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Volumn 1, Issue 4, 2007, Pages 606-617

An interior-point method for large-scale ℓ1-regularized least squares

Author keywords

1 regularization; Basis pursuit denoising; Compressed sensing; Compressive sampling; Convex optimization; Interior point methods; Least squares; Preconditioned conjugate gradients

Indexed keywords

ALGORITHMS; MAGNETIC RESONANCE IMAGING; MATHEMATICAL PROGRAMMING; OPTIMIZATION; SAMPLING; SPURIOUS SIGNAL NOISE;

EID: 39449109476     PISSN: 19324553     EISSN: None     Source Type: Journal    
DOI: 10.1109/JSTSP.2007.910971     Document Type: Article
Times cited : (1991)

References (63)
  • 6
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate measurements
    • E. Candès, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pure Appl. Math. vol. 59, no. 8, pp. 1207-1223, 2005.
    • (2005) Commun. Pure Appl. Math , vol.59 , Issue.8 , pp. 1207-1223
    • Candès, E.1    Romberg, J.2    Tao, T.3
  • 7
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • Feb
    • E. 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, Feb. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.2 , pp. 489-509
    • Candès, E.1    Romberg, J.2    Tao, T.3
  • 8
    • 0035273106 scopus 로고    scopus 로고
    • Atomic decomposition by basis pursuit
    • S. Chen, D. Donoho, and M. Saunders, "Atomic decomposition by basis pursuit," SIAM Rev., vol. 43, no. 1, pp. 129-159, 2001.
    • (2001) SIAM Rev , vol.43 , Issue.1 , pp. 129-159
    • Chen, S.1    Donoho, D.2    Saunders, M.3
  • 9
    • 7044231546 scopus 로고    scopus 로고
    • An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
    • I. Daubechies, M. Defrise, and C. De Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Commun. Pure Appl. Mathe., vol. 57, pp. 1413-1541, 2004.
    • (2004) Commun. Pure Appl. Mathe , vol.57 , pp. 1413-1541
    • Daubechies, I.1    Defrise, M.2    De Mol, C.3
  • 11
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • Apr
    • D. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.4 , pp. 1289-1306
    • Donoho, D.1
  • 12
    • 33144483155 scopus 로고    scopus 로고
    • Stable recovery of sparse overcomplete representations in the presence of noise
    • Jan
    • D. Donoho, M. Elad, and V. Temlyakov, "Stable recovery of sparse overcomplete representations in the presence of noise," IEEE Trans. Inf. Theory, vol. 52, no. 1, pp. 6-18, Jan. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.1 , pp. 6-18
    • Donoho, D.1    Elad, M.2    Temlyakov, V.3
  • 14
    • 36348939980 scopus 로고    scopus 로고
    • 1-norm minimization problems when the solution may be sparse
    • Online, Available
    • 1-norm minimization problems when the solution may be sparse," Manuscript 2006 [Online]. Available: http://www.stanford.edu/
    • (2006) Manuscript
    • Donoho, D.1    Tsaig, Y.2
  • 18
    • 39449126969 scopus 로고    scopus 로고
    • Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems
    • M. Figueiredo, R. Nowak, and S. Wright, "Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems," IEEE J. Select. Topics Signal Process., 2007.
    • (2007) IEEE J. Select. Topics Signal Process
    • Figueiredo, M.1    Nowak, R.2    Wright, S.3
  • 19
    • 39449087210 scopus 로고    scopus 로고
    • J. Friedman, T. Hastie T, and R. Tibshirani, Pathwise Coordinate Optimization 2007 [Online]. Available: Www-stat.stanford.edu/hastie/ pub.htm
    • J. Friedman, T. Hastie T, and R. Tibshirani, Pathwise Coordinate Optimization 2007 [Online]. Available: Www-stat.stanford.edu/hastie/ pub.htm
  • 20
    • 26844461512 scopus 로고    scopus 로고
    • Recovery of exact sparse representations in the presence of noise
    • Oct
