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Volumn 11, Issue 11, 2002, Pages 1295-1303

An adaptive level set method for nondifferentiable constrained image recovery

Author keywords

Image recovery; Level set method; Nondifferentiable optimization; Reconstruction; Restoration; Total variation

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; DISCRETE FOURIER TRANSFORMS; GRADIENT METHODS; IMAGE ENHANCEMENT; MATRIX ALGEBRA; OPTIMIZATION; SET THEORY;

EID: 0036871107     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2002.804527     Document Type: Article
Times cited : (58)

References (43)
  • 1
    • 36149030663 scopus 로고
    • Analysis of bounded variation penalty methods for ill-posed problems
    • R. Acar and C. R. Vogel, "Analysis of bounded variation penalty methods for ill-posed problems," Inv. Probl., vol. 10, pp. 1217-1229, 1994.
    • (1994) Inv. Probl. , vol.10 , pp. 1217-1229
    • Acar, R.1    Vogel, C.R.2
  • 2
    • 0023346450 scopus 로고
    • A generalization of Polyak's convergence result for subgradient optimization
    • E. Allen, R. Helgason, J. Kennington, and B. Shetty, "A generalization of Polyak's convergence result for subgradient optimization," Math. Progr., vol. 37, pp. 309-317, 1987.
    • (1987) Math. Progr. , vol.37 , pp. 309-317
    • Allen, E.1    Helgason, R.2    Kennington, J.3    Shetty, B.4
  • 3
    • 0031124308 scopus 로고    scopus 로고
    • A property of the minimum vectors of a regularizing functional defined by means of the absolute norm
    • Apr.
    • S. Alliney, "A property of the minimum vectors of a regularizing functional defined by means of the absolute norm," IEEE Trans. Signal Processing, vol. 45, pp. 913-917, Apr. 1997.
    • (1997) IEEE Trans. Signal Processing , vol.45 , pp. 913-917
    • Alliney, S.1
  • 6
    • 0030246542 scopus 로고    scopus 로고
    • On projection algorithms for solving convex feasibility problems
    • Sept.
    • H. H. Bauschke and J. M. Borwein, "On projection algorithms for solving convex feasibility problems," SIAM Rev., vol. 38, pp. 367-426, Sept. 1996.
    • (1996) SIAM Rev. , vol.38 , pp. 367-426
    • Bauschke, H.H.1    Borwein, J.M.2
  • 8
    • 0001336448 scopus 로고
    • The method of successive projection for finding a common point of convex sets
    • May
    • L. M. Brègman, "The method of successive projection for finding a common point of convex sets," Sov. Math. Dokl., vol. 6, pp. 688-692, May 1965.
    • (1965) Sov. Math. Dokl. , vol.6 , pp. 688-692
    • Brègman, L.M.1
  • 9
    • 0023438279 scopus 로고
    • On some optimization techniques in image reconstruction from projections
    • Y. Censor and G. T. Herman, "On some optimization techniques in image reconstruction from projections," Appl. Numer. Math., vol. 3, pp. 365-391, 1987.
    • (1987) Appl. Numer. Math. , vol.3 , pp. 365-391
    • Censor, Y.1    Herman, G.T.2
  • 10
    • 0031492191 scopus 로고    scopus 로고
    • Image recovery via total variation minimization and related problems
    • A. Chambolle and P. L. Lions, "Image recovery via total variation minimization and related problems," Numer. Math., vol. 76, pp. 167-188, 1997.
    • (1997) Numer. Math. , vol.76 , pp. 167-188
    • Chambolle, A.1    Lions, P.L.2
  • 11
    • 0027541192 scopus 로고
    • The foundations of set theoretic estimation
    • Feb.
    • P. L. Combettes, "The foundations of set theoretic estimation," Proc. IEEE, vol. 81, pp. 182-208, Feb. 1993.
    • (1993) Proc. IEEE , vol.81 , pp. 182-208
    • Combettes, P.L.1
  • 12
    • 0027579732 scopus 로고
    • Signal recovery by best feasible approximation
    • Apr.
    • ____, "Signal recovery by best feasible approximation," IEEE Trans. Image Processing, vol. 2, pp. 269-271, Apr. 1993.
    • (1993) IEEE Trans. Image Processing , vol.2 , pp. 269-271
    • Combettes, P.L.1
  • 13
    • 0028543165 scopus 로고
    • Inconsistent signal feasibility problems: Least-squares solutions in a product space
    • Nov.
    • ____, "Inconsistent signal feasibility problems: Least-squares solutions in a product space," IEEE Trans. Signal Processing, vol. 42, pp. 2955-2966, Nov. 1994.
    • (1994) IEEE Trans. Signal Processing , vol.42 , pp. 2955-2966
