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Volumn 1, Issue 1, 2008, Pages 2-25

Efficient reconstruction of piecewise constant images using nonsmooth nonconvex minimization

Author keywords

Constrained optimization; Continuation; Deblurring; Graduated nonconvexity (GNC); Image restoration; Interior point method; Inverse problems; Nonsmooth and nonconvex optimization; Regularization; Unsupervised segmentation

Indexed keywords

CONSTRAINED OPTIMIZATION; DIFFERENTIAL EQUATIONS; IMAGE ENHANCEMENT; IMAGE RECONSTRUCTION; IMAGE SEGMENTATION; LINEAR PROGRAMMING; MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS; RESTORATION; SIMULATED ANNEALING;

EID: 84907772842     PISSN: None     EISSN: 19364954     Source Type: Journal    
DOI: 10.1137/070692285     Document Type: Article
Times cited : (183)

References (53)
  • 3
    • 31144459533 scopus 로고    scopus 로고
    • Semi-blind image restoration via Mumford-Shah regularization
    • L. Bar, N. Sochen, and N. Kiryati, Semi-blind image restoration via Mumford-Shah regularization, IEEE Trans. Image Process., 15 (2006), pp. 483-493.
    • (2006) IEEE Trans. Image Process. , vol.15 , pp. 483-493
    • Bar, L.1    Sochen, N.2    Kiryati, N.3
  • 4
    • 0028397608 scopus 로고
    • A deterministic algorithm for reconstructing images with interacting discontinuities
    • L. Bedini, I. Gerace, and A. Tonazzini, A deterministic algorithm for reconstructing images with interacting discontinuities, CVGIP: Graph. Models Image Process., 56 (1994), pp. 109-123.
    • (1994) CVGIP: Graph. Models Image Process. , vol.56 , pp. 109-123
    • Bedini, L.1    Gerace, I.2    Tonazzini, A.3
  • 5
    • 0028495770 scopus 로고
    • A GNC algorithm for constrained image reconstruction with continuous-value line process
    • L. Bedini, I. Gerace, and A. Tonazzini, A GNC algorithm for constrained image reconstruction with continuous-value line process, Pattern Recogn. Lett., 15 (1994), pp. 907-918.
    • (1994) Pattern Recogn. Lett. , vol.15 , pp. 907-918
    • Bedini, L.1    Gerace, I.2    Tonazzini, A.3
  • 6
    • 0000013152 scopus 로고
    • On the statistical analysis of dirty pictures
    • J. E. Besag, On the statistical analysis of dirty pictures, J. Roy. Statist. Soc. Ser. B, 48 (1986), pp. 259-302.
    • (1986) J. Roy. Statist. Soc. Ser. B , vol.48 , pp. 259-302
    • Besag, J.E.1
  • 7
    • 84947672901 scopus 로고
    • Digital image processing: Towards Bayesian image analysis
    • J. E. Besag, Digital image processing: Towards Bayesian image analysis, J. Appl. Statist., 16 (1989), pp. 395-407.
    • (1989) J. Appl. Statist. , vol.16 , pp. 395-407
    • Besag, J.E.1
  • 8
    • 84975602180 scopus 로고
    • Mean field approximation minimizes relative entropy
    • G. Bilbro, W. Snyder, and R. Mann, Mean field approximation minimizes relative entropy, J. Opt. Soc. Amer. A, 8 (1991), pp. 290-294.
    • (1991) J. Opt. Soc. Amer. A , vol.8 , pp. 290-294
    • Bilbro, G.1    Snyder, W.2    Mann, R.3
  • 9
    • 0030194054 scopus 로고    scopus 로고
    • On the unification of line processes, outlier rejection, and robust statistics with applications to early vision
    • M. Black and A. Rangarajan, On the unification of line processes, outlier rejection, and robust statistics with applications to early vision, Internat. J. Comput. Vision, 19 (1996), pp. 57-91.
    • (1996) Internat. J. Comput. Vision , vol.19 , pp. 57-91
    • Black, M.1    Rangarajan, A.2
  • 11
    • 0024480752 scopus 로고
    • Comparison of the efficiency of deterministic and stochastic algorithms for visual reconstruction
    • A. Blake, Comparison of the efficiency of deterministic and stochastic algorithms for visual reconstruction, IEEE Trans. Pattern Anal. Machine Intell., 11 (1989), pp. 2-12.
