메뉴 건너뛰기




Volumn 6, Issue 4, 1997, Pages 493-506

Convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; PARALLEL PROCESSING SYSTEMS; PROBLEM SOLVING; SET THEORY;

EID: 0031118954     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/83.563316     Document Type: Article
Times cited : (174)

References (47)
  • 1
    • 0011353229 scopus 로고
    • An interior points algorithm for the convex feasibility problem
    • Dec.
    • R. Aharoni, A. Berman, and Y. Censor, "An interior points algorithm for the convex feasibility problem," Adv. in Appl. Math., vol. 4, pp. 479-489, Dec. 1983.
    • (1983) Adv. in Appl. Math. , vol.4 , pp. 479-489
    • Aharoni, R.1    Berman, A.2    Censor, Y.3
  • 2
    • 0024627075 scopus 로고
    • Algebraic reconstruction in CT from limited views
    • Mar.
    • A. H. Andersen, "Algebraic reconstruction in CT from limited views," IEEE Trans. Med. Imaging, vol. 8, pp. 50-55, Mar. 1989.
    • (1989) IEEE Trans. Med. Imaging , vol.8 , pp. 50-55
    • Andersen, A.H.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
  • 7
    • 0000887243 scopus 로고
    • Convergence theorems for sequences of nonlinear operators in Banach spaces
    • July
    • F. E. Browder, "Convergence theorems for sequences of nonlinear operators in Banach spaces," Math. Z., vol. 100, pp. 201-225, July 1967.
    • (1967) Math. Z. , vol.100 , pp. 201-225
    • Browder, F.E.1
  • 8
    • 5744237139 scopus 로고
    • On the behavior of a block-iterative projection method for solving convex feasibility problems
    • D. Butnariu and Y. Censor, "On the behavior of a block-iterative projection method for solving convex feasibility problems," Int. J. Comput. Math., vol. 34, pp. 79-94, 1990.
    • (1990) Int. J. Comput. Math. , vol.34 , pp. 79-94
    • Butnariu, D.1    Censor, Y.2
  • 10
    • 34250085515 scopus 로고
    • Parallel application of block-iterative methods in medical imaging and radiation therapy
    • Y. Censor, "Parallel application of block-iterative methods in medical imaging and radiation therapy," Math. Programming, vol. 42, pp. 307-325, 1988.
    • (1988) Math. Programming , vol.42 , pp. 307-325
    • Censor, Y.1
  • 11
    • 34250232993 scopus 로고
    • Cyclic subgradient projections
    • Y. Censor and A. Lent, "Cyclic subgradient projections," Math. Programming, vol. 24, pp. 233-235, 1982.
    • (1982) Math. Programming , vol.24 , pp. 233-235
    • Censor, Y.1    Lent, A.2
  • 12
    • 0026403175 scopus 로고
    • An iterative algorithm for signal reconstruction from bispectrum
    • Dec.
    • A. E. Çetin, "An iterative algorithm for signal reconstruction from bispectrum," IEEE Trans. Signal Processing, vol. 39, pp. 2621-2628, Dec. 1991.
    • (1991) IEEE Trans. Signal Processing , vol.39 , pp. 2621-2628
    • Çetin, A.E.1
  • 13
    • 0028333270 scopus 로고
    • Signal recovery from wavelet transform maxima
    • Jan.
    • A. E. Çetin and R. Ansari, "Signal recovery from wavelet transform maxima," IEEE Trans. Signal Processing, vol. 42, pp. 194-196, Jan. 1994.
    • (1994) IEEE Trans. Signal Processing , vol.42 , pp. 194-196
    • Çetin, A.E.1    Ansari, R.2
  • 14
    • 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
  • 15
    • 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
  • 16
    • 0001488677 scopus 로고
    • Construction d'un point fixe commun à une famille de contractions fermes
    • June
    • _, "Construction d'un point fixe commun à une famille de contractions fermes," C. R. Acad. Sci. Paris Sér. I Math., vol. 320, pp. 1385-1390, June 1995.
    • (1995) C. R. Acad. Sci. Paris Sér. I Math. , vol.320 , pp. 1385-1390
  • 17
    • 0000621610 scopus 로고
    • Iterations of parallel convex projections in Hilbert spaces
    • P. L. Combettes and H. Puh, "Iterations of parallel convex projections in Hilbert spaces," Numer. Funct. Anal. Optim., vol. 15, pp. 225-243, 1994.
    • (1994) Numer. Funct. Anal. Optim. , vol.15 , pp. 225-243
    • Combettes, P.L.1    Puh, H.2
  • 18
    • 0024629439 scopus 로고
    • Methods for digital restoration of signals degraded by a stochastic impulse response
    • Mar.
