메뉴 건너뛰기




Volumn 59, Issue 4, 2011, Pages 1895-1901

An alternative lagrange-dual based algorithm for sparse signal reconstruction

Author keywords

Dual program; gradient type method; sparse signal reconstruction; strong duality theorem

Indexed keywords

DUAL PROGRAM; GRADIENT-TYPE METHOD; LAGRANGE; MINIMIZATION PROBLEMS; NUMERICAL EXAMPLE; OPTIMIZATION PROBLEMS; ORIGINAL SIGNAL; SPARSE SIGNAL RECONSTRUCTION; STATE OF THE ART; STRONG DUALITY;

EID: 79952655935     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2010.2103066     Document Type: Article
Times cited : (37)

References (49)
  • 1
    • 0043005300 scopus 로고    scopus 로고
    • Learning a sparse representation for object detection
    • S. Agarwal and D. Roth, "Learning a sparse representation for object detection," in ECCV, 2002, pp. 97-101.
    • (2002) ECCV , pp. 97-101
    • Agarwal, S.1    Roth, D.2
  • 3
    • 0242366206 scopus 로고    scopus 로고
    • Simultaneous structure and texture image inpainting
    • Aug.
    • M. Bertalmio, L. Vese, G. Sapiro, and S. Osher, "Simultaneous structure and texture image inpainting," IEEE Trans. Image Process., vol. 12, no. 8, pp. 882-889, Aug. 2003.
    • (2003) IEEE Trans. Image Process. , vol.12 , Issue.8 , pp. 882-889
    • Bertalmio, M.1    Vese, L.2    Sapiro, G.3    Osher, S.4
  • 6
    • 0000732463 scopus 로고
    • A limited memory algorithm for bound constrained optimization
    • R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu, "A limited memory algorithm for bound constrained optimization," SIAM J. Sci. Comput., vol. 16, pp. 1190-1208, 1995.
    • (1995) SIAM J. Sci. Comput. , vol.16 , pp. 1190-1208
    • Byrd, R.H.1    Lu, P.2    Nocedal, J.3    Zhu, C.4
  • 7
    • 84878104490 scopus 로고    scopus 로고
    • Compressive sampling
    • E. J. Cande's, "Compressive sampling," in Proc. Int. Congr. Math., 2006, vol. 3, pp. 1433-1452.
    • (2006) Proc. Int. Congr. Math. , vol.3 , pp. 1433-1452
    • Candes, E.J.1
  • 8
    • 42649140570 scopus 로고    scopus 로고
    • The restricted isometry property and its applications for compressed sensing
    • Paris France
    • E. J. Cande's, "The restricted isometry property and its applications for compressed sensing," Compte Rendus de l'Academie des Sciences. Paris, France, vol. 1, pp. 589-592, 2008.
    • (2008) Compte Rendus de LAcademie des Sciences , vol.1 , pp. 589-592
    • Candes, E.J.1
  • 9
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • Feb.
    • E. J. Cande's, 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
    • Candes, E.J.1    Romberg, J.2    Tao, T.3
  • 10
    • 29144439194 scopus 로고    scopus 로고
    • Decoding by linear programming
    • DOI 10.1109/TIT.2005.858979
    • E. J. Cande's and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4203-4215, Dec. 2005. (Pubitemid 41800353)
    • (2005) IEEE Transactions on Information Theory , vol.51 , Issue.12 , pp. 4203-4215
    • Candes, E.J.1    Tao, T.2
  • 11
    • 85032750937 scopus 로고    scopus 로고
    • An introduction to compressive sampling
    • E. J. Cande's and M. Wakin, "An introduction to compressive sampling," IEEE Signal. Process. Mag., vol. 25, pp. 21-30, 2008.
    • (2008) IEEE Signal. Process. Mag. , vol.25 , pp. 21-30
    • Candes, E.J.1    Wakin, M.2
  • 12
    • 51449107132 scopus 로고    scopus 로고
    • Effective separation of sparse and non-sparse image features for denoising
    • ICASSP Apr.
    • A. Chakrabarti and F. Hirakawa, "Effective separation of sparse and non-sparse image features for denoising," in Proc. Int. Conf. Acoust., Speech, Signal Process. (ICASSP), Apr. 2008, pp. 857-860.
    • (2008) Proc. Int. Conf. Acoust. Speech Signal Process. , pp. 857-860
    • Chakrabarti, A.1    Hirakawa, F.2
  • 14
    • 0035452299 scopus 로고    scopus 로고
    • Backward sequential elimination for sparse vector subset selection
    • DOI 10.1016/S0165-1684(01)00064-0, PII S0165168401000640