    • (1989) IEEE Trans. Pattern Anal. Machine Intell. , vol.11 , pp. 2-12
    • Blake, A.1
  • 12
    • 0027624429 scopus 로고
    • A generalized Gaussian image model for edge-preserving MAP estimation
    • C. Bouman and K. Sauer, A generalized Gaussian image model for edge-preserving MAP estimation, IEEE Trans. Image Process., 2 (1993), pp. 296-310.
    • (1993) IEEE Trans. Image Process. , vol.2 , pp. 296-310
    • Bouman, C.1    Sauer, K.2
  • 13
    • 0027659445 scopus 로고
    • Image sequence filtering in quantum-limited noise with applications to low-dose fluoroscopy
    • C. L. Chan, A. K. Katsaggelos, and A. V. Sahakian, Image sequence filtering in quantum-limited noise with applications to low-dose fluoroscopy, IEEE Trans. Med. Imag., 12 (1993), pp. 610-621.
    • (1993) IEEE Trans. Med. Imag. , vol.12 , pp. 610-621
    • Chan, C.L.1    Katsaggelos, A.K.2    Sahakian, A.V.3
  • 16
    • 0036871107 scopus 로고    scopus 로고
    • An adaptive level set method for nondifferentiable constrained image recovery
    • P. Combettes and J. Luo, An adaptive level set method for nondifferentiable constrained image recovery, IEEE Trans. Image Process., 11 (2002), pp. 1295-1304.
    • (2002) IEEE Trans. Image Process. , vol.11 , pp. 1295-1304
    • Combettes, P.1    Luo, J.2
  • 17
    • 0032002170 scopus 로고    scopus 로고
    • Globally convergent edge-preserving regularized reconstruction: An application to limited-angle tomography
    • A. Delaney and Y. Bresler, Globally convergent edge-preserving regularized reconstruction: An application to limited-angle tomography, IEEE Trans. Image Process., 7 (1998), pp. 204-221.
    • (1998) IEEE Trans. Image Process. , vol.7 , pp. 204-221
    • Delaney, A.1    Bresler, Y.2
  • 18
    • 0024928175 scopus 로고
    • Image reconstruction and restoration: Overview of common estimation structure and problems
    • G. Demoment, Image reconstruction and restoration: Overview of common estimation structure and problems, IEEE Trans. Acoust. Speech Signal Process., 37 (1989), pp. 2024-2036.
    • (1989) IEEE Trans. Acoust. Speech Signal Process. , vol.37 , pp. 2024-2036
    • Demoment, G.1
  • 19
    • 33751208047 scopus 로고    scopus 로고
    • Efficient minimization methods of mixed ℓ2-ℓ1 and ℓ1-ℓ1 norms for image restoration
    • H. Fu, M. K. Ng, M. Nikolova, and J. L. Barlow, Efficient minimization methods of mixed ℓ2-ℓ1 and ℓ1-ℓ1 norms for image restoration, SIAM J. Sci. Comput., 27 (2006), pp. 1881-1902.
    • (2006) SIAM J. Sci. Comput. , vol.27 , pp. 1881-1902
    • Fu, H.1    Ng, M.K.2    Nikolova, M.3    Barlow, J.L.4
  • 20
    • 0026835074 scopus 로고
    • Constrained restoration and recovery of discontinuities
    • D. Geman and G. Reynolds, Constrained restoration and recovery of discontinuities, IEEE Trans. Pattern Anal. Mach. Intell., 14 (1992), pp. 367-383.
    • (1992) IEEE Trans. Pattern Anal. Mach. Intell. , vol.14 , pp. 367-383
    • Geman, D.1    Reynolds, G.2
  • 21
    • 0029341230 scopus 로고
    • Nonlinear image recovery with half-quadratic regularization
    • D. Geman and C. Yang, Nonlinear image recovery with half-quadratic regularization, IEEE Trans. Image Process., 4 (1995), pp. 932-946.
    • (1995) IEEE Trans. Image Process. , vol.4 , pp. 932-946
    • Geman, D.1    Yang, C.2
  • 22
    • 0021518209 scopus 로고
    • Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images
    • S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Trans. Pattern Anal. Mach. Intell., 6 (1984), pp. 721-741.
    • (1984) IEEE Trans. Pattern Anal. Mach. Intell. , vol.6 , pp. 721-741
    • Geman, S.1    Geman, D.2
  • 24
    • 33645038355 scopus 로고    scopus 로고
    • Second-order cone programming methods for total variation-based image restoration
