메뉴 건너뛰기




Volumn 54, Issue 2-3, 2013, Pages 350-368

An efficient algorithm for ℓ0minimization in wavelet frame based image restoration

Author keywords

0minimization; Augmented Lagrangian; Image restoration; Wavelet frames

Indexed keywords

AUGMENTED LAGRANGIANS; CT IMAGE RECONSTRUCTION; IMAGE DEBLURRING; IMAGE RESTORATION PROBLEM; MULTI-SCALE MODELING; NUMERICAL EXPERIMENTS; PIECEWISE SMOOTH FUNCTIONS; WAVELET FRAME;

EID: 84879915572     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-012-9597-4     Document Type: Article
Times cited : (97)

References (63)
  • 1
    • 0042430598 scopus 로고    scopus 로고
    • Wavelet algorithms for high-resolution image reconstruction
    • Chan, R., Chan, T., Shen, L., Shen, Z.: Wavelet algorithms for high-resolution image reconstruction. SIAM J. Sci. Comput. 24(4), 1408-1432 (2003)
    • (2003) SIAM J. Sci. Comput. , vol.24 , Issue.4 , pp. 1408-1432
    • Chan, R.1    Chan, T.2    Shen, L.3    Shen, Z.4
  • 2
    • 77952921188 scopus 로고    scopus 로고
    • Split Bregman methods and frame based image restoration
    • Cai, J., Osher, S., Shen, Z.: Split Bregman methods and frame based image restoration. Multiscale Model. Simul. 8(2), 337-369 (2009)
    • (2009) Multiscale Model. Simul. , vol.8 , Issue.2 , pp. 337-369
    • Cai, J.1    Osher, S.2    Shen, Z.3
  • 3
    • 27844460570 scopus 로고    scopus 로고
    • Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA)
    • Elad, M., Starck, J., Querre, P., Donoho, D.: Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA). Appl. Comput. Harmon. Anal. 19(3), 340-358 (2005)
    • (2005) Appl. Comput. Harmon. Anal. , vol.19 , Issue.3 , pp. 340-358
    • Elad, M.1    Starck, J.2    Querre, P.3    Donoho, D.4
  • 4
    • 27744574209 scopus 로고    scopus 로고
    • Image decomposition via the combination of sparse representations and a variational approach
    • Starck, J., Elad, M., Donoho, D.: Image decomposition via the combination of sparse representations and a variational approach. IEEE Trans. Image Process. 14(10), 1570-1582 (2005)
    • (2005) IEEE Trans. Image Process. , vol.14 , Issue.10 , pp. 1570-1582
    • Starck, J.1    Elad, M.2    Donoho, D.3
  • 8
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • Candes, 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
    • Candes, E.1    Romberg, J.2    Tao, T.3
  • 9
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • Donoho, D.: Compressed sensing. IEEE Trans. Inf. Theory 52, 1289-1306 (2006)
    • (2006) IEEE Trans. Inf. Theory , vol.52 , pp. 1289-1306
    • Donoho, D.1
  • 10
    • 84893709620 scopus 로고    scopus 로고
    • 0minimization of wavelet frame based image restoration
    • 0minimization of wavelet frame based image restoration. UCLA CAM Report, vol. 11-32 (2011)
    • (2011) UCLA CAM Report , vol.11 , Issue.32
    • Zhang, Y.1    Dong, B.2    Lu, Z.3
  • 11
    • 0016950796 scopus 로고
    • Augmented Lagrangians and applications of the proximal point algorithm in convex programming
    • Rockafellar, R.: Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Math. Oper. Res. 97-116 (1976)
    • (1976) Math. Oper. Res. 97-116
    • Rockafellar, R.1
  • 12
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259-268 (1992)
    • (1992) Physica D , vol.60 , pp. 259-268
    • Rudin, L.1    Osher, S.2    Fatemi, E.3
  • 13
    • 0031492191 scopus 로고    scopus 로고
    • Image recovery via total variation minimization and related problems
    • Chambolle, A., Lions, P.: Image recovery via total variation minimization and related problems. Numer. Math. 76(2), 167-188 (1997)
    • (1997) Numer. Math. , vol.76 , Issue.2 , pp. 167-188
    • Chambolle, A.1    Lions, P.2
  • 19
    • 60649121415 scopus 로고    scopus 로고
    • A framelet-based approach for image inpainting
    • Chan, R., Shen, L., Shen, Z.: A framelet-based approach for image inpainting. Res. Rep. 4, 325 (2005)
    • (2005) Res. Rep. , vol.4 , pp. 325
    • Chan, R.1    Shen, L.2    Shen, Z.3
