메뉴 건너뛰기




Volumn 23, Issue 9, 2012, Pages 1377-1389

Convergence and rate analysis of neural networks for sparse approximation

Author keywords

Exponential convergence; global stability; locally competitive algorithm; Lyapunov function; nonsmooth objective; sparse approximation

Indexed keywords

COMPETITIVE ALGORITHMS; EXPONENTIAL CONVERGENCE; GLOBAL STABILITY; NONSMOOTH OBJECTIVE; SPARSE APPROXIMATIONS;

EID: 84870977024     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2012.2202400     Document Type: Article
Times cited : (73)

References (45)
  • 2
    • 77952740831 scopus 로고    scopus 로고
    • On the role of sparse and redundant representations in image processing
    • Jun.
    • M. Elad, M. A. T. Figueiredo, and Y. Ma, "On the role of sparse and redundant representations in image processing," Proc. IEEE, vol. 98, no. 6, pp. 972-982, Jun. 2010.
    • (2010) Proc. IEEE , vol.98 , Issue.6 , pp. 972-982
    • Elad, M.1    Figueiredo, M.A.T.2    Ma, Y.3
  • 3
    • 4043166218 scopus 로고    scopus 로고
    • Sparse coding of sensory inputs
    • Aug
    • B. A. Olshausen and D. J. Field, "Sparse coding of sensory inputs," Current Opinion Neurobiol., vol. 14, no. 4, pp. 481-487, Aug. 2004.
    • (2004) Current Opinion Neurobiol , vol.14 , Issue.4 , pp. 481-487
    • Olshausen, B.A.1    Field, D.J.2
  • 4
    • 0029938380 scopus 로고    scopus 로고
    • Emergence of simple-cell receptive field properties by learning a sparse code for natural images
    • Jun
    • B. A. Olshausen and D. J. Field, "Emergence of simple-cell receptive field properties by learning a sparse code for natural images," Nature, vol. 381, no. 6583, pp. 607-609, Jun. 1996.
    • (1996) Nature , vol.381 , Issue.6583 , pp. 607-609
    • Olshausen, B.A.1    Field, D.J.2
  • 5
    • 0030779611 scopus 로고    scopus 로고
    • Sparse coding with an overcomplete basis set: A strategy employed by V1?
    • Dec
    • B. A. Olshausen and D. J. Field, "Sparse coding with an overcomplete basis set: A strategy employed by V1?" Vis. Res., vol. 37, no. 23, pp. 3311-3325, Dec. 1997.
    • (1997) Vis. Res , vol.37 , Issue.23 , pp. 3311-3325
    • Olshausen, B.A.1    Field, D.J.2
  • 6
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • Feb
    • E. J. Candes, 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
  • 7
    • 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
  • 8
    • 39449109476 scopus 로고    scopus 로고
    • An interior-point method for large-scale L1-regularized least squares
    • Dec
    • S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, "An interior-point method for large-scale L1-regularized least squares," IEEE J. Sel. Topics Signal Process., vol. 1, no. 4, pp. 606-617, Dec. 2007.
    • (2007) IEEE J. Sel. Topics Signal Process , vol.1 , Issue.4 , pp. 606-617
    • Kim, S.-J.1    Koh, K.2    Lustig, M.3    Boyd, S.4    Gorinevsky, D.5
  • 9
    • 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. 586-598, Dec. 2007.
    • (2007) IEEE J. Sel. Topics Signal Process , vol.1 , Issue.4 , pp. 586-598
    • Figueiredo, M.A.T.1    Nowak, R.D.2    Wright, S.J.3
  • 10
    • 7044231546 scopus 로고    scopus 로고
    • An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
    • Aug
    • 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, no. 11, pp. 1413-1457, Aug. 2004.
    • (2004) Commun. Pure Appl. Math , vol.57 , Issue.11 , pp. 1413-1457
    • Daubechies, I.1    Defrise, M.2    De Mol, C.3
  • 12
    • 0020118274 scopus 로고
    • Neural networks and physical systems with emergent collective computational abilities
    • Apr
    • J. J. Hopfield, "Neural networks and physical systems with emergent collective computational abilities," Proc. Nat. Acad. Sci., vol. 79, no. 8, pp. 2554-2558, Apr. 1982.
    • (1982) Proc. Nat. Acad. Sci , vol.79 , Issue.8 , pp. 2554-2558
    • Hopfield, J.J.1
  • 13
    • 68849100982 scopus 로고    scopus 로고
    • Configurable analog signal processing
    • Dec
    • C. Twigg and P. Hasler, "Configurable analog signal processing," Digital Signal Process., vol. 19, no. 6, pp. 904-922, Dec. 2009.
    • (2009) Digital Signal Process , vol.19 , Issue.6 , pp. 904-922
