메뉴 건너뛰기




Volumn 5207, Issue 1, 2003, Pages 216-227

Approximation with highly redundant dictionaries

Author keywords

Basis Pursuit; Coherence; Dictionary; Linear programming; Matching Pursuit; Nonlinear approximation; Quadratic programming; Spark; Sparse decomposition; Spread

Indexed keywords

APPROXIMATION THEORY; DECOMPOSITION; LINEAR PROGRAMMING; QUADRATIC PROGRAMMING; VECTORS;

EID: 1242308394     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.504776     Document Type: Conference Paper
Times cited : (10)

References (41)
  • 2
    • 0027842081 scopus 로고
    • Matching pursuit with time-frequency dictionaries
    • Dec.
    • S. Mallat and Z. Zhang, "Matching pursuit with time-frequency dictionaries," IEEE Trans. Signal Process. 41, pp. 3397-3415, Dec. 1993.
    • (1993) IEEE Trans. Signal Process. , vol.41 , pp. 3397-3415
    • Mallat, S.1    Zhang, Z.2
  • 3
    • 0002305149 scopus 로고
    • On absolute convergence of orthogonal series
    • S. B. Stechkin, "On absolute convergence of orthogonal series, " Dok. Akad. Nauk SSSR 102, pp. 37-40, 1955.
    • (1955) Dok. Akad. Nauk SSSR , vol.102 , pp. 37-40
    • Stechkin, S.B.1
  • 4
    • 0039439070 scopus 로고    scopus 로고
    • Some remarks on greedy algorithms
    • R. A. DeVore and V. N. Temlyakov, "Some remarks on greedy algorithms," Adv. Comput. Math. 5(2-3), pp. 173-187, 1996.
    • (1996) Adv. Comput. Math. , vol.5 , Issue.2-3 , pp. 173-187
    • Devore, R.A.1    Temlyakov, V.N.2
  • 5
    • 3042630917 scopus 로고    scopus 로고
    • Nonlinear approximation with dictionaries. I. Direct estimates
    • to appear
    • R. Gribonval and M. Nielsen, "Nonlinear approximation with dictionaries. I. Direct estimates.," J. Fourier Anal. and Appl., 2003. to appear.
    • (2003) J. Fourier Anal. and Appl.
    • Gribonval, R.1    Nielsen, M.2
  • 8
    • 0344127910 scopus 로고    scopus 로고
    • Sparse decompositions in unions of bases
    • IRISA, Nov. submitted to IEEE Trans. Inf. Th.
    • R. Gribonval and M. Nielsen, "Sparse decompositions in unions of bases," Tech. Rep. 1499, IRISA, Nov. 2002. submitted to IEEE Trans. Inf. Th.
    • (2002) Tech. Rep. , vol.1499
    • Gribonval, R.1    Nielsen, M.2
  • 9
    • 0031541839 scopus 로고    scopus 로고
    • Adaptive greedy approximations
    • G. Davis, S. Mallat, and M. Avellaneda, "Adaptive greedy approximations," Constr. Approx. 13(1), pp. 57-98, 1997.
    • (1997) Constr. Approx. , vol.13 , Issue.1 , pp. 57-98
    • Davis, G.1    Mallat, S.2    Avellaneda, M.3
  • 12
    • 0035504028 scopus 로고    scopus 로고
    • Uncertainty principles and ideal atomic decompositions
    • Nov.
    • D. Donoho and X. Huo, "Uncertainty principles and ideal atomic decompositions," IEEE Trans. Inform. Theory 47, pp. 2845-2862, Nov. 2001.
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 2845-2862
    • Donoho, D.1    Huo, X.2
  • 13
    • 0036714214 scopus 로고    scopus 로고
    • A generalized uncertainty principle and sparse representations in pairs of bases
    • Sept.
    • M. Elad and A. Bruckstein, "A generalized uncertainty principle and sparse representations in pairs of bases," IEEE Trans. Inform. Theory 48, pp. 2558-2567, Sept. 2002.
    • (2002) IEEE Trans. Inform. Theory , vol.48 , pp. 2558-2567
    • Elad, M.1    Bruckstein, A.2
  • 14
    • 0344990510 scopus 로고    scopus 로고
    • On sparse representations in pairs of bases
    • Nov. accepted
    • A. Feuer and A. Nemirovsky, "On sparse representations in pairs of bases," IEEE Trans. Inform. Theory, Nov. 2002. accepted.
    • (2002) IEEE Trans. Inform. Theory
    • Feuer, A.1    Nemirovsky, A.2
  • 15
    • 0344559450 scopus 로고    scopus 로고
    • On sparse representations in arbitrary redundant bases
    • tech. rep., IRISA, Dec.
    • J.-J. Fuchs, "On sparse representations in arbitrary redundant bases," tech. rep., IRISA, Dec. 2002. submitted to IEEE Trans. Inf. Th.