    • J. Fuchs, "Recovery of exact sparse representations in the presence of noise," IEEE Trans. Inf. Theory, vol. 51, no. 10, pp. 3601-3608, Oct. 2005.
    • (2005) IEEE Trans. Inf. Theory , vol.51 , Issue.10 , pp. 3601-3608
    • Fuchs, J.1
  • 21
    • 8744288576 scopus 로고    scopus 로고
    • Monotonic regression filters for trending gradual deterioration faults
    • D. Gorinevsky, "Monotonic regression filters for trending gradual deterioration faults," in Proc. American Control Conf. (ACC), 2004, pp. 5394-5399.
    • (2004) Proc. American Control Conf. (ACC) , pp. 5394-5399
    • Gorinevsky, D.1
  • 22
    • 39449103811 scopus 로고    scopus 로고
    • Optimal estimation of deterioration from diagnostic image sequence
    • Online, Available:, Available from, Submitted to
    • D. Gorinevsky, S.-J. Kim, S. Bear, S. Boyd, and G. Gordon, "Optimal estimation of deterioration from diagnostic image sequence," IEEE Trans. Signal Process. 2007 [Online]. Available: http:// www.stanford.edu/gorin/papers/MonoImage07twocol.pdf, Available from, Submitted to
    • (2007) IEEE Trans. Signal Process
    • Gorinevsky, D.1    Kim, S.-J.2    Bear, S.3    Boyd, S.4    Gordon, G.5
  • 23
    • 53349163971 scopus 로고    scopus 로고
    • 1 regularized minimization with applications to compressed sensing
    • Online, Available
    • 1 regularized minimization with applications to compressed sensing," Manuscript 2007 [Online]. Available: http://www.dsp.ece.rice.edu/cs/
    • (2007) Manuscript
    • Hale, E.1    Yin, W.2    Zhang, Y.3
  • 24
    • 84925605946 scopus 로고    scopus 로고
    • The entire regularization path for the support vector machine
    • T. Hastie, S. Rosset, R. Tibshirani, and J. Zhu, "The entire regularization path for the support vector machine," J. Mach. Learning Res., vol. 5, pp. 1391-1415, 2004.
    • (2004) J. Mach. Learning Res , vol.5 , pp. 1391-1415
    • Hastie, T.1    Rosset, S.2    Tibshirani, R.3    Zhu, J.4
  • 27
    • 0034164342 scopus 로고    scopus 로고
    • Interior point methodology for 3-D PET reconstruction
    • C. Johnson, J. Seidel, and A. Sofer, "Interior point methodology for 3-D PET reconstruction," IEEE Trans. Med. Imag., vol. 19, no. 4, pp. 271-285, 2000.
    • (2000) IEEE Trans. Med. Imag , vol.19 , Issue.4 , pp. 271-285
    • Johnson, C.1    Seidel, J.2    Sofer, A.3
  • 28
    • 0002914778 scopus 로고
    • Iterative methods for linear and nonlinear equations
    • SIAM: Philadelphia, PA
    • C. T. Kelley, "Iterative methods for linear and nonlinear equations," Frontiers in Applied Mathematics, vol. 16, 1995, SIAM: Philadelphia, PA.
    • (1995) Frontiers in Applied Mathematics , vol.16
    • Kelley, C.T.1
  • 29
    • 0034287156 scopus 로고    scopus 로고
    • Asymptotics for lasso-type estimators
    • K. Knight and W. Fu, "Asymptotics for lasso-type estimators," Ann. Statist., vol. 28, no. 5, pp. 1356-1378, 2000.
    • (2000) Ann. Statist , vol.28 , Issue.5 , pp. 1356-1378
    • Knight, K.1    Fu, W.2
  • 30
    • 34547688865 scopus 로고    scopus 로고
    • An interior-point method for l 1-regularized logistic regression
    • K. Koh, S.-J. Kim, and S. Boyd, "An interior-point method for l 1-regularized logistic regression," J. Mach. Learning Res., vol. 8, pp. 1519-1555, 2007.
    • (2007) J. Mach. Learning Res , vol.8 , pp. 1519-1555
    • Koh, K.1    Kim, S.-J.2    Boyd, S.3
  • 33
    • 33747163541 scopus 로고    scopus 로고
    • High-dimensional graphs and variable selection with the lasso
    • N. Meinshausen and P. Büuhlmann, "High-dimensional graphs and variable selection with the lasso," Ann. Statist., vol. 34, no. 3, pp. 1436-1462, 2006.
    • (2006) Ann. Statist , vol.34 , Issue.3 , pp. 1436-1462
    • Meinshausen, N.1    Büuhlmann, P.2
  • 34
    • 39449097158 scopus 로고    scopus 로고
    • The MOSEK Optimization Tools Version 2.5. User's Manual and Reference 2002 Online. Available: Www.mosek.com, MOSEK ApS Available from