  • 20
    • 78049353841 scopus 로고    scopus 로고
    • Linearized Bregman iterations for frame-based image deblurring
    • Cai, J., Osher, S., Shen, Z.: Linearized Bregman iterations for frame-based image deblurring. SIAM J. Imaging Sci. 2(1), 226-252 (2009)
    • (2009) SIAM J. Imaging Sci. , vol.2 , Issue.1 , pp. 226-252
    • Cai, J.1    Osher, S.2    Shen, Z.3
  • 21
    • 84864229832 scopus 로고    scopus 로고
    • Image restorations: Total variation, wavelet frames and beyond
    • accepted
    • Cai, J., Dong, B., Osher, S., Shen, Z.: Image restorations: total variation, wavelet frames and beyond. J. Am. Math. Soc. (2012, accepted)
    • (2012) J. Am. Math. Soc.
    • Cai, J.1    Dong, B.2    Osher, S.3    Shen, Z.4
  • 22
    • 0031571549 scopus 로고    scopus 로고
    • Affine systems in L2 (R): The analysis of the analysis operator
    • Ron, A., Shen, Z.: Affine systems in L2 (R): the analysis of the analysis operator. J. Funct. Anal. 148(2), 408-447 (1997)
    • (1997) J. Funct. Anal. , vol.148 , Issue.2 , pp. 408-447
    • Ron, A.1    Shen, Z.2
  • 23
    • 0000133685 scopus 로고
    • Ten lectures on wavelets
    • SIAM, Philadelphia
    • Daubechies, I.: Ten Lectures on Wavelets. CBMS-NSF Lecture Notes, vol. 61. SIAM, Philadelphia (1992)
    • (1992) CBMS-NSF Lecture Notes , vol.61
    • Daubechies, I.1
  • 25
    • 78649765600 scopus 로고    scopus 로고
    • Iteratively solving linear inverse problems under general convex constraints
    • Daubechies, I., Teschke, G., Vese, L.: Iteratively solving linear inverse problems under general convex constraints. Inverse Probl. Theor. Imaging 1(1), 29 (2007)
    • (2007) Inverse Probl. Theor. Imaging , vol.1 , Issue.1 , pp. 29
    • Daubechies, I.1    Teschke, G.2    Vese, L.3
  • 26
    • 67349207267 scopus 로고    scopus 로고
    • Sparse representations and Bayesian image inpainting
    • Fadili, M., Starck, J.: Sparse representations and Bayesian image inpainting. In: Proc. SPARS, vol. 5 (2005)
    • (2005) Proc. SPARS , vol.5
    • Fadili, M.1    Starck, J.2
  • 27
    • 60649102899 scopus 로고    scopus 로고
    • Inpainting and zooming using sparse representations
    • Fadili, M., Starck, J., Murtagh, F: Inpainting and zooming using sparse representations. Comput. J. 52(1), 64 (2009)
    • (2009) Comput. J. , vol.52 , Issue.1 , pp. 64
    • Fadili, M.1    Starck, J.2    Murtagh, F.3
  • 28
    • 0142200827 scopus 로고    scopus 로고
    • An EM algorithm for wavelet-based image restoration
    • Figueiredo, M., Nowak, R.: An EM algorithm for wavelet-based image restoration. IEEE Trans. Image Process. 12(8), 906-916 (2003)
    • (2003) IEEE Trans. Image Process. , vol.12 , Issue.8 , pp. 906-916
    • Figueiredo, M.1    Nowak, R.2
  • 29
    • 33645665466 scopus 로고    scopus 로고
    • A bound optimization approach to wavelet-based image deconvolution
    • ICIP 2005, IEEE, New York
    • Figueiredo, M., Nowak, R.: A bound optimization approach to wavelet-based image deconvolution. In: IEEE International Conference on Image Processing. ICIP 2005, vol. 2, np. II-782. IEEE, New York (2005)
    • (2005) IEEE International Conference on Image Processing , vol.2
    • Figueiredo, M.1    Nowak, R.2
  • 30
    • 67349242989 scopus 로고    scopus 로고
    • Convergence analysis of tight framelet approach for missing data recovery
    • Cai, J., Chan, R., Shen, L., Shen, Z.: Convergence analysis of tight framelet approach for missing data recovery. Adv. Comput. Math. 1-27 (2008)
    • (2008) Adv. Comput. Math. , pp. 1-27
    • Cai, J.1    Chan, R.2    Shen, L.3    Shen, Z.4
  • 31
  • 32
    • 33947416035 scopus 로고    scopus 로고
    • Near-optimal signal recovery from random projections: Universal encoding strategies?
    • Candes, E., Tao, T: Near-optimal signal recovery from random projections: universal encoding strategies? IEEE Trans. Inf. Theory 52(12), 5406-5425 (2006)
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.12 , pp. 5406-5425