    • P. L. Combettes and H. J. Trussell, "Methods for digital restoration of signals degraded by a stochastic impulse response," IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp. 393-401, Mar. 1989.
    • (1989) IEEE Trans. Acoust., Speech, Signal Processing , vol.37 , pp. 393-401
    • Combettes, P.L.1    Trussell, H.J.2
  • 19
    • 0026188767 scopus 로고
    • The use of noise properties in set theoretic estimation
    • July
    • _, "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
  • 20
    • 0023363030 scopus 로고
    • A parallel subgradient projections method for the convex feasibility problem
    • June
    • L. T. Dos Santos, "A parallel subgradient projections method for the convex feasibility problem," J. Comput. Appl. Math., vol. 18, pp. 307-320, June 1987.
    • (1987) J. Comput. Appl. Math. , vol.18 , pp. 307-320
    • Dos Santos, L.T.1
  • 23
    • 0012088394 scopus 로고
    • Relaxed outer projections, weighted averages, and convex feasibility
    • S. D. Flåm and J. Zowe, "Relaxed outer projections, weighted averages, and convex feasibility," BIT, vol. 30, pp. 289-300, 1990.
    • (1990) BIT , vol.30 , pp. 289-300
    • Flåm, S.D.1    Zowe, J.2
  • 24
    • 0015372442 scopus 로고
    • Iterative methods for the three-dimensional reconstruction of an object from projections
    • July
    • P. Gilbert, "Iterative methods for the three-dimensional reconstruction of an object from projections," J. Theoret. Biol., vol. 36, pp. 105-117, July 1972.
    • (1972) J. Theoret. Biol. , vol.36 , pp. 105-117
    • Gilbert, P.1
  • 25
    • 0014905513 scopus 로고
    • Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography
    • Dec.
    • R. Gordon, R. Bender, and G. T. Herman, "Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography," J. Theoret. Biol., vol. 29, pp. 471-481, Dec. 1970.
    • (1970) J. Theoret. Biol. , vol.29 , pp. 471-481
    • Gordon, R.1    Bender, R.2    Herman, G.T.3
  • 26
    • 33845708830 scopus 로고
    • The method of projections for finding the common point of convex sets
    • L. G. Gurin (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
    • Gurin, L.G.1    Polyak, B.T.2    Raik, E.V.3
  • 28
    • 34250130112 scopus 로고
    • Convergence results for an accelerated nonlinear Cimmino algorithm
    • Aug.
    • A. N. Iusem and A. R. De Pierro, "Convergence results for an accelerated nonlinear Cimmino algorithm," Numer. Math., vol. 49, pp. 367-378, Aug. 1986.
    • (1986) Numer. Math. , vol.49 , pp. 367-378
    • Iusem, A.N.1    De Pierro, A.R.2
  • 29
    • 0003429177 scopus 로고
    • A. K. Katsaggelos, Ed., New York: Springer-Verlag
    • A. K. Katsaggelos, Ed., Digital Image Restoration. New York: Springer-Verlag, 1991.
    • (1991) Digital Image Restoration
  • 30
    • 0345295872 scopus 로고
    • Block-iterative surrogate projection methods for convex feasibility problems
    • Jan.
    • K. C. Kiwiel, "Block-iterative surrogate projection methods for convex feasibility problems," Linear Algebra Appl., vol. 215, pp. 225-259, Jan. 1995.
    • (1995) Linear Algebra Appl. , vol.215 , pp. 225-259
    • Kiwiel, K.C.1
  • 31
    • 0019625454 scopus 로고
    • An iterative method for the extrapolation of band-limited functions
    • Oct.
    • A. Lent and H. Tuy, "An iterative method for the extrapolation of band-limited functions," J. Math. Anal. Appl., vol. 83, pp. 554-565, Oct. 1981.
    • (1981) J. Math. Anal. Appl. , vol.83 , pp. 554-565
    • Lent, A.1    Tuy, H.2
  • 32
    • 0021502547 scopus 로고
    • Convergence of the cyclical relaxation method for linear inequalities
    • J. Mandel, "Convergence of the cyclical relaxation method for linear inequalities," Math. Programming, vol. 30, pp. 218-228, 1984.
    • (1984) Math. Programming , vol.30 , pp. 218-228
    • Mandel, J.1
  • 33
    • 0000376657 scopus 로고
    • Fonctionnelles sous-différentiables
    • Dec.
    • J.-J. Moreau, "Fonctionnelles sous-différentiables," C. R. Acad. Sci. Paris Sér. A, vol. 257, pp. 4117-4119, Dec. 1963.