    • S. F. Cotter, K. Kreutz-Delgado, and B. D. Rao, "Backward sequential elimination for sparse vector subset selection," Signal Process., vol. 81, pp. 1849-1864, Sep. 2002. (Pubitemid 32723681)
    • (2001) Signal Processing , vol.81 , Issue.9 , pp. 1849-1864
    • Cotter, S.F.1    Kreutz-Delgado, K.2    Rao, B.D.3
  • 15
    • 0036578648 scopus 로고    scopus 로고
    • Efficient backward elimination algorithm for sparse signal representation using overcomplete dictionaries
    • DOI 10.1109/LSP.2002.1009004, PII S1070990802060418
    • S. F. Cotter, K. Kreutz-Delgado, and B. D. Rao, "Efficient backward elimination algorithm for sparse signal representation using overcomplete dictionaries," IEEE Signal Process. Lett., vol. 9, no. 5, pp. 145-147, May 2002. (Pubitemid 34878649)
    • (2002) IEEE Signal Processing Letters , vol.9 , Issue.5 , pp. 145-147
    • Cotter, S.F.1    Kreutz-Delgado, K.2    Rao, B.D.3
  • 16
    • 0034342180 scopus 로고    scopus 로고
    • On the optimality of the backward greedy algorithm for the subset selection problem
    • C. Couvreur and Y. Bresler, "On the optimality of the backward greedy algorithm for the subset selection problem," SIAM J. Matrix Anal. Appl., vol. 21, no. 3, pp. 797-808, 1999.
    • (1999) SIAM J. Matrix Anal. Appl. , vol.21 , Issue.3 , pp. 797-808
    • Couvreur, C.1    Bresler, Y.2
  • 17
    • 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. Defrise, and C. De Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Commun. 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
  • 18
    • 0031541839 scopus 로고    scopus 로고
    • Adaptive greedy approximations
    • Mar. 7
    • G. Davis, S. Mallat, and M. Avellaneda, "Adaptive greedy approximations," Constr. Approx., vol. 13, no. 1, pp. 57-98, Mar. 7, 1997.
    • (1997) Constr. Approx. , vol.13 , Issue.1 , pp. 57-98
    • Davis, G.1    Mallat, S.2    Avellaneda, M.3
  • 19
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • Apr.
    • D. L. 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.L.1
  • 20
    • 33646365077 scopus 로고    scopus 로고
    • 1-norm solution is also the sparsest solution
    • DOI 10.1002/cpa.20132
    • D. L. Donoho, "For most large underdetermined systems of linear equations, the minimal l1 norm solution is also the sparsest solution," Commun. Pure Appl. Math., vol. 59, no. 6, pp. 797-829, 2006. (Pubitemid 43667226)
    • (2006) Communications on Pure and Applied Mathematics , vol.59 , Issue.6 , pp. 797-829
    • Donoho, D.L.1
  • 21
    • 0035504028 scopus 로고    scopus 로고
    • Uncertainty principles and ideal atomic decomposition
    • DOI 10.1109/18.959265, PII S0018944801089465
    • D. L. Donoho and X. Huo, "Uncertainty principles and ideal atomic decomposition," IEEE Trans. Inf. Theory, vol. 47, no. 7, pp. 2845-2862, Nov. 2001. (Pubitemid 33053488)
    • (2001) IEEE Transactions on Information Theory , vol.47 , Issue.7 , pp. 2845-2862
    • Donoho, D.L.1    Huo, X.2
  • 22
    • 0036714214 scopus 로고    scopus 로고
    • A generalized uncertainty principle and sparse representation in pairs of bases
    • DOI 10.1109/TIT.2002.801410, PII 1011092002801410
    • M. Elad and A. M. Bruckstein, "A generalized uncertainty principle and sparse representation in pairs of bases," IEEE Trans. Inf. Theory, vol. 48, no. 9, pp. 2558-2567, Sep. 2002. (Pubitemid 35032680)
    • (2002) IEEE Transactions on Information Theory , vol.48 , Issue.9 , pp. 2558-2567
    • Elad, M.1    Bruckstein, A.M.2
  • 23
    • 33645665466 scopus 로고    scopus 로고
    • A bound optimization approach to wavelet-based image deconvolution
    • DOI 10.1109/ICIP.2005.1530172, 1530172, IEEE International Conference on Image Processing 2005, ICIP 2005
    • M. Figueiredo and R. Nowak, "A bound optimization approach to wavelet-based image deconvolution," in Proc. IEEE Int. Conf. Image Process., 2005, pp. 782-785. (Pubitemid 44539056)
