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Volumn 15, Issue 5, 2006, Pages 1130-1142

On global and local convergence of half-quadratic algorithms

Author keywords

Algorithms; Asymptotic rate; Convergence analysis; Half quadratic (HQ) iterations; Image reconstruction; Image restoration; Robust statistics

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; STATISTICS;

EID: 33645674847     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2005.864173     Document Type: Article
Times cited : (73)

References (44)
  • 1
    • 0004267646 scopus 로고
    • Princeton NJ: Princeton Univ. Press
    • R. T. Rockafellar, Convex Analysis. Princeton, NJ: Princeton Univ. Press, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 2
    • 0026835074 scopus 로고
    • "Constrained restoration and the recovery of discontinuities"
    • Mar
    • D. Geman and G. Reynolds, "Constrained restoration and the recovery of discontinuities," IEEE Trans. Pattern Anal. Mach. Intell., vol. 14, no. 3, pp. 367-383, Mar. 1992.
    • (1992) IEEE Trans. Pattern Anal. Mach. Intell. , vol.14 , Issue.3 , pp. 367-383
    • Geman, D.1    Reynolds, G.2
  • 3
    • 0029341230 scopus 로고
    • "Nonlinear image recovery with half-quadratic regularization"
    • Jul
    • D. Geman and C. Yang, "Nonlinear image recovery with half-quadratic regularization," IEEE Trans. Image Process., vol. 4, no. 7, pp. 932-946, Jul. 1995.
    • (1995) IEEE Trans. Image Process. , vol.4 , Issue.7 , pp. 932-946
    • Geman, D.1    Yang, C.2
  • 4
    • 0035307274 scopus 로고    scopus 로고
    • "Feature-enhanced synthetic aperture radar image formation based on nonquadratic regularization"
    • Apr
    • M. Çetin and W. Karl, "Feature-enhanced synthetic aperture radar image formation based on nonquadratic regularization," IEEE Trans. Image Process., vol. 10, no. 4, pp. 623-631, Apr. 2001.
    • (2001) IEEE Trans. Image Process. , vol.10 , Issue.4 , pp. 623-631
    • Çetin, M.1    Karl, W.2
  • 5
    • 1442356628 scopus 로고    scopus 로고
    • "Modeling anisotropic undersampling of magnetic resonance angiographies and reconstruction of a high-resolution isotropic volume using half-quadratic regularization techniques"
    • Apr
    • E. Roullot, A. Herment, I. Bloch, A. de Cesare, M. Nikolova, and E. Mousseaux, "Modeling anisotropic undersampling of magnetic resonance angiographies and reconstruction of a high-resolution isotropic volume using half-quadratic regularization techniques," Signal Process., vol. 84, pp. 743-762, Apr. 2004.
    • (2004) Signal Process. , vol.84 , pp. 743-762
    • Roullot, E.1    Herment, A.2    Bloch, I.3    de Cesare, A.4    Nikolova, M.5    Mousseaux, E.6
  • 6
    • 15744371907 scopus 로고    scopus 로고
    • "Background removal from spectra by designing and minimizing a nonquadratic cost function"
    • V. Mazet, C. Carteret, D. Brie, J. Idier, and B. Humbert, "Background removal from spectra by designing and minimizing a nonquadratic cost function," Chemometrics Intell. Lab. Syst., vol. 76, pp. 121-133, 2005.
    • (2005) Chemometrics Intell. Lab. Syst. , vol.76 , pp. 121-133
    • Mazet, V.1    Carteret, C.2    Brie, D.3    Idier, J.4    Humbert, B.5
  • 8
    • 0000281286 scopus 로고
    • "Sur le point pour lequel la somme des distances de n points donnés est minimum"
    • E. Weiszfeld, "Sur le point pour lequel la somme des distances de n points donnés est minimum," Tôhoku Math. J., vol. 43, pp. 355-386, 1937.
