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Volumn 57, Issue 11, 2009, Pages 4333-4346

Stagewise weak gradient pursuits

Author keywords

Compressed sensing; Gradient pursuit; Orthogonal matching pursuit; Sparse representations approximations; Stagewise selection; Weak matching pursuit

Indexed keywords

COMPRESSED SENSING; GRADIENT PURSUIT; ORTHOGONAL MATCHING PURSUIT; SPARSE REPRESENTATIONS/APPROXIMATIONS; STAGEWISE SELECTION; WEAK MATCHING PURSUIT;

EID: 70350489674     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2009.2025088     Document Type: Article
Times cited : (147)

References (49)
  • 3
    • 33745715008 scopus 로고    scopus 로고
    • Sparse linear regression in unions of bases via Bayesian variable selection
    • Jul
    • C. Fevotte and S. Godsill, "Sparse linear regression in unions of bases via Bayesian variable selection," IEEE Signal Process. Lett., vol. 13, no. 7, pp. 441-444, Jul. 2006.
    • (2006) IEEE Signal Process. Lett , vol.13 , Issue.7 , pp. 441-444
    • Fevotte, C.1    Godsill, S.2
  • 5
    • 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, pp. 489-509, Feb. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , pp. 489-509
    • Candès, E.1    Romberg, J.2    Tao, T.3
  • 6
    • 0003841249 scopus 로고
    • Adaptive nonlinear approximations,
    • Ph.D. dissertation, New York Univ, New York
    • G. Davis, "Adaptive nonlinear approximations," Ph.D. dissertation, New York Univ., New York, 1994.
    • (1994)
    • Davis, G.1
  • 7
    • 0029291966 scopus 로고
    • Sparse approximate solutions to linear systems
    • Apr
    • B. K. Natarajan, "Sparse approximate solutions to linear systems," SIAM J. Comput., vol. 24, pp. 227-234, Apr. 1995.
    • (1995) SIAM J. Comput , vol.24 , pp. 227-234
    • Natarajan, B.K.1
  • 11
    • 39449126969 scopus 로고    scopus 로고
    • Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems
    • Dec
    • M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, "Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems," IEEE J. Sel. Topics Signal Process., vol. 1, no. 4, pp. 586-597, Dec. 2007.
    • (2007) IEEE J. Sel. Topics Signal Process , vol.1 , Issue.4 , pp. 586-597
    • Figueiredo, M.A.T.1    Nowak, R.D.2    Wright, S.J.3
  • 12
    • 36749005582 scopus 로고    scopus 로고
    • A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration
    • J. Bioucas-Dias and M. Figueiredo, "A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration," IEEE Trans. on Image Process., vol. 16, no. 12, pp. 2992-3004, 2007.
    • (2007) IEEE Trans. on Image Process , vol.16 , Issue.12 , pp. 2992-3004
    • Bioucas-Dias, J.1    Figueiredo, M.2
  • 13
    • 65649137930 scopus 로고    scopus 로고
    • Probing the Pareto frontier for basis pursuit solutions
    • E. van den Berg and M. P. Friedlander, "Probing the Pareto frontier for basis pursuit solutions," SIAM J. Scientif. Comput., vol. 31, no. 2, pp. 890-912, 2008.
    • (2008) SIAM J. Scientif. Comput , vol.31 , Issue.2 , pp. 890-912
    • van den Berg, E.1    Friedlander, M.P.2
  • 14
    • 44449098059 scopus 로고    scopus 로고
    • A semismooth Newton method for Tikhonov functionals with sparsity constraints
    • R. Griesse and D. A. Lorenz, "A semismooth Newton method for Tikhonov functionals with sparsity constraints," Inverse Probl., vol. 24, no. 3, 2008.
    • (2008) Inverse Probl , vol.24 , Issue.3
