolution usingclosed-form thresholding formulas of Lq regularization
    • W. F. Cao, J. Sun, and Z. B. Xu, "Fast image deconvolution usingclosed-form thresholding formulas of Lq regularization,"J. Vis. Commun. Image Represent., vol. 24, no. 1, pp. 1529-1542,2013.
    • (2013) J. Vis. Commun. Image Represent. , vol.24 , Issue.1 , pp. 1529-1542
    • Cao, W.F.1    Sun, J.2    Xu, Z.B.3
  • 24
    • 80455174031 scopus 로고    scopus 로고
    • Hyperspectralunmixing via sparsity-constrained nonnegative matrix factorization
    • Y. T. Qian, S. Jia, J. Zhou, and A. Robles-Kelly, " Hyperspectralunmixing via sparsity-constrained nonnegative matrix factorization,"IEEE Trans. Geosci. Remote Sens., vol. 49, no. 11, pp.4282-4297, 2011.
    • (2011) IEEE Trans. Geosci. Remote Sens. , vol.49 , Issue.11 , pp. 4282-4297
    • Qian, Y.T.1    Jia, S.2    Zhou, J.3    Robles-Kelly, A.4
  • 25
    • 84864296909 scopus 로고    scopus 로고
    • Sparse SAR imaging based onregularization
    • J. S. Zeng, J. Fang, and Z. B. Xu, "Sparse SAR imaging based onregularization," Sci. China Inf. Sci., vol. 55, pp. 1755-1775,2012.
    • (2012) Sci. China Inf. Sci. , vol.55 , pp. 1755-1775
    • Zeng, J.S.1    Fang, J.2    Xu, Z.B.3
  • 26
    • 84874939443 scopus 로고    scopus 로고
    • Acceleratedregularization based SAR imaging via BCR and reducedNewton skills
    • J. S. Zeng, Z. B. Xu, B. C. Zhang, W. Hong, and Y. R.Wu, "Acceleratedregularization based SAR imaging via BCR and reducedNewton skills," Signal Process., vol. 93, pp. 1831-1844, 2013.
    • (2013) Signal Process. , vol.93 , pp. 1831-1844
    • Zeng, J.S.1    Xu, Z.B.2    Zhang, B.C.3    Hong, W.4    Wu, Y.R.5
  • 27
    • 84876145996 scopus 로고    scopus 로고
    • Fractional normregularization: Learning with very few relevantfeatures
    • A. Kaban, "Fractional normregularization: Learning with very few relevantfeatures," IEEE Trans. Neural Netw. Learn. Syst., vol. 24, no. 6,pp. 953-963, 2013.
    • (2013) IEEE Trans. Neural Netw. Learn. Syst. , vol.24 , Issue.6 , pp. 953-963
    • Kaban, A.1
  • 28
    • 84875640374 scopus 로고    scopus 로고
    • Sparse kernel logistic regressionbased on regularization
    • (16) 10.1007/s11432-012-4679-3
    • C. Xu, Z. M. Peng, and W. F. Jing, "Sparse kernel logistic regressionbased on regularization," Sci. China Inf. Sci., vol. 56, no. 4, p.042308(16), 2013, 10.1007/s11432-012-4679-3.
    • (2013) Sci. China Inf. Sci. , vol.56 , Issue.4 , pp. 042308
    • Xu, C.1    Peng, Z.M.2    Jing, W.F.3
  • 29
    • 84879049361 scopus 로고    scopus 로고
    • Sparse logistic regression with a L1/2 penalty for geneselection in cancer classification
    • 10.1186/1471-2105-14-198
    • Y. Liang, C. Liu, X. Z. Luan, K. S. Leung, T. M. Chan, Z. B. Xu,and H. Zhang, "Sparse logistic regression with a L1/2 penalty for geneselection in cancer classification," in Proc. BMC Bioinformatics 2013,vol. 14, p. 198, 10.1186/1471-2105-14-198.