    • (1937) Tôhoku Math. J. , vol.43 , pp. 355-386
    • Weiszfeld, E.1
  • 9
    • 0017474071 scopus 로고
    • "Bayesian methods in nonlinear digital image restoration"
    • Mar. vol. COM-26
    • B. R. Hunt, "Bayesian methods in nonlinear digital image restoration," IEEE Trans. Commun., vol. COM-26, no. 3, pp. 219-229, Mar. 1977.
    • (1977) IEEE Trans. Commun. , Issue.3 , pp. 219-229
    • Hunt, B.R.1
  • 10
    • 0141954912 scopus 로고    scopus 로고
    • "3D edge-preserving image enhancement for computed tomography"
    • Oct
    • N. Villain, Y. Goussard, J. Idier, and M. Allain, "3D edge-preserving image enhancement for computed tomography," IEEE Trans. Med. Imag., vol. 22, no. 10, pp. 1275-1287, Oct. 2003.
    • (2003) IEEE Trans. Med. Imag. , vol.22 , Issue.10 , pp. 1275-1287
    • Villain, N.1    Goussard, Y.2    Idier, J.3    Allain, M.4
  • 12
    • 0030109399 scopus 로고    scopus 로고
    • "A unified approach to statistical tomography using coordinate descent optimization"
    • Mar
    • C. A. Bouman and K. D. Sauer, "A unified approach to statistical tomography using coordinate descent optimization," IEEE Trans. Image Process., vol. 5, no. 3, pp. 480-492, Mar. 1996.
    • (1996) IEEE Trans. Image Process. , vol.5 , Issue.3 , pp. 480-492
    • Bouman, C.A.1    Sauer, K.D.2
  • 13
    • 0036911214 scopus 로고    scopus 로고
    • "Regularized approach in 3-D helical computed tomography"
    • Houston, TX, Oct
    • M. Allain, J. Idier, and Y. Goussard, "Regularized approach in 3-D helical computed tomography," in Proc. IEEE EMBS, vol. 2, Houston, TX, Oct. 2002, pp. 843-844.
    • (2002) Proc. IEEE EMBS , vol.2 , pp. 843-844
    • Allain, M.1    Idier, J.2    Goussard, Y.3
  • 14
    • 0024928175 scopus 로고
    • "Image reconstruction and restoration: Overview of common estimation structure and problems"
    • Dec. vol. ASSP-37
    • G. Demoment, "Image reconstruction and restoration: Overview of common estimation structure and problems," IEEE Trans. Acoust. Speech, Signal Process., vol. ASSP-37, no. 12, pp. 2024-2036, Dec. 1989.
    • (1989) IEEE Trans. Acoust. Speech, Signal Process. , Issue.12 , pp. 2024-2036
    • Demoment, G.1
  • 15
    • 0027624429 scopus 로고
    • "A generalized Gaussian image model for edge-preserving MAP estimation"
    • Jul
    • C. A. Bouman and K. D. Sauer, "A generalized Gaussian image model for edge-preserving MAP estimation," IEEE Trans. Image Process., vol. 2, no. 3, pp. 296-310, Jul. 1993.
    • (1993) IEEE Trans. Image Process. , vol.2 , Issue.3 , pp. 296-310
    • Bouman, C.A.1    Sauer, K.D.2
  • 16
    • 0031077064 scopus 로고    scopus 로고
    • "Deterministic edge-preserving regularization in computed imaging"
    • Feb
    • P. Charbonnier, L. Blanc-Féraud, G. Aubert, and M. Barlaud, "Deterministic edge-preserving regularization in computed imaging," IEEE Trans. Image Process., vol. 6, no. 2, pp. 298-311, Feb. 1997.
    • (1997) IEEE Trans. Image Process , vol.6 , Issue.2 , pp. 298-311
    • Charbonnier, P.1    Blanc-Féraud, L.2    Aubert, G.3    Barlaud, M.4
  • 17
    • 0002200424 scopus 로고
    • "Statistical methods for tomographic image reconstruction"
    • S. Geman and D. McClure, "Statistical methods for tomographic image reconstruction," in Proc. 46th Session ICI, Bull. ICI, vol. 52, 1987, pp. 5-21.