    • The MOSEK Optimization Tools Version 2.5. User's Manual and Reference 2002 Online. Available: Www.mosek.com, MOSEK ApS Available from
  • 35
    • 39449086329 scopus 로고    scopus 로고
    • G. Narkiss and M. Zibulevsky, Sequential Subspace Optimization Method for Large-Scale Unconstrained Problems The Technion, Haifa, Israel, Tech. Rep. CCIT No 559, 2005.
    • G. Narkiss and M. Zibulevsky, Sequential Subspace Optimization Method for Large-Scale Unconstrained Problems The Technion, Haifa, Israel, Tech. Rep. CCIT No 559, 2005.
  • 36
    • 39449100138 scopus 로고    scopus 로고
    • Y. Nesterov, Gradient methods for minimizing composite objective function, 2007, CORE Discussion Paper 2007/76 [Online]. Available: http://www.optimization-online.org/DB_HTML/2007/09/1784.html
    • Y. Nesterov, "Gradient methods for minimizing composite objective function," 2007, CORE Discussion Paper 2007/76 [Online]. Available: http://www.optimization-online.org/DB_HTML/2007/09/1784.html
  • 37
    • 0003254248 scopus 로고
    • Interior-point polynomial methods in convex programming
    • SIAM: Philadelphia, PA
    • Y. Nesterov and A. Nemirovsky, "Interior-point polynomial methods in convex programming," Studies in Applied Mathematics, vol. 13, 1994, SIAM: Philadelphia, PA.
    • (1994) Studies in Applied Mathematics , vol.13
    • Nesterov, Y.1    Nemirovsky, A.2
  • 38
    • 0032163862 scopus 로고    scopus 로고
    • Solving ill-conditioned and singular linear systems: A tutorial on regularization
    • A. Neumaier, "Solving ill-conditioned and singular linear systems: A tutorial on regularization," SIAM Rev., vol. 40, no. 3, pp. 636-666, 1998.
    • (1998) SIAM Rev , vol.40 , Issue.3 , pp. 636-666
    • Neumaier, A.1
  • 40
    • 0034215549 scopus 로고    scopus 로고
    • A new approach to variable selection in least squares problems
    • M. Osborne, B. Presnell, and B. Turlach, "A new approach to variable selection in least squares problems," IMA J. Numer. Anal., vol. 20, no. 3, pp. 389-403, 2000.
    • (2000) IMA J. Numer. Anal , vol.20 , Issue.3 , pp. 389-403
    • Osborne, M.1    Presnell, B.2    Turlach, B.3
  • 41
    • 19844370110 scopus 로고    scopus 로고
    • An iterative regularization method for total variation based image restoration
    • S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, "An iterative regularization method for total variation based image restoration," SIAM J. Multiscale Modeling and Simulation, vol. 4, no. 2, pp. 460-489, 2005.
    • (2005) SIAM J. Multiscale Modeling and Simulation , vol.4 , Issue.2 , pp. 460-489
    • Osher, S.1    Burger, M.2    Goldfarb, D.3    Xu, J.4    Yin, W.5
  • 42
    • 0039943513 scopus 로고
    • LSQR: An algorithm for sparse linear equations and sparse least squares
    • C. Paige and M. Saunders, "LSQR: An algorithm for sparse linear equations and sparse least squares," ACM Trans. Mathemat. Software vol. 8, no. 1, pp. 43-71, 1982.
    • (1982) ACM Trans. Mathemat. Software , vol.8 , Issue.1 , pp. 43-71
    • Paige, C.1    Saunders, M.2
  • 43
    • 39449132039 scopus 로고    scopus 로고
    • B. Polyak, Introduction to optimization, Optimization Software 1987, Translated from Russian.
    • B. Polyak, "Introduction to optimization," Optimization Software 1987, Translated from Russian.
  • 44
    • 0034147823 scopus 로고    scopus 로고
    • A truncated primal-infeasible dual-feasible network interior point method
    • L. Portugal, M. Resende, G. Veiga, and J. Júdice, "A truncated primal-infeasible dual-feasible network interior point method," Networks, vol. 35, no. 2, pp. 91-108, 2000.
    • (2000) Networks , vol.35 , Issue.2 , pp. 91-108
    • Portugal, L.1    Resende, M.2    Veiga, G.3    Júdice, J.4
  • 45