    • Proc. BMC Bioinformatics 2013 , vol.14 , pp. 198
    • Liang, Y.1    Liu, C.2    Luan, X.Z.3    Leung, K.S.4    Chan, T.M.5    Xu, Z.B.6    Zhang, H.7
  • 30
    • 84855570036 scopus 로고    scopus 로고
    • Eliminating verticalstrip defects on silicon steel surface by regularization
    • 10.1155/2011/854674, Article ID 854674
    • W. F. Jing, D. Y. Meng, C. Qiao, and Z.M. Peng, "Eliminating verticalstrip defects on silicon steel surface by regularization," Math.Problems Eng., p. 13, 2011, 10.1155/2011/854674, Article ID 854674.
    • (2011) Math.Problems Eng. , pp. 13
    • Jing, W.F.1    Meng, D.Y.2    Qiao, C.3    Peng, Z.M.4
  • 31
    • 57349100926 scopus 로고    scopus 로고
    • Linear convergence of iterative softthresholding
    • K. Bredies and D. A. Lorenz, "Linear convergence of iterative softthresholding,"J. Fourier Anal. Appl., vol. 14, pp. 813-837, 2008.
    • (2008) J. Fourier Anal. Appl. , vol.14 , pp. 813-837
    • Bredies, K.1    Lorenz, D.A.2
  • 32
    • 57349145416 scopus 로고    scopus 로고
    • Iterative thresholding for sparse approximation
    • T. Blumensath and M. E. Davies, "Iterative thresholding for sparse approximation,"J. Fourier Anal. Appl., vol. 14, no. 5, pp. 629-654, 2008.
    • (2008) J. Fourier Anal. Appl. , vol.14 , Issue.5 , pp. 629-654
    • Blumensath, T.1    Davies, M.E.2
  • 33
    • 7044231546 scopus 로고    scopus 로고
    • An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
    • DOI 10.1002/cpa.20042
    • I. Daubechies, M. Defries, and C. De Mol, "An iterative thresholdingalgorithm for linear inverse problems with a sparsity constraint,"Comm. Pure Appl. Math., vol. 57, pp. 1413-1457, 2004. (Pubitemid 39427442)
    • (2004) Communications on Pure and Applied Mathematics , vol.57 , Issue.11 , pp. 1413-1457
    • Daubechies, I.1    Defrise, M.2    De Mol, C.3
  • 34
    • 84870050604 scopus 로고    scopus 로고
    • Sparse recovery algorithms: Sufficient conditions in termsof restricted isometry constants
    • Springer Proceedings in Mathematics, San Antonio, TX, USA, 2010
    • S. Foucart, "Sparse recovery algorithms: Sufficient conditions in termsof restricted isometry constants," in Proc. Approximation Theory XIII,Springer Proceedings in Mathematics, San Antonio, TX, USA, 2010,vol. 13, pp. 65-77.
    • Proc. Approximation Theory XIII , vol.13 , pp. 65-77
    • Foucart, S.1
  • 37
    • 84898677209 scopus 로고    scopus 로고
    • [Online]. Available
    • [Online]. Available: http://arxiv.org/abs/1103.4984
  • 39
    • 84898686257 scopus 로고    scopus 로고
    • [Online]. Available
    • [Online]. Available: http://arxiv.org/abs/1211.0665
  • 40
    • 52349092455 scopus 로고    scopus 로고
    • On sparse reconstruction from Fourierand Gaussian measurements
    • M. Rudelson and R. Vershynin, "On sparse reconstruction from Fourierand Gaussian measurements," Comm. Pure Appl. Math., vol. 61, pp.1025-1045, 2008.
    • (2008) Comm. Pure Appl. Math. , vol.61 , pp. 1025-1045
    • Rudelson, M.1    Vershynin, R.2
  • 41
    • 55649115527 scopus 로고    scopus 로고
    • A simpleproof of the restricted isometry property for random matrices
    • R. Baraniuk, M. Davenport, R. DeVore, and M. B. Wakin, "A simpleproof of the restricted isometry property for random matrices," Constr.Approx., vol. 28, pp. 253-263, 2008.