    • D. Goldfarb and W. Yin, Second-order cone programming methods for total variation-based image restoration, SIAM J. Sci. Comput., 27 (2005), pp. 622-645.
    • (2005) SIAM J. Sci. Comput. , vol.27 , pp. 622-645
    • Goldfarb, D.1    Yin, W.2
  • 25
    • 0025404969 scopus 로고
    • Bayesian reconstructions from emission tomography data using a modified EM algorithm
    • P. J. Green, Bayesian reconstructions from emission tomography data using a modified EM algorithm, IEEE Trans. Med. Imag., 9 (1990), pp. 84-93.
    • (1990) IEEE Trans. Med. Imag. , vol.9 , pp. 84-93
    • Green, P.J.1
  • 26
    • 0032165960 scopus 로고    scopus 로고
    • Variational image segmentation using boundary functions
    • G. Hewer, C. Kenney, and B. Manjunath, Variational image segmentation using boundary functions, IEEE Trans. Image Process., 7 (1998), pp. 1269-1281.
    • (1998) IEEE Trans. Image Process. , vol.7 , pp. 1269-1281
    • Hewer, G.1    Kenney, C.2    Manjunath, B.3
  • 28
    • 26444479778 scopus 로고
    • Optimization by simulated annealing
    • S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, Optimization by simulated annealing, Science, 220 (1983), pp. 671-680.
    • (1983) Science , vol.220 , pp. 671-680
    • Kirkpatrick, S.1    Gelatt, C.D.2    Vecchi, M.P.3
  • 29
    • 0025587714 scopus 로고
    • Convergence of EM image reconstruction algorithms with Gibbs priors
    • K. Lange, Convergence of EM image reconstruction algorithms with Gibbs priors, IEEE Trans. Med. Imag., 9 (1990), pp. 439-446.
    • (1990) IEEE Trans. Med. Imag. , vol.9 , pp. 439-446
    • Lange, K.1
  • 30
    • 0001863842 scopus 로고
    • Constructing simple stable descriptions for image partitioning
    • Y. Leclerc, Constructing simple stable descriptions for image partitioning, Int. J. Comput. Vis., 3 (1989), pp. 73-102.
    • (1989) Int. J. Comput. Vis. , vol.3 , pp. 73-102
    • Leclerc, Y.1
  • 32
    • 0024163847 scopus 로고
    • Restoration of blurred TV pictures caused by uniform linear motion
    • Z. K. Liu and J. Y. Xiao, Restoration of blurred TV pictures caused by uniform linear motion, CVGIP: Graph. Models Image Process., 44 (1988), pp. 30-34.
    • (1988) CVGIP: Graph. Models Image Process. , vol.44 , pp. 30-34
    • Liu, Z.K.1    Xiao, J.Y.2
  • 33
    • 33745633093 scopus 로고    scopus 로고
    • A segmentation-based regularization term for image deconvolution
    • M. Mignotte, A segmentation-based regularization term for image deconvolution, IEEE Trans. Image Process., 15 (2006), pp. 1973-1984.
    • (2006) IEEE Trans. Image Process. , vol.15 , pp. 1973-1984
    • Mignotte, M.1
  • 36
    • 0001236757 scopus 로고    scopus 로고
    • Inversion of large-support ill-posed linear operators using a piecewise Gaussian MRF
    • M. Nikolova, J. Idier, and A. Mohammad-Djafari, Inversion of large-support ill-posed linear operators using a piecewise Gaussian MRF, IEEE Trans. Image Process., 8 (1998), pp. 571-585.
    • (1998) IEEE Trans. Image Process. , vol.8 , pp. 571-585
    • Nikolova, M.1    Idier, J.2    Mohammad-Djafari, A.3
  • 37
    • 0013212015 scopus 로고    scopus 로고
    • Markovian reconstruction using a GNC approach
    • M. Nikolova, Markovian reconstruction using a GNC approach, IEEE Trans. Image Process., 8 (1999), pp. 1204-1220.
    • (1999) IEEE Trans. Image Process. , vol.8 , pp. 1204-1220
    • Nikolova, M.1
  • 38
    • 0038042413 scopus 로고    scopus 로고
    • Minimizers of cost-functions involving nonsmooth data-fidelity terms. Application to the processing of outliers
    • M. Nikolova, Minimizers of cost-functions involving nonsmooth data-fidelity terms. Application to the processing of outliers, SIAM J. Numer. Anal., 40 (2002), pp. 965-994.
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 965-994