    • Candes, E.1    Tao, T.2
  • 33
    • 29144439194 scopus 로고    scopus 로고
    • Decoding by linear programming
    • Candes, E., Tao, T: Decoding by linear programming. IEEE Trans. Inf. Theory 51(12), 4203-4215 (2005)
    • (2005) IEEE Trans. Inf. Theory , vol.51 , Issue.12 , pp. 4203-4215
    • Candes, E.1    Tao, T.2
  • 34
    • 84863162148 scopus 로고    scopus 로고
    • Penalty decomposition methods for l 0-norm minimization
    • Department of Mathematics, Simon Fraser University, Canada
    • Lu, Z., Zhang, Y: Penalty decomposition methods for l 0-norm minimization. Technical report, Department of Mathematics, Simon Fraser University, Canada (2010)
    • (2010) Technical Report
    • Lu, Z.1    Zhang, Y.2
  • 35
    • 34548724437 scopus 로고    scopus 로고
    • Exact reconstructions of sparse signals via nonconvex minimization
    • Chartrand, R.: Exact reconstructions of sparse signals via nonconvex minimization. IEEE Signal Process. Lett. 14, 707-710 (2007)
    • (2007) IEEE Signal Process. Lett. , vol.14 , pp. 707-710
    • Chartrand, R.1
  • 37
  • 39
    • 84969334819 scopus 로고    scopus 로고
    • The split Bregman algorithm for L1 regularized problems
    • Goldstein, T., Osher, S.: The split Bregman algorithm for L1 regularized problems. SIAM J. Imaging Sci. 2(2), 323-343 (2009)
    • (2009) SIAM J. Imaging Sci. , vol.2 , Issue.2 , pp. 323-343
    • Goldstein, T.1    Osher, S.2
  • 40
    • 78149463074 scopus 로고    scopus 로고
    • Bregmanized nonlocal regularization for deconvolution and sparse reconstruction
    • Zhang, X., Burger, M., Bresson, X., Osher, S.: Bregmanized nonlocal regularization for deconvolution and sparse reconstruction. SIAM J. Imaging Sci. 3, 253 (2010)
    • (2010) SIAM J. Imaging Sci. , vol.3 , pp. 253
    • Zhang, X.1    Burger, M.2    Bresson, X.3    Osher, S.4
  • 41
    • 0002211517 scopus 로고
    • A dual algorithm for the solution of nonlinear variational problems via finite element approximation
    • Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Comput. Math. Appl. 2(1), 17-40 (1976)
    • (1976) Comput. Math. Appl. , vol.2 , Issue.1 , pp. 17-40
    • Gabay, D.1    Mercier, B.2
  • 43
    • 0027113845 scopus 로고
    • On the Douglas "Rachford splitting method and the proximal point algorithm for maximal monotone operators"
    • Eckstein, J., Bertsekas, D.: On the Douglas "Rachford splitting method and the proximal point algorithm for maximal monotone operators". Math. Program. 55(1), 293-318 (1992)
    • (1992) Math. Program. , vol.55 , Issue.1 , pp. 293-318
    • Eckstein, J.1    Bertsekas, D.2
  • 44
    • 0014604308 scopus 로고
    • Multiplier and gradient methods
    • Hestenes, M.: Multiplier and gradient methods. J. Optim. Theory Appl. 4(5), 303-320 (1969)
    • (1969) J. Optim. Theory Appl. , vol.4 , Issue.5 , pp. 303-320
    • Hestenes, M.1
  • 45
    • 0002380692 scopus 로고
    • A method for non-linear constraints in minimization problems
    • Fletcher, R. ed., Academic Press, New York
    • Powell, M.: A method for non-linear constraints in minimization problems. In: Fletcher, R. (ed.) Optimization, pp. 283-298. Academic Press, New York (1969)
    • (1969) Optimization , pp. 283-298
    • Powell, M.1
  • 47
    • 79551532991 scopus 로고    scopus 로고
    • Applications of Lagrangian-based alternating direction methods and connections to split Bregman
    • Esser, E.: Applications of Lagrangian-based alternating direction methods and connections to split Bregman. CAM Rep. 9, 31 (2009)
    • (2009) CAM Rep. , vol.9 , pp. 31
    • Esser, E.1
  • 48
    • 69049118419 scopus 로고    scopus 로고
    • Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model
    • Tai, X., Wu, C.: Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model. In: Scale Space and Variational Methods in Computer Vision, pp. 502-513 (2009)
    • (2009) Scale Space and Variational Methods in Computer Vision , pp. 502-513
    • Tai, X.1    Wu, C.2
  • 49
    • 0029307534 scopus 로고