    • Griesse, R.1    Lorenz, D.A.2
  • 17
    • 0001224048 scopus 로고    scopus 로고
    • Sparse Bayesian learning and the relevance vector machine
    • M. E. Tipping, "Sparse Bayesian learning and the relevance vector machine," J. Mach. Learn. Res., vol. 1, pp. 211-244, 2001.
    • (2001) J. Mach. Learn. Res , vol.1 , pp. 211-244
    • Tipping, M.E.1
  • 18
    • 3543103176 scopus 로고    scopus 로고
    • Sparse Bayesian learning for basis selection
    • Aug
    • D. Wipf and B. D. Rao, "Sparse Bayesian learning for basis selection," IEEE Trans. Signal Process., vol. 52, no. 8, pp. 2153-2164, Aug. 2004.
    • (2004) IEEE Trans. Signal Process , vol.52 , Issue.8 , pp. 2153-2164
    • Wipf, D.1    Rao, B.D.2
  • 19
    • 0031526204 scopus 로고    scopus 로고
    • Approaches for Bayesian variable selection
    • R. E. McCulloch and E. I. George, "Approaches for Bayesian variable selection," Statist. Sinica, vol. 7, no. 2, pp. 339-374, 1997.
    • (1997) Statist. Sinica , vol.7 , Issue.2 , pp. 339-374
    • McCulloch, R.E.1    George, E.I.2
  • 21
    • 0000647838 scopus 로고    scopus 로고
    • Variable selection and model comparison in regression
    • J.M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Eds. London, U.K, Oxford Univ. Press
    • J. Geweke, "Variable selection and model comparison in regression," in Bayesian Statistics 5, J.M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Eds. London, U.K.: Oxford Univ. Press, 1996.
    • (1996) Bayesian Statistics 5
    • Geweke, J.1
  • 22
    • 0027842081 scopus 로고
    • Matching pursuits with time-frequency dictionaries
    • Dec
    • S. Mallat and Z. Zhang, "Matching pursuits with time-frequency dictionaries," IEEE Trans. Signal Process., vol. 41, no. 12, pp. 3397-3415, Dec. 1993.
    • (1993) IEEE Trans. Signal Process , vol.41 , Issue.12 , pp. 3397-3415
    • Mallat, S.1    Zhang, Z.2
  • 23
    • 0027814133 scopus 로고
    • Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition
    • presented at the, Nov
    • Y. C. Pati, R. Rezaifar, and P. S. Krishnaprasad, "Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition," presented at the 27th Asilomar Conf. Signals, Systems, Comput., Nov. 1993.
    • (1993) 27th Asilomar Conf. Signals, Systems, Comput
    • Pati, Y.C.1    Rezaifar, R.2    Krishnaprasad, P.S.3
  • 24
    • 0024771664 scopus 로고
    • Orthogonal least squares methods and their application to nonlinear system identification
    • S. Chen, S. A. Billings, and W. Luo, "Orthogonal least squares methods and their application to nonlinear system identification," Int. J. Control, vol. 50, no. 5, pp. 1873-1896, 1989.
    • (1989) Int. J. Control , vol.50 , Issue.5 , pp. 1873-1896
    • Chen, S.1    Billings, S.A.2    Luo, W.3
  • 25
    • 0036643065 scopus 로고    scopus 로고
    • Kernel matching pursuit
    • P. Vincent and Y. Bengio, "Kernel matching pursuit," Mach. Learn. vol. 48, pp. 169-191, 2002.
    • (2002) Mach. Learn , vol.48 , pp. 169-191
    • Vincent, P.1    Bengio, Y.2
  • 27
    • 57949093358 scopus 로고    scopus 로고
    • COSAMP: Iterative signal recovery from incomplete and inaccurate samples
    • to be published
    • D. Needell and J. Tropp, "COSAMP: Iterative signal recovery from incomplete and inaccurate samples," Appl. Comput. Harmon. Anal., 2008, to be published.
    • (2008) Appl. Comput. Harmon. Anal
    • Needell, D.1    Tropp, J.2
  • 28