    • 39449135213 scopus 로고    scopus 로고
    • T. Robertson, F. Wright, R., and Dykstra, Order Restricted Statistical Inference. New York: Wiley, 1988.
    • T. Robertson, F. Wright, R., and Dykstra, Order Restricted Statistical Inference. New York: Wiley, 1988.
  • 46
    • 84898950954 scopus 로고    scopus 로고
    • Tracking curved regularized optimization solution paths
    • S. Rosset, L. Saul, Y. Weiss, and L. Bottou, Eds, Cambridge, MA: MIT Press
    • S. Rosset,, L. Saul, Y. Weiss, and L. Bottou, Eds., "Tracking curved regularized optimization solution paths," in Advances in Neural Information Processing Systems 17. Cambridge, MA: MIT Press, 2005.
    • (2005) Advances in Neural Information Processing Systems 17
  • 47
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physics D, vol. 60, pp. 259-268, 1992.
    • (1992) Physics D , vol.60 , pp. 259-268
    • Rudin, L.1    Osher, S.2    Fatemi, E.3
  • 52
    • 0001287271 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the lasso
    • R. Tibshirani, "Regression shrinkage and selection via the lasso," J. Roy. Statist. Soc., ser. B, vol. 58, no. 1, pp. 267-288, 1996.
    • (1996) J. Roy. Statist. Soc., ser. B , vol.58 , Issue.1 , pp. 267-288
    • Tibshirani, R.1
  • 53
    • 33645712308 scopus 로고    scopus 로고
    • Just relax: Convex programming methods for identifying sparse signals in noise
    • Mar
    • J. Tropp, "Just relax: Convex programming methods for identifying sparse signals in noise," IEEE Trans. Inf. Theory, vol. 52, no. 3, pp. 1030-1051, Mar. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.3 , pp. 1030-1051
    • Tropp, J.1
  • 54
    • 30844433547 scopus 로고    scopus 로고
    • Extensions of compressed sensing
    • Y. Tsaig and D. Donoho, "Extensions of compressed sensing," Signal Process., vol. 86, no. 3, pp. 549-571, 2006.
    • (2006) Signal Process , vol.86 , Issue.3 , pp. 549-571
    • Tsaig, Y.1    Donoho, D.2
  • 55
    • 0029338589 scopus 로고
    • A primal-dual potential reduction method for problems involving matrix inequalities
    • L. Vandenberghe and S. Boyd, "A primal-dual potential reduction method for problems involving matrix inequalities," Mathemat. Programm., ser. B, vol. 69, pp. 205-236, 1995.
    • (1995) Mathemat. Programm., ser. B , vol.69 , pp. 205-236
    • Vandenberghe, L.1    Boyd, S.2
  • 60
    • 33645035051 scopus 로고    scopus 로고
    • Model selection and estimation in regression with grouped variables
    • M. Yuan and L. Lin, "Model selection and estimation in regression with grouped variables," J. Roy. Statist. Soc., ser. B, vol. 68, no. 1, pp. 49-67, 2006.
    • (2006) J. Roy. Statist. Soc., ser. B , vol.68 , Issue.1 , pp. 49-67
    • Yuan, M.1    Lin, L.2
  • 61
    • 33845263263 scopus 로고    scopus 로고
    • On model selection consistency of lasso
    • P. Zhao and B. Yu, "On model selection consistency of lasso," J. Mach. Learning Res., vol. 7, pp. 2541-2563, 2006.
    • (2006) J. Mach. Learning Res , vol.7 , pp. 2541-2563
    • Zhao, P.1    Yu, B.2
  • 62
    • 33846114377 scopus 로고    scopus 로고
    • The adaptive lasso and its oracle properties
    • H. Zou, "The adaptive lasso and its oracle properties," J. Amer. Statist. Assoc., vol. 101, no. 476, pp. 1418-1429, 2006.
    • (2006) J. Amer. Statist. Assoc , vol.101 , Issue.476 , pp. 1418-1429
    • Zou, H.1
  • 63
    • 16244401458 scopus 로고    scopus 로고
    • Regularization and variable selection via the elastic net
    • Journal of the Roy. Statist. Soc
    • H. Zou and T. Hastie, "Regularization and variable selection via the elastic net," Journal of the Roy. Statist. Soc., ser. B, vol. 67, no. 2, pp. 301-320, 2005.
    • (2005) ser. B , vol.67 , Issue.2 , pp. 301-320
    • Zou, H.1    Hastie, T.2


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