    • Twigg, C.1    Hasler, P.2
  • 14
    • 51849128608 scopus 로고    scopus 로고
    • Sparse coding via thresholding and local competition in neural circuits
    • Oct
    • C. J. Rozell, D. H. Johnson, R. G. Baraniuk, and B. A. Olshausen, "Sparse coding via thresholding and local competition in neural circuits," Neural Comput., vol. 20, no. 10, pp. 2526-2563, Oct. 2008.
    • (2008) Neural Comput , vol.20 , Issue.10 , pp. 2526-2563
    • Rozell, C.J.1    Johnson, D.H.2    Baraniuk, R.G.3    Olshausen, B.A.4
  • 15
    • 2442472068 scopus 로고    scopus 로고
    • Uniform stability of switched linear systems: Extensions of LaSalle's invariance principle
    • Apr
    • J. P. Hespanha, "Uniform stability of switched linear systems: Extensions of LaSalle's invariance principle," IEEE Trans. Autom. Control, vol. 49, no. 4, pp. 470-482, Apr. 2004.
    • (2004) IEEE Trans. Autom. Control , vol.49 , Issue.4 , pp. 470-482
    • Hespanha, J.P.1
  • 16
    • 34548629454 scopus 로고    scopus 로고
    • A simplified dual neural network for quadratic programming with its KWTA application
    • Nov
    • S. Liu and J. Wang, "A simplified dual neural network for quadratic programming with its KWTA application," IEEE Trans. Neural Netw., vol. 17, no. 6, pp. 1500-1510, Nov. 2006.
    • (2006) IEEE Trans. Neural Netw , vol.17 , Issue.6 , pp. 1500-1510
    • Liu, S.1    Wang, J.2
  • 17
    • 0028497220 scopus 로고
    • Exponential stability and oscillation of Hopfield graded response neural network
    • Sep
    • H. Yang and T. S. Dillon, "Exponential stability and oscillation of Hopfield graded response neural network," IEEE Trans. Neural Netw., vol. 5, no. 5, pp. 719-729, Sep. 1994.
    • (1994) IEEE Trans. Neural Netw , vol.5 , Issue.5 , pp. 719-729
    • Yang, H.1    Dillon, T.S.2
  • 18
    • 0001284544 scopus 로고    scopus 로고
    • A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints
    • Nov
    • X.-B. Liang and J. Wang, "A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints," IEEE Trans. Neural Netw., vol. 11, no. 6, pp. 1251-1262, Nov. 2000.
    • (2000) IEEE Trans. Neural Netw , vol.11 , Issue.6 , pp. 1251-1262
    • Liang, X.-B.1    Wang, J.2
  • 19
    • 10944255986 scopus 로고    scopus 로고
    • Absolute stability of analytic neural networks: An approach based on finite trajectory length
    • Dec
    • M. Forti and A. Tesi, "Absolute stability of analytic neural networks: An approach based on finite trajectory length," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 51, no. 12, pp. 2460-2469, Dec. 2004.
    • (2004) IEEE Trans. Circuits Syst. I, Reg. Papers , vol.51 , Issue.12 , pp. 2460-2469
    • Forti, M.1    Tesi, A.2
  • 20
    • 58049205433 scopus 로고    scopus 로고
    • Convergence analysis of a class of nonsmooth gradient systems
    • Dec
    • W. Lu and J. Wang, "Convergence analysis of a class of nonsmooth gradient systems," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 55, no. 11, pp. 3514-3527, Dec. 2008.
    • (2008) IEEE Trans. Circuits Syst. I, Reg. Papers , vol.55 , Issue.11 , pp. 3514-3527
    • Lu, W.1    Wang, J.2
  • 21
    • 4143078142 scopus 로고    scopus 로고
    • A recurrent neural network with exponential convergence for solving convex quadratic program and related linear piecewise equations
    • Sep
    • Y. Xia, G. Feng, and J. Wang, "A recurrent neural network with exponential convergence for solving convex quadratic program and related linear piecewise equations," Neural Netw., vol. 17, no. 7, pp. 1003-1015, Sep. 2004.
    • (2004) Neural Netw , vol.17 , Issue.7 , pp. 1003-1015
    • Xia, Y.1    Feng, G.2    Wang, J.3
  • 22
    • 33751211222 scopus 로고    scopus 로고
    • Support vector classifiers via gradient systems with discontinuous righthand sides
    • Dec
    • L. V. Ferreira, E. Kaszkurewicz, and A. Bhaya, "Support vector classifiers via gradient systems with discontinuous righthand sides," Neural Netw., vol. 19, no. 10, pp. 1612-1623, Dec. 2006.
    • (2006) Neural Netw , vol.19 , Issue.10 , pp. 1612-1623
    • Ferreira, L.V.1    Kaszkurewicz, E.2    Bhaya, A.3
  • 23
    • 0029345226 scopus 로고
    • New conditions for global stability of neural networks with application to linear and quadratic programming problems