    • (2002) IEEE Trans. Inf. Th.
    • Fuchs, J.-J.1
  • 17
    • 1242316836 scopus 로고    scopus 로고
    • Greed is good: Algorithmic results for sparse approximation
    • Texas Institute for Computational Engineering and Sciences, In preparation
    • J. Tropp, "Greed is good: Algorithmic results for sparse approximation," tech. rep., Texas Institute for Computational Engineering and Sciences, 2003. In preparation.
    • (2003) Tech. Rep.
    • Tropp, J.1
  • 18
    • 1242316844 scopus 로고    scopus 로고
    • Exponential convergence of Matching Pursuit in quasi-incoherent dictionaries
    • IRISA, in preparation
    • R. Gribonval and P. Vandergheynst, "Exponential convergence of Matching Pursuit in quasi-incoherent dictionaries," tech. rep., IRISA, 2003. in preparation.
    • (2003) Tech. Rep.
    • Gribonval, R.1    Vandergheynst, P.2
  • 20
    • 0242381665 scopus 로고    scopus 로고
    • Some remarks on nonlinear approximation with Schauder bases
    • R. Gribonval and M. Nielsen, "Some remarks on nonlinear approximation with Schauder bases," East J. Approx. 7(3), pp. 267-285, 2001.
    • (2001) East J. Approx. , vol.7 , Issue.3 , pp. 267-285
    • Gribonval, R.1    Nielsen, M.2
  • 21
    • 0001596752 scopus 로고    scopus 로고
    • A remark on greedy approximation in Banach spaces
    • S. Konyagin and V. Temlyakov, "A remark on greedy approximation in Banach spaces," East J. Approx. 5(3), pp. 365-379, 1999.
    • (1999) East J. Approx. , vol.5 , Issue.3 , pp. 365-379
    • Konyagin, S.1    Temlyakov, V.2
  • 22
    • 85009724776 scopus 로고    scopus 로고
    • Nonlinear approximation
    • Cambridge Univ. Press, Cambridge, 1998
    • R. A. DeVore, "Nonlinear approximation," in Acta numerica, 1998, pp. 51-150, Cambridge Univ. Press, Cambridge, 1998.
    • (1998) Acta Numerica , pp. 51-150
    • Devore, R.A.1
  • 23
    • 1242294321 scopus 로고    scopus 로고
    • On approximation with spline generated framelets
    • to appear
    • R. Gribonval and M. Nielsen, "On approximation with spline generated framelets," Constr. Approx., 2003. to appear.
    • (2003) Constr. Approx.
    • Gribonval, R.1    Nielsen, M.2
  • 24
    • 84856261091 scopus 로고    scopus 로고
    • On the quasi-greedy property and uniformly bounded orthonormal systems
    • Aalborg Univ., Dept of Math., Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, 9220 Aalborg East, Denmark, submitted to J. Approx. Th.
    • R. Gribonval and M. Nielsen, "On the quasi-greedy property and uniformly bounded orthonormal systems," Tech. Rep. R-2003-09, Aalborg Univ., Dept of Math., Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, 9220 Aalborg East, Denmark, 2003. submitted to J. Approx. Th.
    • (2003) Tech. Rep. , vol.R-2003-09
    • Gribonval, R.1    Nielsen, M.2
  • 28
    • 0000263797 scopus 로고
    • Projection pursuit
    • P. Huber, "Projection pursuit," The Annals of Statistics 13(2), pp. 435-475, 1985.
    • (1985) The Annals of Statistics , vol.13 , Issue.2 , pp. 435-475
    • Huber, P.1
  • 30
    • 0000523636 scopus 로고
    • On a conjecture of Huber concerning the convergence of PP-regression
    • L. Jones, "On a conjecture of Huber concerning the convergence of PP-regression," The Annals of Statistics 15, pp. 880-882, 1987.
    • (1987) The Annals of Statistics , vol.15 , pp. 880-882
    • Jones, L.1
  • 31
    • 0242266071 scopus 로고    scopus 로고
    • Two lower estimates in greedy approximation
    • E. Livschitz and V. Temlyakov, "Two lower estimates in greedy approximation," Constr. Approx. 19, 2003.
    • (2003) Constr. Approx. , vol.19
    • Livschitz, E.1    Temlyakov, V.2
  • 32
    • 0038521828 scopus 로고    scopus 로고
    • Nonlinear approximation with walsh atoms
    • A. Le M'ehaut'e, C. Rabut, and L. Schumaker, eds., Vanderbilt University Press