    • (2005) Proceedings - International Conference on Image Processing, ICIP , vol.2 , pp. 782-785
    • Figueiredo, M.A.T.1    Nowak, R.D.2
  • 24
    • 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. Sel. Topics Signal Process., vol. 1, pp. 586-598, 2007.
    • (2007) IEEE J. Sel. Topics Signal Process. , vol.1 , pp. 586-598
    • Figueiredo, M.1    Nowak, R.2    Wright, S.3
  • 25
    • 4644223536 scopus 로고    scopus 로고
    • Recovery of exact sparse representations in the presence of noise
    • ICASSP Montreal QC Canada May
    • J. J. Fuchs, "Recovery of exact sparse representations in the presence of noise," in Proc. IEEE Int. Conf. Acoust., Speec, Signal Process. (ICASSP), Montreal, QC, Canada, May 2004, vol. II, pp. 533-536.
    • (2004) Proc. IEEE Int. Conf. Acoust. Speec Signal Process. , vol.2 , pp. 533-536
    • Fuchs, J.J.1
  • 26
    • 2942640138 scopus 로고    scopus 로고
    • More on sparse representations in arbitrary bases
    • J. J. Fuchs, "More on sparse representations in arbitrary bases," IEEE Trans. Inf. Theory, vol. 50, pp. 1341-1344, 2004.
    • (2004) IEEE Trans. Inf. Theory , vol.50 , pp. 1341-1344
    • Fuchs, J.J.1
  • 28
    • 53349163971 scopus 로고    scopus 로고
    • A fixed-point continuation method for l1-regularized minimization with applications to compressed sensing
    • Dept. Rice Univ. Houston TX CAAM Tech. Rep. TR07-07 Jul.
    • E. T. Hale, W. Yin, and Y. Zhang, "A fixed-point continuation method for l1-regularized minimization with applications to compressed sensing," Comput. Appl. Math. Dept., Rice Univ., Houston, TX, CAAM Tech. Rep. TR07-07, Jul. 2007.
    • (2007) Comput. Appl. Math.
    • Hale, E.T.1    Yin, W.2    Zhang, Y.3
  • 29
    • 78650759634 scopus 로고    scopus 로고
    • A deterministic sub-linear time sparse Fourier algorithm via non-adaptive compressed sensing methods
    • M. A. Iwen, "A deterministic sub-linear time sparse Fourier algorithm via non-adaptive compressed sensing methods," in Proc. ACM-SIAM Symp. Discrete Algorithms (SODA), 2008, pp. 20-29.
    • (2008) Proc. ACM-SIAM Symp. Discrete Algorithms SODA , pp. 20-29
    • Iwen, M.A.1
  • 31
    • 3342925349 scopus 로고    scopus 로고
    • Improved iterative algorithm for sparse object reconstruction and its performance evaluation with micro-CT data
    • Jun.
    • M. H. Li, H. Kudo, J. C. Hu, and R. H. Johnson, "Improved iterative algorithm for sparse object reconstruction and its performance evaluation with micro-CT data," IEEE Trans. Nucl. Sci., vol. 51, no. 3, pp. 659-666, Jun. 2004.
    • (2004) IEEE Trans. Nucl. Sci. , vol.51 , Issue.3 , pp. 659-666
    • Li, M.H.1    Kudo, H.2    Hu, J.C.3    Johnson, R.H.4
  • 33
    • 0027842081 scopus 로고
    • Matching pursuits with time-frequency dictionaries
    • Dec.
    • S. G. Mallat and Z. Zhang, "Matching pursuits with time-frequency dictionaries," IEEE Trans. Signal Precess., vol. 41, no. 12, pp. 3379-3415, Dec. 1993.
    • (1993) IEEE Trans. Signal Precess. , vol.41 , Issue.12 , pp. 3379-3415
    • Mallat, S.G.1    Zhang, Z.2
  • 34
    • 0018543889 scopus 로고
    • Nonlinear perturbation of linear programs
    • O. L. Mangasarian and R. R. Meyer, "Nonlinear perturbation of linear programs," SIAM J Control Optim., vol. 17, no. 6, pp. 745-752, 1979.
    • (1979) SIAM J Control Optim. , vol.17 , Issue.6 , pp. 745-752
    • Mangasarian, O.L.1    Meyer, R.R.2
  • 36
    • 0029291966 scopus 로고
    • Sparse approximate solutions to linear systems
    • B. K. Natarajan, "Sparse approximate solutions to linear systems," SIAM J. Comput., vol. 24, no. 2, pp. 227-234, 1995.
    • (1995) SIAM J. Comput. , vol.24 , Issue.2 , pp. 227-234
    • Natarajan, B.K.1
  • 37
    • 62749175137 scopus 로고    scopus 로고
    • CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
    • D. Needell and J. A. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples," Appl. Comput. Harmon. Anal., vol. 26, pp. 301-321, 2009.