    • Jul
    • M. Forti and A. Tesi, "New conditions for global stability of neural networks with application to linear and quadratic programming problems," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 42, no. 7, pp. 354-366, Jul. 1995.
    • (1995) IEEE Trans. Circuits Syst. I, Fundam. Theory Appl , vol.42 , Issue.7 , pp. 354-366
    • Forti, M.1    Tesi, A.2
  • 24
    • 68049124938 scopus 로고    scopus 로고
    • Dynamical behaviors of a class of recurrent neural networks with discontinuous neuron activations
    • Dec
    • L. Li and L. Huang, "Dynamical behaviors of a class of recurrent neural networks with discontinuous neuron activations," Appl. Math. Model., vol. 33, no. 12, pp. 4326-4336, Dec. 2009.
    • (2009) Appl. Math. Model , vol.33 , Issue.12 , pp. 4326-4336
    • Li, L.1    Huang, L.2
  • 25
    • 4744373635 scopus 로고    scopus 로고
    • Generalized neural network for nonsmooth nonlinear programming problems
    • Sep
    • M. Forti, P. Nistri, and M. Quincampoix, "Generalized neural network for nonsmooth nonlinear programming problems," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 51, no. 9, pp. 1741-1754, Sep. 2004.
    • (2004) IEEE Trans. Circuits Syst. I, Reg. Papers , vol.51 , Issue.9 , pp. 1741-1754
    • Forti, M.1    Nistri, P.2    Quincampoix, M.3
  • 26
    • 37849187126 scopus 로고    scopus 로고
    • Convergence of neural networks for programming problems via a nonsmooth Łojasiewicz inequality
    • Nov
    • M. Forti, P. Nistri, and M. Quincampoix, "Convergence of neural networks for programming problems via a nonsmooth Łojasiewicz inequality," IEEE Trans. Neural Netw., vol. 17, no. 6, pp. 1471-1486, Nov. 2006.
    • (2006) IEEE Trans. Neural Netw , vol.17 , Issue.6 , pp. 1471-1486
    • Forti, M.1    Nistri, P.2    Quincampoix, M.3
  • 27
    • 54749093290 scopus 로고    scopus 로고
    • Subgradient-based neural networks for nonsmooth convex optimization problems
    • Sep
    • X. Xue and W. Bian, "Subgradient-based neural networks for nonsmooth convex optimization problems," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 55, no. 8, pp. 2378-2391, Sep. 2008.
    • (2008) IEEE Trans. Circuits Syst. I, Reg. Papers , vol.55 , Issue.8 , pp. 2378-2391
    • Xue, X.1    Bian, W.2
  • 28
    • 79953827554 scopus 로고    scopus 로고
    • Finite-time convergent recurrent neural network with a hard-limiting activation function for constrained optimization with piecewise-linear objective functions
    • Apr.
    • Q. S. Liu and J. Wang, "Finite-time convergent recurrent neural network with a hard-limiting activation function for constrained optimization with piecewise-linear objective functions," IEEE Trans. Neural Netw., vol. 22, no. 4, pp. 601-613, Apr. 2011.
    • (2011) IEEE Trans. Neural Netw , vol.22 , Issue.4 , pp. 601-613
    • Liu, Q.S.1    Wang, J.2
  • 29
    • 61349147303 scopus 로고    scopus 로고
    • Stability and stabilizability of switched linear systems: A survey of recent results
    • Feb
    • H. Lin and P. J. Antsaklis, "Stability and stabilizability of switched linear systems: A survey of recent results," IEEE Trans. Autom. Control, vol. 54, no. 2, pp. 308-322, Feb. 2009.
    • (2009) IEEE Trans. Autom. Control , vol.54 , Issue.2 , pp. 308-322
    • Lin, H.1    Antsaklis, P.J.2
  • 30
    • 0034321873 scopus 로고    scopus 로고
    • On the computational power of winner-take-all
    • W. Maass, "On the computational power of winner-take-all," Neural Comput., vol. 12, no. 11, pp. 2519-2535, 2000.
    • (2000) Neural Comput , vol.12 , Issue.11 , pp. 2519-2535
    • Maass, W.1
  • 31
    • 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
  • 32
    • 0035273106 scopus 로고    scopus 로고
    • Atomic decomposition by basis pursuit
    • Mar
    • S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM Rev., vol. 43, no. 1, pp. 129-159, Mar. 2001.
    • (2001) SIAM Rev , vol.43 , Issue.1 , pp. 129-159
    • Chen, S.S.1    Donoho, D.L.2    Saunders, M.A.3
  • 33
    • 22144488449 scopus 로고    scopus 로고
    • Sparse nonnegative solutions of underdetermined linear equations by linear programming
