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Volumn 59, Issue 3, 2014, Pages 565-589

A variable fixing version of the two-block nonlinear constrained Gauss–Seidel algorithm forℓ1-Regularized least-squares

Author keywords

Active set; Gauss Seidel algorithm; Sparse approximation; 1 Regularized least squares

Indexed keywords

APPROXIMATION ALGORITHMS; GAUSSIAN DISTRIBUTION; ITERATIVE METHODS;

EID: 84926636639     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-014-9653-0     Document Type: Article
Times cited : (5)

References (29)
  • 1
    • 77955783919 scopus 로고    scopus 로고
    • Fast image recovery using variable splitting and constrained optimization
    • Afonso, M.V., Bioucas-Dias, J.M., Figueiredo, M.A.T.: Fast image recovery using variable splitting and constrained optimization. IEEE Trans. Image Process. 19(9), 2–45 (2010)
    • (2010) IEEE Trans. Image Process. , vol.19 , Issue.9 , pp. 2-45
    • Afonso, M.V.1    Bioucas-Dias, J.M.2    Figueiredo, M.A.T.3
  • 2
    • 85014561619 scopus 로고    scopus 로고
    • A fast iterative shrinkage–threshold algorithm for linear inverse problems
    • Beck, A., Teboulle, M.: A fast iterative shrinkage–threshold algorithm for linear inverse problems. SIAM J. Imaging Sci. 2, 183–202 (2009)
    • (2009) SIAM J. Imaging Sci. , vol.2 , pp. 183-202
    • Beck, A.1    Teboulle, M.2
  • 4
    • 36749005582 scopus 로고    scopus 로고
    • A new twist: two-step iterative shrinkage/thresholding algorithms for image restoration
    • Bioucas-Dias, J., Figueiredo, M.: A new twist: two-step iterative shrinkage/thresholding algorithms for image restoration. IEEE Trans. Image Process. 16, 2992–3004 (2007)
    • (2007) IEEE Trans. Image Process. , vol.16 , pp. 2992-3004
    • Bioucas-Dias, J.1    Figueiredo, M.2
  • 5
    • 59749104367 scopus 로고    scopus 로고
    • From sparse solutions of systems of equations to sparse modeling of signals and images
    • Bruckstein, A.M., Donoho, D.L., Elad, M.: From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Rev. 51(1), 34–81 (2009)
    • (2009) SIAM Rev. , vol.51 , Issue.1 , pp. 34-81
    • Bruckstein, A.M.1    Donoho, D.L.2    Elad, M.3
  • 6
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
    • Candès, E., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52(2), 489–509 (2006)
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.2 , pp. 489-509
    • Candès, E.1    Romberg, J.2    Tao, T.3
  • 7
    • 33744726904 scopus 로고    scopus 로고
    • Quantitative robust uncertainty principles and optimally sparse decompositions
    • Candès, E., Romberg, J.: Quantitative robust uncertainty principles and optimally sparse decompositions. Found. Comput. Math. 6(2), 227–254 (2006)
    • (2006) Found. Comput. Math. , vol.6 , Issue.2 , pp. 227-254
    • Candès, E.1    Romberg, J.2
  • 8
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate measurements
    • Candès, E., Romberg, J., Tao, T.: Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math. 59(8), 1207–1223 (2006)
    • (2006) Commun. Pure Appl. Math. , vol.59 , Issue.8 , pp. 1207-1223
    • Candès, E.1    Romberg, J.2    Tao, T.3
  • 9
    • 0035273106 scopus 로고    scopus 로고
    • Atomic decomposition basis pursuit
    • Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition basis pursuit. SIAM Rev. 43, 129–159 (2001)
    • (2001) SIAM Rev. , vol.43 , pp. 129-159
    • Chen, S.S.1    Donoho, D.L.2    Saunders, M.A.3
  • 10
    • 7044231546 scopus 로고    scopus 로고
    • An iterative thresholding algorithm for linear inverse problems with sparsity constraints
    • Daubechies, I., Defrise, M., Mol, C.D.: An iterative thresholding algorithm for linear inverse problems with sparsity constraints. Commun. Pure Appl. Math. 57, 1413–1457 (2004)
    • (2004) Commun. Pure Appl. Math. , vol.57 , pp. 1413-1457
    • Daubechies, I.1    Defrise, M.2    Mol, C.D.3
  • 11
    • 28244496090 scopus 로고    scopus 로고
    • Benchmarking optimization software with performance profiles
    • Dolan, E.D., Moré, J.J.: Benchmarking optimization software with performance profiles. Math. Program 91, 201221 (2002)
    • (2002) Math. Program , vol.91 , pp. 201221
    • Dolan, E.D.1    Moré, J.J.2
  • 12
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • Donoho, D.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.4 , pp. 1289-1306
    • Donoho, D.1
  • 13
    • 0032244001 scopus 로고    scopus 로고
    • On the accurate identification of active constraints
    • Facchinei, F., Fischer, A., Kanzow, C.: On the accurate identification of active constraints. SIAM J. Optim. 9, 14–32 (1999)
    • (1999) SIAM J. Optim. , vol.9 , pp. 14-32
    • Facchinei, F.1    Fischer, A.2    Kanzow, C.3
  • 14
    • 39449126969 scopus 로고    scopus 로고
    • Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems
    • Figueiredo, M., Nowak, R., Wright, S.: Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J. Sel. Top. Signal Process. 1, 586–598 (2007)