    • 69949164527 scopus 로고    scopus 로고
    • Iterative hard thresholding for compressed sensing
    • to be published
    • T. Blumensath and M. Davies, "Iterative hard thresholding for compressed sensing," Appl. Comput. Harmon. Anal., 2009, to be published.
    • (2009) Appl. Comput. Harmon. Anal
    • Blumensath, T.1    Davies, M.2
  • 30
    • 35548934118 scopus 로고    scopus 로고
    • Sparse solutions of underdetermined linear equations by stagewise orthogonal matching pursuit
    • Online, Available:, submitted for publication
    • D. Donoho, Y. Tsaig, I. Drori, and J. Starck, "Sparse solutions of underdetermined linear equations by stagewise orthogonal matching pursuit," IEEE Trans. Inf. Theory, 2006 [Online]. Available: http://www-stat.stanford.edu/~donoho/Reports/2006/StOMP-20060403.pdf, submitted for publication
    • (2006) IEEE Trans. Inf. Theory
    • Donoho, D.1    Tsaig, Y.2    Drori, I.3    Starck, J.4
  • 31
    • 64749092799 scopus 로고    scopus 로고
    • Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit
    • D. Needell and R. Vershynin, "Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit," Found. Comput. Math., vol. 9, no. 3, pp. 317-334, 2009.
    • (2009) Found. Comput. Math , vol.9 , Issue.3 , pp. 317-334
    • Needell, D.1    Vershynin, R.2
  • 32
    • 57849144332 scopus 로고    scopus 로고
    • Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit
    • to be published
    • D. Needell and R. Vershynin, "Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit," IEEE J. Sel. Topics Signal Process., 2008, to be published.
    • (2008) IEEE J. Sel. Topics Signal Process
    • Needell, D.1    Vershynin, R.2
  • 34
    • 0004236492 scopus 로고    scopus 로고
    • 3rd ed. Baltimore, MD: The Johns Hopkins Univ. Press
    • G. H. Golub and F. Van Loan, Matrix Computations, 3rd ed. Baltimore, MD: The Johns Hopkins Univ. Press, 1996.
    • (1996) Matrix Computations
    • Golub, G.H.1    Van Loan, F.2
  • 35
    • 29144439194 scopus 로고    scopus 로고
    • Decoding by linear programming
    • Dec
    • E. J. Candès and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4203-4215, Dec. 2004.
    • (2004) IEEE Trans. Inf. Theory , vol.51 , Issue.12 , pp. 4203-4215
    • Candès, E.J.1    Tao, T.2
  • 38
    • 0010846477 scopus 로고
    • Linear convergence of the conjugate gradient method
    • H. Crowder and P. Wolfe, "Linear convergence of the conjugate gradient method," Numeric. Comput., vol. 16, no. 4, pp. 431-433, 1972.
    • (1972) Numeric. Comput , vol.16 , Issue.4 , pp. 431-433
    • Crowder, H.1    Wolfe, P.2
  • 39
    • 36849088522 scopus 로고    scopus 로고
    • Sparse MRI: The application of compressed sensing for rapid MR imaging
    • Dec
    • M. Lustig, D. L. Donoho, and J. M. Pauly, "Sparse MRI: The application of compressed sensing for rapid MR imaging," Magn. Resonance Med. vol. 58, no. 6, pp. 1182-1195, Dec. 2007.
    • (2007) Magn. Resonance Med , vol.58 , Issue.6 , pp. 1182-1195
    • Lustig, M.1    Donoho, D.L.2    Pauly, J.M.3
  • 40
    • 0345529042 scopus 로고    scopus 로고
    • Sparse decompositions in incoherent dictionaries
    • presented at the, Barcelona, Spain, Sep
    • R. Gribonval and M. Nielsen, "Sparse decompositions in incoherent dictionaries," presented at the IEEE Int. Conf. Image Process. (ICIP), Barcelona, Spain, Sep. 2003.
    • (2003) IEEE Int. Conf. Image Process. (ICIP)