    • (1987) Proc. 46th Session ICI, Bull. ICI , vol.52 , pp. 5-21
    • Geman, S.1    McClure, D.2
  • 19
    • 0028546246 scopus 로고
    • "Iterative reweighted least-squares design of FIR filters"
    • Nov
    • C. Burrus, J. Barreto, and I. Selesnick, "Iterative reweighted least-squares design of FIR filters," IEEE Trans. Signal Process., vol. 42, no. 11, pp. 2926-2936, Nov. 1994.
    • (1994) IEEE Trans. Signal Process. , vol.42 , Issue.11 , pp. 2926-2936
    • Burrus, C.1    Barreto, J.2    Selesnick, I.3
  • 20
  • 21
    • 0035398793 scopus 로고    scopus 로고
    • "Convex half-quadratic criteria and interacting auxiliary variables for image restoration"
    • Jul
    • J. Idier, "Convex half-quadratic criteria and interacting auxiliary variables for image restoration," IEEE Trans. Image Process., vol. 10, no. 7, pp. 1001-1009, Jul. 2001.
    • (2001) IEEE Trans. Image Process. , vol.10 , Issue.7 , pp. 1001-1009
    • Idier, J.1
  • 22
    • 0036448043 scopus 로고    scopus 로고
    • "On global and local convergence of half-quadratic algorithms"
    • Rochester, MN, Sep
    • M. Allain, J. Idier, and Y. Goussard, "On global and local convergence of half-quadratic algorithms," in Proc. IEEE ICIP, vol. 2, Rochester, MN, Sep. 2002.
    • (2002) Proc. IEEE ICIP , vol.2
    • Allain, M.1    Idier, J.2    Goussard, Y.3
  • 23
    • 84997822230 scopus 로고
    • "Two deterministic half-quadratic regularization algorithms for computed imaging"
    • Austin, TX, Nov
    • P. Charbonnier, L. Blanc-Féraud, G. Aubert, and M. Barlaud, "Two deterministic half-quadratic regularization algorithms for computed imaging," in Proc. IEEE ICIP, vol. 2, Austin, TX, Nov. 1994, pp. 168-172.
    • (1994) Proc. IEEE ICIP , vol.2 , pp. 168-172
    • Charbonnier, P.1    Blanc-Féraud, L.2    Aubert, G.3    Barlaud, M.4
  • 24
    • 4544321807 scopus 로고    scopus 로고
    • "Extended forms of Geman and Yang algorithm: Application to MRI reconstruction"
    • Montreal, QC, Canada, May
    • S. Husse, Y. Goussard, and J. Idier, "Extended forms of Geman and Yang algorithm: Application to MRI reconstruction," in Proc. IEEE ICASSP, vol. III, Montreal, QC, Canada, May 2004, pp. 513-516.
    • (2004) Proc. IEEE ICASSP , vol.3 , pp. 513-516
    • Husse, S.1    Goussard, Y.2    Idier, J.3
  • 25
    • 0032002170 scopus 로고    scopus 로고
    • "Globally convergent edge-preserving regularized reconstruction: An application to limited-angle tomography"
    • Feb
    • A. H. Delaney and Y. Bresler, "Globally convergent edge-preserving regularized reconstruction: An application to limited-angle tomography," IEEE Trans. Image Process., vol. 7, no. 2, pp. 204-221, Feb. 1998.
    • (1998) IEEE Trans. Image Process. , vol.7 , Issue.2 , pp. 204-221
    • Delaney, A.H.1    Bresler, Y.2
  • 26
    • 0031182107 scopus 로고    scopus 로고
    • 2 minimization with application to tomography"
    • 2 minimization with application to tomography," Geophysics, vol. 62, pp. 1183-1195, 1997.