    • De-noising by soft-thresholding
    • Donoho, D.: De-noising by soft-thresholding. IEEE Trans. Inf. Theory 41, 613-627 (1995)
    • (1995) IEEE Trans. Inf. Theory , vol.41 , pp. 613-627
    • Donoho, D.1
  • 50
    • 35248814904 scopus 로고    scopus 로고
    • Rotationally invariant wavelet shrinkage
    • Mrázek, P., Weickert, J.: Rotationally invariant wavelet shrinkage. Pattern Recognit 156-163 (2003)
    • (2003) Pattern Recognit , pp. 156-163
    • Mrázek, P.1    Weickert, J.2
  • 51
    • 0009970854 scopus 로고    scopus 로고
    • Augmented Lagrangian methods and proximal point methods for convex optimization
    • Iusem, A.: Augmented Lagrangian methods and proximal point methods for convex optimization. Investig. Oper. 8, 11-49 (1999)
    • (1999) Investig. Oper. , vol.8 , pp. 11-49
    • Iusem, A.1
  • 52
    • 0001702688 scopus 로고
    • Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming
    • Eckstein, J.: Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming. Math. Oper. Res. 202-226 (1993)
    • (1993) Math. Oper. Res. , pp. 202-226
    • Eckstein, J.1
  • 53
    • 67651035078 scopus 로고    scopus 로고
    • An efficient primal-dual hybrid gradient algorithm for total variation image restoration
    • Zhu, M., Chan, T.: An efficient primal-dual hybrid gradient algorithm for total variation image restoration. Mathematics Department, UCLA, CAM Report, pp. 08-34 (2007)
    • (2007) Mathematics Department, UCLA, CAM Report , pp. 08-34
    • Zhu, M.1    Chan, T.2
  • 55
    • 85012251675 scopus 로고    scopus 로고
    • A new alternating minimization algorithm for total variation image reconstruction
    • Wang, Y., Yang, J., Yin, W., Zhang, Y.: A new alternating minimization algorithm for total variation image reconstruction. SIAM J. Imaging Sci. 1(3), 248-272 (2008)
    • (2008) SIAM J. Imaging Sci. , vol.1 , Issue.3 , pp. 248-272
    • Wang, Y.1    Yang, J.2    Yin, W.3    Zhang, Y.4
  • 56
    • 77949723995 scopus 로고    scopus 로고
    • A fast tvl1-l2 minimization algorithm for signal reconstruction from partial Fourier data
    • Yang, J., Zhang, Y., Yin, W.: A fast tvl1-l2 minimization algorithm for signal reconstruction from partial Fourier data. IEEE J. Sel. Top. Signal Process. 4, 288-297 (2009)
    • (2009) IEEE J. Sel. Top. Signal Process. , vol.4 , pp. 288-297
    • Yang, J.1    Zhang, Y.2    Yin, W.3
  • 57
    • 78651555630 scopus 로고    scopus 로고
    • Sparse signal reconstruction via iterative support detection
    • Wang, Y., Yin, W.: Sparse signal reconstruction via iterative support detection. SIAM J. Imaging Sci. 3(3), 462-491 (2010)
    • (2010) SIAM J. Imaging Sci. , vol.3 , Issue.3 , pp. 462-491
    • Wang, Y.1    Yin, W.2
  • 58
    • 84863015738 scopus 로고    scopus 로고
    • Fast algorithms for image reconstruction with application to partially parallel MR imaging
    • Chen, Y., Hager, W., Huang, F., Phan, D., Ye, X., Yin, W.: Fast algorithms for image reconstruction with application to partially parallel MR imaging. SIAM J. Imaging Sci. 5(1), 90-118 (2010)
    • (2010) SIAM J. Imaging Sci. , vol.5 , Issue.1 , pp. 90-118
    • Chen, Y.1    Hager, W.2    Huang, F.3    Phan, D.4    Ye, X.5    Yin, W.6
  • 60
    • 0442312210 scopus 로고    scopus 로고
    • Regularization of wavelet approximations
    • Antoniadis, A., Fan, J.: Regularization of wavelet approximations. J. Am. Stat. Assoc. 96(455), 939-967 (2001)
    • (2001) J. Am. Stat. Assoc. , vol.96 , Issue.455 , pp. 939-967
    • Antoniadis, A.1    Fan, J.2
  • 63
    • 0037876458 scopus 로고    scopus 로고
    • Ergodic, primal convergence in dual subgradient schemes for convex programming
    • Larsson, T., Patriksson, M., Strömberg, A.: Ergodic, primal convergence in dual subgradient schemes for convex programming. Math. Program. 86(2), 283-312 (1999)
    • (1999) Math. Program. , vol.86 , Issue.2 , pp. 283-312
    • Larsson, T.1    Patriksson, M.2    Strömberg, A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.