    • Nikolova, M.1
  • 39
    • 1242284980 scopus 로고    scopus 로고
    • A variational approach to remove outliers and impulse noise
    • M. Nikolova, A variational approach to remove outliers and impulse noise, J. Math. Imaging Vision, 20 (2004), pp. 99-120.
    • (2004) J. Math. Imaging Vision , vol.20 , pp. 99-120
    • Nikolova, M.1
  • 40
    • 3142712959 scopus 로고    scopus 로고
    • Weakly constrained minimization application to the estimation of images and signals involving constant regions
    • M. Nikolova, Weakly constrained minimization application to the estimation of images and signals involving constant regions, J. Math. Imaging Vision, 21 (2004), pp. 155-175.
    • (2004) J. Math. Imaging Vision , vol.21 , pp. 155-175
    • Nikolova, M.1
  • 42
    • 0025465145 scopus 로고
    • Scale-space and edge detection using anisotropic diffusion
    • P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Mach. Intell., 12 (1990), pp. 629-639.
    • (1990) IEEE Trans. Pattern Anal. Mach. Intell. , vol.12 , pp. 629-639
    • Perona, P.1    Malik, J.2
  • 43
    • 0033341429 scopus 로고    scopus 로고
    • Simulated annealing, acceleration techniques, and image restoration
    • M. Robini, T. Rastello, and I. Magnin, Simulated annealing, acceleration techniques, and image restoration, IEEE Trans. Image Process., 8 (1999), pp. 1374-1387.
    • (1999) IEEE Trans. Image Process. , vol.8 , pp. 1374-1387
    • Robini, M.1    Rastello, T.2    Magnin, I.3
  • 44
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • L. Rudin, S. Osher, and C. Fatemi, Nonlinear total variation based noise removal algorithms, Phys. D, 60 (1992), pp. 259-268.
    • (1992) Phys. D , vol.60 , pp. 259-268
    • Rudin, L.1    Osher, S.2    Fatemi, C.3
  • 45
    • 0032123237 scopus 로고    scopus 로고
    • ML parameter estimation for Markov random fields, with applications to Bayesian tomography
    • S. Saquib, C. Bouman, and K. Sauer, ML parameter estimation for Markov random fields, with applications to Bayesian tomography, IEEE Trans. Image Process., 7 (1998), pp. 1029-1044.
    • (1998) IEEE Trans. Image Process. , vol.7 , pp. 1029-1044
    • Saquib, S.1    Bouman, C.2    Sauer, K.3
  • 49
    • 0032022521 scopus 로고    scopus 로고
    • Variational approach for edge-preserving regularization using coupled PDEs
    • S. Teboul, L. Blanc-Féraud, G. Aubert, and M. Barlaud, Variational approach for edge-preserving regularization using coupled PDEs, IEEE Trans. Image Process., 7 (1998), pp. 387-397.
    • (1998) IEEE Trans. Image Process. , vol.7 , pp. 387-397
    • Teboul, S.1    Blanc-Féraud, L.2    Aubert, G.3    Barlaud, M.4
  • 51
    • 0003451737 scopus 로고    scopus 로고
    • Ph.D. Thesis, Department of Mathematical Modelling, Technical University of Denmark, Lyngby, Denmark
    • P. Toft, The Radon Transform - Theory and Implementation, Ph.D. Thesis, Department of Mathematical Modelling, Technical University of Denmark, Lyngby, Denmark, 1996.
    • (1996) The Radon Transform - Theory and Implementation
    • Toft, P.1
  • 52
    • 0011699714 scopus 로고
    • Numerical solutions by the continuation method
    • E. Wasserstrom, Numerical solutions by the continuation method, SIAM Rev., 15 (1973), pp. 89-119.
    • (1973) SIAM Rev. , vol.15 , pp. 89-119
    • Wasserstrom, E.1
  • 53
    • 84971922797 scopus 로고
    • Interior methods for constrained optimization
    • 1992, Acta Numer., Cambridge University Press, Cambridge, UK
    • M. Wright, Interior methods for constrained optimization, in Acta Numerica, 1992, Acta Numer., Cambridge University Press, Cambridge, UK, 1992, pp. 341-407.
    • (1992) Acta Numerica , pp. 341-407
    • Wright, M.1


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