    • (2009) Appl. Comput. Harmon. Anal. , vol.26 , pp. 301-321
    • Needell, D.1    Tropp, J.A.2
  • 38
    • 45049084813 scopus 로고    scopus 로고
    • Unsupervised learning of human action categories using spatial-temporal words
    • J. C. Niebles, H. Wang, and L. Fei-Fei, "Unsupervised learning of human action categories using spatial-temporal words," Int. J. Comput. Vis., vol. 79, p. 299C318, 2008.
    • (2008) Int. J. Comput. Vis. , vol.79
    • Niebles, J.C.1    Wang, H.2    Fei-Fei, L.3
  • 40
    • 70349600872 scopus 로고    scopus 로고
    • Dual-augmented lagrangian method for efficient sparse reconstruction
    • Dec.
    • R. Tomioka and M. Sugiyama, "Dual-augmented Lagrangian method for efficient sparse reconstruction," IEEE Signal Process. Lett., vol. 16, no. 12, pp. 1067-1070, Dec. 2009.
    • (2009) IEEE Signal Process. Lett. , vol.16 , Issue.12 , pp. 1067-1070
    • Tomioka, R.1    Sugiyama, M.2
  • 41
    • 33645712308 scopus 로고    scopus 로고
    • Just relax: Convex programming methods for identifying sparse signals in noise
    • DOI 10.1109/TIT.2005.864420
    • J. A. Tropp, "Just relax: Convex programming methods for identifying sparse signals," IEEE Trans. Inf. Theory, vol. 51, pp. 1030-1051, 2006. (Pubitemid 46444890)
    • (2006) IEEE Transactions on Information Theory , vol.52 , Issue.3 , pp. 1030-1051
    • Tropp, J.A.1
  • 43
    • 64649083745 scopus 로고    scopus 로고
    • Signal recovery from random measurements via orthogonal matching pursuit
    • Dec.
    • J. A. Tropp and A. C. Gilbert, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Trans. Inf. Theory, vol. 53, no. 12, pp. 4655-4666, Dec. 2007.
    • (2007) IEEE Trans. Inf. Theory , vol.53 , Issue.12 , pp. 4655-4666
    • Tropp, J.A.1    Gilbert, A.C.2
  • 44
    • 30844458202 scopus 로고    scopus 로고
    • 1-norm solution and the sparsest solution
    • DOI 10.1016/j.sigpro.2005.05.028, PII S0165168405002203, Sparse Approximations in Signal and Image Processing
    • Y. Tsaig and D. L. Donoho, "Breakdown of equivalence between the minimal l1 -norm solution and the sparsest solution," Signal Process., vol. 86, no. 3, pp. 533-548, Mar. 2006. (Pubitemid 43106570)
    • (2006) Signal Processing , vol.86 , Issue.3 , pp. 533-548
    • Tsaig, Y.1    Donoho, D.L.2
  • 45
    • 30844433547 scopus 로고    scopus 로고
    • Extensions of compressed sensing
    • DOI 10.1016/j.sigpro.2005.05.029, PII S0165168405002215, Sparse Approximations in Signal and Image Processing
    • Y. Tsaig and D. L. Donoho, "Extensions of compressed sensing," Signal Process., vol. 86, no. 3, pp. 549-571, Mar. 2006. (Pubitemid 43106571)
    • (2006) Signal Processing , vol.86 , Issue.3 , pp. 549-571
    • Tsaig, Y.1    Donoho, D.L.2
  • 47
    • 72749110068 scopus 로고    scopus 로고
    • Semi-supervised learning by sparse representation
    • S. Yan and H. Wang, "Semi-supervised learning by sparse representation," in Proc. SIAM Int. Conf. Data Min. (SDM), 2009, pp. 792-801.
    • (2009) Proc. SIAM Int. Conf. Data Min. SDM , pp. 792-801
    • Yan, S.1    Wang, H.2
  • 48
    • 79955559521 scopus 로고    scopus 로고
    • A coordinate gradient descent method for l1-regularized convex minimization
    • to be published
    • S. Yun and K.-C. Toh, "A coordinate gradient descent method for l1-regularized convex minimization," Comput. Optim. Appl., to be published.
    • Comput. Optim. Appl.
    • Yun, S.1    Toh, K.C.2
  • 49
    • 0000660321 scopus 로고    scopus 로고
    • Blind source separation by sparse decomposition in a signal dictionary
    • DOI 10.1162/089976601300014385
    • M. Zibulewsky and B. Pearlmutter, "Blind source separation by sparse decomposition on a signal dictionary," Neural Comput., vol. 13, pp. 863-882, 2001. (Pubitemid 33594308)
    • (2001) Neural Computation , vol.13 , Issue.4 , pp. 863-882
    • Zibulevsky, M.1    Pearlmutter, B.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.