    • (1963) C. R. Acad. Sci. Paris Sér. A , vol.257 , pp. 4117-4119
    • Moreau, J.-J.1
  • 34
    • 0027715692 scopus 로고
    • Resolution enhancement of biomagnetic images using the method of alternating projections
    • Apr.
    • S. Oh, C. Ramon, R. J. Marks II, A. C. Nelson, and M. G. Meyer, "Resolution enhancement of biomagnetic images using the method of alternating projections," IEEE Trans. Biomed. Eng., vol. 40, pp. 323-328, Apr. 1993.
    • (1993) IEEE Trans. Biomed. Eng. , vol.40 , pp. 323-328
    • Oh, S.1    Ramon, C.2    Marks II, R.J.3    Nelson, A.C.4    Meyer, M.G.5
  • 35
    • 0023981933 scopus 로고
    • Strong convergence of projection-like methods in Hilbert spaces
    • Mar.
    • N. Ottavy, "Strong convergence of projection-like methods in Hilbert spaces," J. Optim. Theory Appl., vol. 56, pp. 433-461, Mar. 1988.
    • (1988) J. Optim. Theory Appl. , vol.56 , pp. 433-461
    • Ottavy, N.1
  • 36
    • 0028463810 scopus 로고
    • POCS-based restoration of space-varying blurred images
    • July
    • M. K. Özkan, A. M. Tekalp, and M. I. Sezan, "POCS-based restoration of space-varying blurred images," IEEE Trans. Image Processing, vol. 3, pp. 450-454, July 1994.
    • (1994) IEEE Trans. Image Processing , vol.3 , pp. 450-454
    • Özkan, M.K.1    Tekalp, A.M.2    Sezan, M.I.3
  • 38
    • 0021201713 scopus 로고
    • Decomposition through formalization in a product space
    • Jan.
    • and "Decomposition through formalization in a product space," Math. Programming, vol. 28, pp. 96-115, Jan. 1984.
    • (1984) Math. Programming , vol.28 , pp. 96-115
  • 39
    • 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
  • 40
    • 0028467717 scopus 로고
    • An adaptive regularized method for deconvolution of signals with edges by convex projections
    • July
    • C. Sánchez-Avila, "An adaptive regularized method for deconvolution of signals with edges by convex projections," IEEE Trans. Signal Processing, vol. 42, pp. 1849-1851, July 1994.
    • (1994) IEEE Trans. Signal Processing , vol.42 , pp. 1849-1851
    • Sánchez-Avila, C.1
  • 41
    • 0020191820 scopus 로고
    • Image restoration by the method of convex projections: Part 2, applications and numerical results
    • Oct.
    • M. I. Sezan and H. Stark, "Image restoration by the method of convex projections: Part 2, applications and numerical results," IEEE Trans. Med. Imag., vol. 1, pp. 95-101, Oct. 1982.
    • (1982) IEEE Trans. Med. Imag. , vol.1 , pp. 95-101
    • Sezan, M.I.1    Stark, H.2
  • 42
    • 0026237983 scopus 로고
    • Prototype image constraints for set-theoretic image restoration
    • Oct.
    • M. I. Sezan and H. J. Trussell, "Prototype image constraints for set-theoretic image restoration," IEEE Trans. Signal Processing, vol. 39, pp. 2275-2285, Oct. 1991.
    • (1991) IEEE Trans. Signal Processing , vol.39 , pp. 2275-2285
    • Sezan, M.I.1    Trussell, H.J.2
  • 43
    • 0023981667 scopus 로고
    • A projection operator for the restoration of divergence-free vector fields
    • Mar.
    • P. Y. Simard and G. E. Mailloux, "A projection operator for the restoration of divergence-free vector fields," IEEE Trans. Pattern Anal. Machine Intell., vol. 10, pp. 248-256, Mar. 1988.
    • (1988) IEEE Trans. Pattern Anal. Machine Intell. , vol.10 , pp. 248-256
    • Simard, P.Y.1    Mailloux, G.E.2
  • 46
    • 0022241077 scopus 로고
    • The Landweber iteration and projection onto convex sets
    • Dec.
    • _, "The Landweber iteration and projection onto convex sets," IEEE Trans. Acoust., Speech, Signal Processing, vol. 33, pp. 1632-1634, Dec. 1985.
    • (1985) IEEE Trans. Acoust., Speech, Signal Processing , vol.33 , pp. 1632-1634
  • 47
    • 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. Imaging, vol. 1, pp. 81-94, Oct. 1982.
    • (1982) IEEE Trans. Med. Imaging , vol.1 , pp. 81-94
    • Youla, D.C.1    Webb, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.