    • Gribonval, R.1    Nielsen, M.2
  • 41
    • 2942640138 scopus 로고    scopus 로고
    • On sparse representations in arbitrary redundant bases
    • Jun
    • J.-J. Fuchs, "On sparse representations in arbitrary redundant bases," IEEE Trans. Inf. Theory, vol. 50, no. 6, pp. 1341-1344, Jun. 2004.
    • (2004) IEEE Trans. Inf. Theory , vol.50 , Issue.6 , pp. 1341-1344
    • Fuchs, J.-J.1
  • 42
    • 26844461512 scopus 로고    scopus 로고
    • Recovery of exact sparse representations in the presence of bounded noise
    • Oct
    • J.-J. Fuchs, "Recovery of exact sparse representations in the presence of bounded 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.-J.1
  • 43
    • 0037418225 scopus 로고    scopus 로고
    • Optimally-sparse representation in general (nonorthogonal) dictionaries via l1 minimization
    • D. L. Donoho and M. Elad, "Optimally-sparse representation in general (nonorthogonal) dictionaries via l1 minimization," Proc. Nat. Acad. Sci., vol. 100, pp. 2197-2202, 2003.
    • (2003) Proc. Nat. Acad. Sci , vol.100 , pp. 2197-2202
    • Donoho, D.L.1    Elad, M.2
  • 44
    • 3142664885 scopus 로고    scopus 로고
    • Stable recovery of sparse overcomplete representations in the presence of noise
    • Feb
    • D. L. Donoho, M. Elad, and V. Temlyakov, "Stable recovery of sparse overcomplete representations in the presence of noise," IEEE Trans. Inf. Theory, Feb. 2004.
    • (2004) IEEE Trans. Inf. Theory
    • Donoho, D.L.1    Elad, M.2    Temlyakov, V.3
  • 45
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • D. Donoho, "Compressed sensing," IEEE Trans. on Information Theory vol. 52, no. 4, pp. 1289-1306, 2006.
    • (2006) IEEE Trans. on Information Theory , vol.52 , Issue.4 , pp. 1289-1306
    • Donoho, D.1
  • 46
    • 5444237123 scopus 로고    scopus 로고
    • Greed is good: Algorithmic results for sparse approximation
    • J. A. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Trans. Inf. Theory, vol. 50, pp. 2231-2242, 2004.
    • (2004) IEEE Trans. Inf. Theory , vol.50 , pp. 2231-2242
    • Tropp, J.A.1
  • 47
    • 64649083745 scopus 로고    scopus 로고
    • Signal recovery from partial information via orthogonal matching pursuit
    • J. A. Tropp and A. C. Gilbert, "Signal recovery from partial information via orthogonal matching pursuit," IEEE Trans. Inf. Theory, vol. 53, pp. 4655-4666, 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.53 , pp. 4655-4666
    • Tropp, J.A.1    Gilbert, A.C.2
  • 48
    • 32944458952 scopus 로고    scopus 로고
    • On the exponential convergence of matching pursuits in quasi-incoherent dictionaries
    • R. Gribonval and P. Vandergheynst, "On the exponential convergence of matching pursuits in quasi-incoherent dictionaries," IEEE Trans. Inf. Theory, vol. 52, pp. 255-261, 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , pp. 255-261
    • Gribonval, R.1    Vandergheynst, P.2
  • 49
    • 42649140570 scopus 로고    scopus 로고
    • The restricted isometry property and its implications for compressed sensing
    • Compte Rendus de l'Academie des Sciences, Paris, France
    • E. Candès, "The restricted isometry property and its implications for compressed sensing," Compte Rendus de l'Academie des Sciences, Paris, France, Serie I, 346, 2008, pp. 589-592.
    • (2008) Serie I , vol.346 , pp. 589-592
    • Candès, E.1


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