    • Combettes, P.L.1
  • 14
    • 77954607855 scopus 로고    scopus 로고
    • The convex feasibility problem in image recovery
    • New York: Academic
    • ____, "The convex feasibility problem in image recovery," in Advances in Imaging and Electron Physics. New York: Academic, 1996, vol. 95, pp. 155-270.
    • (1996) Advances in Imaging and Electron Physics , vol.95 , pp. 155-270
    • Combettes, P.L.1
  • 15
    • 0031118954 scopus 로고    scopus 로고
    • Convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections
    • Apr.
    • ____, "Convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections," IEEE Trans. Image Processing, vol. 6, pp. 493-506, Apr. 1997.
    • (1997) IEEE Trans. Image Processing , vol.6 , pp. 493-506
    • Combettes, P.L.1
  • 16
    • 0033889575 scopus 로고    scopus 로고
    • Strong convergence of block-iterative outer approximation methods for convex optimization
    • Feb.
    • ____, "Strong convergence of block-iterative outer approximation methods for convex optimization," SIAM J. Contr. Optim., vol. 38, pp. 538-575, Feb. 2000.
    • (2000) SIAM J. Contr. Optim. , vol.38 , pp. 538-565
    • Combettes, P.L.1
  • 17
    • 0032653272 scopus 로고    scopus 로고
    • Hard-constrained inconsistent signal feasibility problems
    • Sept.
    • P. L. Combettes and P. Bondon, "Hard-constrained inconsistent signal feasibility problems," IEEE Trans. Signal Processing, vol. 47, pp. 2460-2468, Sept. 1999.
    • (1999) IEEE Trans. Signal Processing , vol.47 , pp. 2460-2468
    • Combettes, P.L.1    Bondon, P.2
  • 18
    • 0026188767 scopus 로고
    • The use of noise properties in set theoretic estimation
    • July
    • P. L. Combettes and H. J. Trussell, "The use of noise properties in set theoretic estimation," IEEE Trans. Signal Processing, vol. 39, pp. 1630-1641, July 1991.
    • (1991) IEEE Trans. Signal Processing , vol.39 , pp. 1630-1641
    • Combettes, P.L.1    Trussell, H.J.2
  • 20
    • 0000908433 scopus 로고    scopus 로고
    • Convergence of a simple subgradient level method
    • J.-L. Goffin and K. C. Kiwiel, "Convergence of a simple subgradient level method," Math. Progr., vol. 85, pp. 207-211, 1999.
    • (1999) Math. Progr. , vol.85 , pp. 207-211
    • Goffin, J.-L.1    Kiwiel, K.C.2
  • 21
    • 0022091196 scopus 로고
    • Signal synthesis in the presence of an inconsistent set of constraints
    • July
    • M. Goldburg and R. J. Marks II, "Signal synthesis in the presence of an inconsistent set of constraints," IEEE Trans. Circuits Syst., vol. CAS-32, pp. 647-663, July 1985.
    • (1985) IEEE Trans. Circuits Syst. , vol.CAS-32 , pp. 647-663
    • Goldburg, M.1    Marks R.J. II2
  • 22
    • 33845708830 scopus 로고
    • The method of projections for finding the common point of convex sets
    • L. G. Gubin, B. T. Polyak, and E. V. Raik, "The method of projections for finding the common point of convex sets," USSR Comput. Math. Math. Phys., vol. 7, pp. 1-24, 1967.
    • (1967) USSR Comput. Math. Math. Phys. , vol.7 , pp. 1-24
    • Gubin, L.G.1    Polyak, B.T.2    Raik, E.V.3
  • 23
    • 0033682338 scopus 로고    scopus 로고
    • Adaptive image reconstruction using information measures
    • U. Hermann and D. Noll, "Adaptive image reconstruction using information measures," SIAM J. Contr. Optim., vol. 38, pp. 1223-1240, 2000.
    • (2000) SIAM J. Contr. Optim. , vol.38 , pp. 1223-1240
    • Hermann, U.1    Noll, D.2
  • 25
    • 0025745988 scopus 로고
    • Variable target value subgradient method
    • S. Kim, H. Ahn, and S. C. Cho, "Variable target value subgradient method," Math. Progr., vol. 49, pp. 359-369, 1991.
    • (1991) Math. Progr. , vol.49 , pp. 359-369
    • Kim, S.1    Ahn, H.2    Cho, S.C.3
  • 26
    • 0030104971 scopus 로고    scopus 로고
    • The efficiency of subgradient projection methods for convex optimization. Part I: General level methods and Part II: Implementations and extensions
    • Mar.
    • K. C. Kiwiel, "The efficiency of subgradient projection methods for convex optimization. Part I: General level methods and Part II: Implementations and extensions." SIAM J. Contr. Optim., vol. 34, pp. 660/667-676/697 Mar. 1996.