    • (2007) IEEE J. Sel. Top. Signal Process. , vol.1 , pp. 586-598
    • Figueiredo, M.1    Nowak, R.2    Wright, S.3
  • 15
    • 0003336489 scopus 로고
    • A class of methods for nonlinear programming with termination and convergence properties
    • Abadie J, (ed), North-Holland, The Netherlands:
    • Fletcher, R.: A class of methods for nonlinear programming with termination and convergence properties. In: Abadie, J. (ed.) Integer and Nonlinear Programming, pp. 157–175. North-Holland, The Netherlands (1970)
    • (1970) Integer and Nonlinear Programming , pp. 157-175
    • Fletcher, R.1
  • 16
    • 84898064383 scopus 로고    scopus 로고
    • Matrix-free interior point method for compressed sensing problems
    • Fountoulakis, K., Gondzio, J., Zhlobich, P.: Matrix-free interior point method for compressed sensing problems. Math. Program. Comput. 6(1), 1–31 (2014)
    • (2014) Math. Program. Comput. , vol.6 , Issue.1 , pp. 1-31
    • Fountoulakis, K.1    Gondzio, J.2    Zhlobich, P.3
  • 17
    • 0032665409 scopus 로고    scopus 로고
    • Globally convergent block-coordinate techniques for unconstrained optimization
    • Grippo, L., Sciandrone, M.: Globally convergent block-coordinate techniques for unconstrained optimization. Optim. Methods Softw. 10(4), 587–637 (1999)
    • (1999) Optim. Methods Softw. , vol.10 , Issue.4 , pp. 587-637
    • Grippo, L.1    Sciandrone, M.2
  • 18
    • 0033904057 scopus 로고    scopus 로고
    • On the convergence of the block nonlinear Gauss–Seidel method under convex constraints
    • Grippo, L., Sciandrone, M.: On the convergence of the block nonlinear Gauss–Seidel method under convex constraints. Oper. Res. Lett. 26(3), 127–136 (2000)
    • (2000) Oper. Res. Lett. , vol.26 , Issue.3 , pp. 127-136
    • Grippo, L.1    Sciandrone, M.2
  • 19
    • 77950363235 scopus 로고    scopus 로고
    • A numerical study of fixed-point continuation applied to compressed sensing
    • Hale, E.T., Yin, W., Zhang, Y.: A numerical study of fixed-point continuation applied to compressed sensing. J. Comput. Math. 28(2), 170194 (2010)
    • (2010) J. Comput. Math. , vol.28 , Issue.2 , pp. 170194
    • Hale, E.T.1    Yin, W.2    Zhang, Y.3
  • 21
    • 0014604308 scopus 로고
    • Multiplier and gradient methods
    • Hestenes, M.R.: Multiplier and gradient methods. J. Optim. Methods Appl. 4, 303–320 (1969)
    • (1969) J. Optim. Methods Appl. , vol.4 , pp. 303-320
    • Hestenes, M.R.1
  • 23
    • 0002380692 scopus 로고
    • A method for nonlinear constraints in minimization problems
    • Fletcher R, (ed), Academic Press, New York:
    • Powell, M.J.D.: A method for nonlinear constraints in minimization problems. In: Fletcher, R. (ed.) Optimization, pp. 283–298. Academic Press, New York (1969)
    • (1969) Optimization , pp. 283-298
    • Powell, M.J.D.1
  • 24
    • 0001287271 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the Lasso
    • Tibshirani, R.: Regression shrinkage and selection via the Lasso. J. R. Stat. Soc. Ser. B 58(1), 267–288 (1996)
    • (1996) J. R. Stat. Soc. Ser. B , vol.58 , Issue.1 , pp. 267-288
    • Tibshirani, R.1
  • 25
    • 46749146509 scopus 로고    scopus 로고
    • A coordinate gradient descent method for nonsmooth separable minimization
    • Tseng, P., Yun, S.: A coordinate gradient descent method for nonsmooth separable minimization. Math. Program. 117(1), 387–423 (2009)
    • (2009) Math. Program. , vol.117 , Issue.1 , pp. 387-423
    • Tseng, P.1    Yun, S.2
  • 26
    • 77955666600 scopus 로고    scopus 로고
    • A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization and continuation
    • Wen, Z., Yin, W., Goldfarb, D., Zhang, Y.: A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization and continuation. SIAM J. Sci. Comput. 32(4), 1832–1857 (2010)
    • (2010) SIAM J. Sci. Comput. , vol.32 , Issue.4 , pp. 1832-1857
    • Wen, Z.1    Yin, W.2    Goldfarb, D.3    Zhang, Y.4
  • 27
    • 84864195124 scopus 로고    scopus 로고
    • On the convergence of an active-set method for $$\ell _1$$ℓ1 minimization
    • Wen, Z., Yin, W., Zhang, H., Goldfarb, D.: On the convergence of an active-set method for $$\ell _1$$ℓ1 minimization. Optim. Methods Softw. 27(6), 1127–1146 (2012)
    • (2012) Optim. Methods Softw , vol.27 , Issue.6 , pp. 1127-1146
    • Wen, Z.1    Yin, W.2    Zhang, H.3    Goldfarb, D.4
  • 29
    • 84898875155 scopus 로고    scopus 로고
    • Solving regularized linear least-squares problems by alternating direction methods with applications to image restoration
    • Zhang, J.J., Morini, B.: Solving regularized linear least-squares problems by alternating direction methods with applications to image restoration. Electron. Trans. Numer. Anal. (ETNA) 40, 356–372 (2013)
    • (2013) Electron. Trans. Numer. Anal. (ETNA) , vol.40 , pp. 356-372
    • Zhang, J.J.1    Morini, B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.