    • (1997) Geophysics , vol.62 , pp. 1183-1195
    • Bube, K.P.1    Langan, R.T.2
  • 27
    • 0000668458 scopus 로고    scopus 로고
    • "On the convergence of the lagged diffusivity fixed point method in total variation image restoration"
    • T. F. Chan and P. Mulet, "On the convergence of the lagged diffusivity fixed point method in total variation image restoration," SIAM J. Numer. Anal., vol. 36, no. 2, pp. 354-367, 1999.
    • (1999) SIAM J. Numer. Anal. , vol.36 , Issue.2 , pp. 354-367
    • Chan, T.F.1    Mulet, P.2
  • 28
    • 0008520850 scopus 로고
    • "Linear convergence of generalized Weiszfeld's method"
    • H. Voss and H. Eckhardt, "Linear convergence of generalized Weiszfeld's method," Computing, vol. 25, pp. 243-251, 1980.
    • (1980) Computing , vol.25 , pp. 243-251
    • Voss, H.1    Eckhardt, H.2
  • 29
    • 77950023906 scopus 로고    scopus 로고
    • "Optimization transfer using surrogate objective functions (with discussion)"
    • Mar
    • K. Lange, D. R. Hunter, and I. Yang, "Optimization transfer using surrogate objective functions (with discussion)," J. Comput. Graph. Statist., vol. 9, no. 1, pp. 1-20, Mar. 2000.
    • (2000) J. Comput. Graph. Statist. , vol.9 , Issue.1 , pp. 1-20
    • Lange, K.1    Hunter, D.R.2    Yang, I.3
  • 30
    • 0031106957 scopus 로고    scopus 로고
    • "Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction"
    • Apr
    • J. Fessler, E. Ficaro, N. Clinthorne, and K. Lange, "Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction," IEEE Trans. Med. Imag., vol. 16, no. 2, pp. 166-175, Apr. 1997.
    • (1997) IEEE Trans. Med. Imag. , vol.16 , Issue.2 , pp. 166-175
    • Fessler, J.1    Ficaro, E.2    Clinthorne, N.3    Lange, K.4
  • 31
    • 0033181297 scopus 로고    scopus 로고
    • "Monotonic algorithms for transmission tomography"
    • Sep
    • H. Erdogan and J. Fessler, "Monotonic algorithms for transmission tomography," IEEE Trans. Med. Imag., vol. 18, no. 9, pp. 801-814, Sep. 1999.
    • (1999) IEEE Trans. Med. Imag. , vol.18 , Issue.9 , pp. 801-814
    • Erdogan, H.1    Fessler, J.2
  • 32
    • 0034298767 scopus 로고    scopus 로고
    • "Parallelizable Bayesian tomography algorithms with rapid, guaranteed convergence"
    • Oct
    • J. Zheng, S. S. Saquib, K. Sauer, and C. A. Bouman, "Parallelizable Bayesian tomography algorithms with rapid, guaranteed convergence," IEEE Trans. Image Process., vol. 9, no. 10, pp. 1745-1759, Oct. 2000.
    • (2000) IEEE Trans. Image Process. , vol.9 , Issue.10 , pp. 1745-1759
    • Zheng, J.1    Saquib, S.S.2    Sauer, K.3    Bouman, C.A.4
  • 33
    • 0036504690 scopus 로고    scopus 로고
    • "Image recovery using partitioned-separable paraboloidal surrogate coordinate ascent algorithms"
    • Mar
    • S. Sotthivirat and J. Fessler, "Image recovery using partitioned-separable paraboloidal surrogate coordinate ascent algorithms," IEEE Trans. Image Process., vol. 11, no. 3, pp. 306-317, Mar. 2002.