    • (1996) SIAM J. Contr. Optim. , vol.34
    • Kiwiel, K.C.1
  • 27
    • 0022908688 scopus 로고
    • An optimal technique for constraint-based image restoration and reconstruction
    • Dec.
    • R. M. Leahy and C. E. Goutis, "An optimal technique for constraint-based image restoration and reconstruction," IEEE Trans. Acoust., Speech, Signal Processing, vol. 34, pp. 1629-1642, Dec. 1986.
    • (1986) IEEE Trans. Acoust., Speech, Signal Processing , vol.34 , pp. 1629-1642
    • Leahy, R.M.1    Goutis, C.E.2
  • 29
    • 0030171218 scopus 로고    scopus 로고
    • A computational algorithm for minimizing total variation in image reconstruction
    • June
    • Y. Li and F. Santosa, "A computational algorithm for minimizing total variation in image reconstruction," IEEE Trans. Image Processing, vol. 5, pp. 987-995, June 1996.
    • (1996) IEEE Trans. Image Processing , vol.5 , pp. 987-995
    • Li, Y.1    Santosa, F.2
  • 30
    • 0036602309 scopus 로고    scopus 로고
    • Optical wavefront reconstruction: Theory and numerical methods
    • D. R. Luke, J. V. Burke, and R. G. Lyon, "Optical wavefront reconstruction: Theory and numerical methods," SIAM Rev., vol. 44, pp. 169-224, 2002.
    • (2002) SIAM Rev. , vol.44 , pp. 169-224
    • Luke, D.R.1    Burke, J.V.2    Lyon, R.G.3
  • 31
    • 0032350054 scopus 로고    scopus 로고
    • Reconstruction with noisy data: An approach via eigenvalue optimization
    • Feb.
    • D. Noll, "Reconstruction with noisy data: An approach via eigenvalue optimization," SIAM J. Optim., vol. 8, pp. 82-104, Feb. 1998.
    • (1998) SIAM J. Optim. , vol.8 , pp. 82-104
    • Noll, D.1
  • 32
    • 49849127729 scopus 로고
    • Minimization of unsmooth functionals
    • B. T. Polyak, "Minimization of unsmooth functionals," USSR Comput. Math. Math. Phys., vol. 9, pp. 14-29, 1969.
    • (1969) USSR Comput. Math. Math. Phys. , vol.9 , pp. 14-29
    • Polyak, B.T.1
  • 34
    • 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
  • 35
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • L. I. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Phys. D, vol. 60, pp. 259-268, 1992.
    • (1992) Phys. D , vol.60 , pp. 259-268
    • Rudin, L.I.1    Osher, S.2    Fatemi, E.3
  • 38
    • 0001632008 scopus 로고
    • General structure of regularization procedures in image reconstruction
    • March
    • D. M. Titterington, "General structure of regularization procedures in image reconstruction," Astron. Astrophys., vol. 144, pp. 381-387, March 1985.
    • (1985) Astron. Astrophys. , vol.144 , pp. 381-387
    • Titterington, D.M.1
  • 40
    • 0001556589 scopus 로고    scopus 로고
    • Iterative methods for total variation denoising
    • Jan.
    • C. R. Vogel and M. E. Oman, "Iterative methods for total variation denoising," SIAM J. Sci. Comput., vol. 17, pp. 227-238, Jan. 1996.
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 227-238
    • Vogel, C.R.1    Oman, M.E.2
  • 41
    • 0032096686 scopus 로고    scopus 로고
    • Fast, robust total variation-based reconstruction of noisy, blurred images
    • June
    • ____, "Fast, robust total variation-based reconstruction of noisy, blurred images," IEEE Trans. Image Processing, vol. 7, pp. 813-824, June 1998.
    • (1998) IEEE Trans. Image Processing , vol.7 , pp. 813-824
    • Vogel, C.R.1    Oman, M.E.2
  • 42
    • 0022705171 scopus 로고
    • Extensions of a result on the synthesis of signals in the presence of inconsistent constraints
    • Apr.
    • D. C. Youla and V. Velasco, "Extensions of a result on the synthesis of signals in the presence of inconsistent constraints." IEEE Trans. Circuits Syst., vol. CAS-33, pp. 465-468, Apr. 1986.
    • (1986) IEEE Trans. Circuits Syst. , vol.CAS-33 , pp. 465-468
    • Youla, D.C.1    Velasco, V.2
  • 43
    • 0020191832 scopus 로고
    • Image restoration by the method of convex projections: Part 1-Theory
    • Oct.
    • D. C. Youla and H. Webb, "Image restoration by the method of convex projections: Part 1-Theory," IEEE Trans. Med. Imag., vol. MI-1, pp. 81-94, Oct. 1982.
    • (1982) IEEE Trans. Med. Imag. , vol.MI-1 , pp. 81-94
    • Youla, D.C.1    Webb, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.