    • D. L. Donoho and J. Tanner, "Sparse nonnegative solutions of underdetermined linear equations by linear programming," Proc. Nat. Acad. Sci. United States Amer., vol. 102, no. 27, pp. 9446-9451, 2005.
    • (2005) Proc. Nat. Acad. Sci. United States Amer , vol.102 , Issue.27 , pp. 9446-9451
    • Donoho, D.L.1    Tanner, J.2
  • 34
    • 8444239052 scopus 로고    scopus 로고
    • The Bayesian brain: The role of uncertainty in neural coding and computation
    • D. C. Knill and R. Pouget, "The Bayesian brain: The role of uncertainty in neural coding and computation," Trends Neurosci., vol. 27, no. 12, pp. 712-719, 2004.
    • (2004) Trends Neurosci , vol.27 , Issue.12 , pp. 712-719
    • Knill, D.C.1    Pouget, R.2
  • 35
    • 33847100046 scopus 로고    scopus 로고
    • A network that uses few active neurones to code visual input predicts the diverse shapes of cortical receptive fields
    • Apr
    • M. Rehn and F. T. Sommer, "A network that uses few active neurones to code visual input predicts the diverse shapes of cortical receptive fields," J. Comput. Neurosci., vol. 22, no. 2, pp. 135-146, Apr. 2007.
    • (2007) J. Comput. Neurosci , vol.22 , Issue.2 , pp. 135-146
    • Rehn, M.1    Sommer, F.T.2
  • 36
    • 33644513420 scopus 로고    scopus 로고
    • Efficient auditory coding
    • Feb
    • E. C. Smith and M. S. Lewicki, "Efficient auditory coding," Nature, vol. 439, no. 7079, pp. 978-982, Feb. 2006.
    • (2006) Nature , vol.439 , Issue.7079 , pp. 978-982
    • Smith, E.C.1    Lewicki, M.S.2
  • 37
    • 33846786895 scopus 로고    scopus 로고
    • Sparse approximation of images inspired from the functional architecture of the primary visual areas
    • S. Fischer, R. Redondo, L. Perrinet, and G. Cristóbal, "Sparse approximation of images inspired from the functional architecture of the primary visual areas," EURASIP J. Adv. Signal Process., vol. 2007, no. 1, pp. 1-17, 2007.
    • (2007) EURASIP J. Adv. Signal Process , vol.2007 , Issue.1 , pp. 1-17
    • Fischer, S.1    Redondo, R.2    Perrinet, L.3    Cristóbal, G.4
  • 38
    • 28644445613 scopus 로고    scopus 로고
    • Feature detection using spikes: The greedy approach
    • Jul
    • L. Perrinet, "Feature detection using spikes: The greedy approach," J. Physiol. (Paris), vol. 98, nos. 4-6, pp. 530-539, Jul. 2004.
    • (2004) J. Physiol. (Paris) , vol.98 , Issue.4-6 , pp. 530-539
    • Perrinet, L.1
  • 39
    • 36749005582 scopus 로고    scopus 로고
    • A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration
    • Dec
    • J. M. Bioucas-Dias and M. A. T. Figueiredo, "A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration," IEEE Trans. Image Process., vol. 16, no. 12, pp. 2992-3004, Dec. 2007.
    • (2007) IEEE Trans. Image Process , vol.16 , Issue.12 , pp. 2992-3004
    • Bioucas-Dias, J.M.1    Figueiredo, M.A.T.2
  • 41
    • 33646910241 scopus 로고    scopus 로고
    • Perspectives and results on the stability and stabilizability of hybrid systems
    • Jul
    • R. A. DeCarlo, M. S. Branicky, S. Pettersson, and B. Lennartson, "Perspectives and results on the stability and stabilizability of hybrid systems," Proc. IEEE, vol. 88, no. 7, pp. 1069-1082, Jul. 2000.
    • (2000) Proc. IEEE , vol.88 , Issue.7 , pp. 1069-1082
    • Decarlo, R.A.1    Branicky, M.S.2    Pettersson, S.3    Lennartson, B.4
  • 43
    • 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
  • 44
    • 36249023228 scopus 로고    scopus 로고
    • The Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems
    • J. Bolte, A. Daniilidis, and A. Lewis, "The Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems," SIAM J. Optim., vol. 17, no. 4, pp. 1205-1223, 2007.
    • (2007) SIAM J. Optim , vol.17 , Issue.4 , pp. 1205-1223
    • Bolte, J.1    Daniilidis, A.2    Lewis, A.3
  • 45
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate measurements
    • Aug
    • E. J. Candes, J. K. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pure Appl. Math., vol. 59, no. 8, pp. 1207-1223, Aug. 2006.
    • (2006) Commun. Pure Appl. Math , vol.59 , Issue.8 , pp. 1207-1223
    • Candes, E.J.1    Romberg, J.K.2    Tao, T.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.