    • (2002) IEEE Trans. Image Process. , vol.11 , Issue.3 , pp. 306-317
    • Sotthivirat, S.1    Fessler, J.2
  • 34
    • 0141979762 scopus 로고    scopus 로고
    • "Approche pénalisée en tomographie hélicoïdale. Application à la conception d'une prothèse personnalisée du genou"
    • Ph.D. dissertation (in French), Univ. de Paris-Sud, Orsay, France, Dec. [Online]
    • M.Allain, "Approche pénalisée en tomographie hélicoïdale. Application à la conception d'une prothèse personnalisée du genou," Ph.D. dissertation (in French), Univ. de Paris-Sud, Orsay, France, Dec. 2002. [Online] http://tel.ccsd.cnrs.fr/documents/archives0 /00/00/37/56.
    • (2002)
    • Allain, M.1
  • 38
    • 0036448917 scopus 로고    scopus 로고
    • "Comparison of the main forms of half quadratic regularization"
    • Rochester, MN, Sep
    • M. Nikolova and M. Ng, "Comparison of the main forms of half quadratic regularization," in Proc. IEEE ICIP, Rochester, MN, Sep. 2002, pp. 349-352.
    • (2002) Proc. IEEE ICIP , pp. 349-352
    • Nikolova, M.1    Ng, M.2
  • 39
    • 33646596282 scopus 로고    scopus 로고
    • "Analysis of Half-Quadratic Minimization Methods for Signal and Image Recovery"
    • M. Nikolova and M. Ng, "Analysis of Half-Quadratic Minimization Methods for Signal and Image Recovery," SIAM J. Sci. Comput., vol. 27, no. 3, pp. 937-966, 2005.
    • (2005) SIAM J. Sci. Comput. , vol.27 , Issue.3 , pp. 937-966
    • Nikolova, M.1    Ng, M.2
  • 40
    • 0027542459 scopus 로고
    • "A local update strategy for iterative reconstruction from projections"
    • Feb
    • K. D. Sauer and C. A. Bouman, "A local update strategy for iterative reconstruction from projections," IEEE Trans. Signal Process., vol. 41, no. 2, pp. 534-548, Feb. 1993.
    • (1993) IEEE Trans. Signal Process. , vol.41 , Issue.2 , pp. 534-548
    • Sauer, K.D.1    Bouman, C.A.2
  • 41
    • 0345565859 scopus 로고    scopus 로고
    • "Image reconstruction in MRI: Regularized approach by Markov random fields"
    • Barcelona, Spain
    • S. Husse and Y. Goussard, "Image reconstruction in MRI: Regularized approach by Markov random fields," in Proc. IEEE ICIP, vol. 2, Barcelona, Spain, 2003, pp. 851-854.
    • (2003) Proc. IEEE ICIP , vol.2 , pp. 851-854
    • Husse, S.1    Goussard, Y.2
  • 42
    • 0141630498 scopus 로고    scopus 로고
    • "Half-quadratic regularization for MRI image restoration"
    • R. Deriche, P. Kornprobst, M. Nikolova, and M. Ng, "Half-quadratic regularization for MRI image restoration," in Proc. IEEE ICIP, vol. 6, 2003, pp. 585-588.
    • (2003) Proc. IEEE ICIP , vol.6 , pp. 585-588
    • Deriche, R.1    Kornprobst, P.2    Nikolova, M.3    Ng, M.4
  • 43
    • 0035172896 scopus 로고    scopus 로고
    • "Fast image reconstruction algorithms combining half-quadratic regularization and preconditioning"
    • Thessaloniki, Greece, Oct
    • M. Nikolova and M. Ng, "Fast image reconstruction algorithms combining half-quadratic regularization and preconditioning," in Proc. IEEE ICIP, Thessaloniki, Greece, Oct. 2001, pp. 277-280.
    • (2001) Proc. IEEE ICIP , pp. 277-280
    • Nikolova, M.1    Ng, M.2
  • 44
    • 0002919496 scopus 로고    scopus 로고
    • "Grouped-coordinate descent algorithms for robust edge-preserving image restoration"
    • J. Fessler, "Grouped-coordinate descent algorithms for robust edge-preserving image restoration," Proc. SPIE, vol. 3170, pp. 184-194, 1997.
    • (1997) Proc. SPIE , vol.3170 , pp. 184-194
    • Fessler, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.