    • L. Villemoes, "Nonlinear approximation with walsh atoms," in Proceedings of "Surface Fitting and Multiresolution Methods", Chamonix 1996, A. Le M'ehaut'e, C. Rabut, and L. Schumaker, eds., pp. 329-336, Vanderbilt University Press, 1997.
    • (1997) Proceedings of "Surface Fitting and Multiresolution Methods", Chamonix 1996 , pp. 329-336
    • Villemoes, L.1
  • 33
    • 1242339505 scopus 로고    scopus 로고
    • Nonlinear approximation with dictionaries. II. Inverse estimates
    • Aalborg Univ., Dept of Math., Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, 9220 Aalborg East, Denmark, Nov. submitted to Constructive Apprimation
    • R. Gribonval and M. Nielsen, "Nonlinear approximation with dictionaries. II. Inverse estimates," Tech. Rep. R-02-2019, Aalborg Univ., Dept of Math., Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, 9220 Aalborg East, Denmark, Nov. 2002. submitted to Constructive Apprimation.
    • (2002) Tech. Rep. , vol.R-02-2019
    • Gribonval, R.1    Nielsen, M.2
  • 34
    • 0003521663 scopus 로고
    • Theory and applications, Translated from the 1987 Russian original by W. R. Wade, Kluwer Academic Publishers Group, Dordrecht
    • B. Golubov, A. Efimov, and V. Skvortsov, Walsh series and transforms, Theory and applications, Translated from the 1987 Russian original by W. R. Wade, Kluwer Academic Publishers Group, Dordrecht, 1991.
    • (1991) Walsh Series and Transforms
    • Golubov, B.1    Efimov, A.2    Skvortsov, V.3
  • 36
    • 0344127908 scopus 로고    scopus 로고
    • Grassmannian frames with applications to coding and communications
    • tech. rep., Preprint
    • T. Strohmer and R. Heath, "Grassmannian frames with applications to coding and communications," tech. rep., 2002. Preprint, submitted to Appl.Comp.Harm.Anal.
    • (2002) Appl. Comp. Harm. Anal.
    • Strohmer, T.1    Heath, R.2
  • 37
    • 0029938380 scopus 로고    scopus 로고
    • Emergence of simple-cell receptive field properties by learning a sparse code for natural images
    • D. Field and B. Olshausen, "Emergence of simple-cell receptive field properties by learning a sparse code for natural images," Nature 381, pp. 607-609, 1996.
    • (1996) Nature , vol.381 , pp. 607-609
    • Field, D.1    Olshausen, B.2
  • 38
    • 0030832881 scopus 로고    scopus 로고
    • The 'independent components' of natural scenes are edge filters
    • A. Bell and T. Sejnowski, "The 'independent components' of natural scenes are edge filters," Vision Research 37(23), pp. 3327-3338, 1997.
    • (1997) Vision Research , vol.37 , Issue.23 , pp. 3327-3338
    • Bell, A.1    Sejnowski, T.2
  • 39
    • 0000147501 scopus 로고    scopus 로고
    • Learning the higher-order structure of a natural sound
    • A. Bell and T. Sejnowski, "Learning the higher-order structure of a natural sound," Network 7(2), 1996.
    • (1996) Network , vol.7 , Issue.2
    • Bell, A.1    Sejnowski, T.2
  • 40
    • 0036212160 scopus 로고    scopus 로고
    • Efficient coding of natural sounds
    • M. Lewicki, "Efficient coding of natural sounds," Nature Neuosci. 5(4), pp. 356-363, 2002.
    • (2002) Nature Neuosci. , vol.5 , Issue.4 , pp. 356-363
    • Lewicki, M.1
  • 41
    • 0038705107 scopus 로고    scopus 로고
    • If edges are the independent components of natural images, what are the independent components of natural sounds?
    • San Diego, California, Dec.
    • S. Abdallah and M. Plumbley, "If edges are the independent components of natural images, what are the independent components of natural sounds?," in Proc. of the Int. Conf. on Indep. Component Anal. and Blind Signal Separation (ICA2001), pp. 534-539, (San Diego, California), Dec. 2001.
    • (2001) Proc. of the Int. Conf. on Indep. Component Anal. and Blind Signal Separation (ICA2001) , pp. 534-539
    • Abdallah, S.1    Plumbley, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.