    • (2008) Constr.Approx. , vol.28 , pp. 253-263
    • Baraniuk, R.1    Davenport, M.2    Devore, R.3    Wakin, M.B.4
  • 42
    • 34548275795 scopus 로고    scopus 로고
    • The Dantzig selector: Stastical estimationwhen is much larger than
    • E. J. Candès and T. Tao, "The Dantzig selector: Stastical estimationwhen is much larger than ," Ann. Statist., vol. 35, no. 6, pp.2313-2351, 2007.
    • (2007) Ann. Statist. , vol.35 , Issue.6 , pp. 2313-2351
    • Candès, E.J.1    Tao, T.2
  • 43
    • 84879055175 scopus 로고    scopus 로고
    • Compressed sensing and affine rank minimizationunder restricted isometry
    • T. T. Cai and A. Zhang, "Compressed sensing and affine rank minimizationunder restricted isometry," IEEE Trans. Signal Process., vol.61, no. 13, pp. 3279-3290, 2013.
    • (2013) IEEE Trans. Signal Process. , vol.61 , Issue.13 , pp. 3279-3290
    • Cai, T.T.1    Zhang, A.2
  • 45
    • 84875260710 scopus 로고    scopus 로고
    • A hybrid simulated annealing thresholdingalgorithm for compressed sensing
    • F. M. Xu and S. H.Wang, "A hybrid simulated annealing thresholdingalgorithm for compressed sensing," Signal Process., vol. 93, pp.1577-1585, 2013.
    • (2013) Signal Process. , vol.93 , pp. 1577-1585
    • Xu, F.M.1    Wang, S.H.2
  • 46
    • 62549128663 scopus 로고    scopus 로고
    • Sparsest solutions of undertermined linearsystems via-minimization for
    • S. Foucart and M. J. Lai, "Sparsest solutions of undertermined linearsystems via-minimization for ," Appl. Comput. Harmon.Anal., vol. 26, pp. 395-407, 2009.
    • (2009) Appl. Comput. Harmon.Anal. , vol.26 , pp. 395-407
    • Foucart, S.1    Lai, M.J.2
  • 48
    • 84898686255 scopus 로고    scopus 로고
    • [Online]. Available
    • [Online].Available: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10. 1.1.156.9058
  • 50
    • 0031102203 scopus 로고    scopus 로고
    • Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm
    • I. F. Gorodnitsky and B. D. Rao, "Sparse signal reconstruction fromlimited data using FOCUSS: A re-weighted minimum norm algorithm,"IEEE Trans. Signal Process., vol. 45, no. 3, pp. 600-616, 1997. (Pubitemid 127765947)
    • (1997) IEEE Transactions on Signal Processing , vol.45 , Issue.3 , pp. 600-616
    • Gorodnitsky, I.F.1    Rao, B.D.2
  • 51
    • 77949704355 scopus 로고    scopus 로고
    • Iterativelyreweighted least squares minimization for sparse recovery
    • I. Daubechies, R. Devore,M. Fornasier, and C. S. Gunturk, "Iterativelyreweighted least squares minimization for sparse recovery," Comm.Pure Appl. Math., vol. 63, pp. 1-38, 2010.
    • (2010) Comm.Pure Appl. Math. , vol.63 , pp. 1-38
    • Daubechies, I.1    Devore, R.2    Fornasier, M.3    Gunturk, C.S.4
  • 52
    • 84898686256 scopus 로고    scopus 로고
    • Convergence of the reweighted minimizationalgorithm for minimization
    • to be published
    • X. Chen and W. Zhou, "Convergence of the reweighted minimizationalgorithm for minimization," Comput. Optim. Appl., 2013,to be published.
    • (2013) Comput. Optim. Appl.
    • Chen, X.1    Zhou, W.2
  • 53
    • 69949164527 scopus 로고    scopus 로고
    • Iterative hard thresholding for compressedsensing
    • T. Blumensath andM. E. Davies, "Iterative hard thresholding for compressedsensing," Appl. Comput. l Harmon. Anal., vol. 27, pp. 265-274,2008.
    • (2008) Appl. Comput. L Harmon. Anal. , vol.27 , pp. 265-274
    • Blumensath, T.1    Davies, M.E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.