메뉴 건너뛰기




Volumn 19, Issue 2, 2013, Pages 256-269

Two-Subspace Projection Method for Coherent Overdetermined Systems

Author keywords

Computer tomography; Kaczmarz method; Randomized Kaczmarz method; Signal processing

Indexed keywords


EID: 84875385168     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00041-012-9248-z     Document Type: Article
Times cited : (66)

References (20)
  • 1
    • 0027306936 scopus 로고
    • New variants of the POCS method using affine subspaces of finite codimension, with applications to irregular sampling
    • Boston
    • Cenker, C., Feichtinger, H. G., Mayer, M., Steier, H., Strohmer, T.: New variants of the POCS method using affine subspaces of finite codimension, with applications to irregular sampling. In: Conf. SPIE 92, Boston, pp. 299-310 (1992).
    • (1992) Conf. SPIE 92 , pp. 299-310
    • Cenker, C.1    Feichtinger, H.G.2    Mayer, M.3    Steier, H.4    Strohmer, T.5
  • 2
    • 0002206795 scopus 로고
    • Strong underrelaxation in Kaczmarz's method for inconsistent systems
    • Censor, Y., Eggermont, P. P. B., Gordon, D.: Strong underrelaxation in Kaczmarz's method for inconsistent systems. Numer. Math. 41(1), 83-92 (1983).
    • (1983) Numer. Math. , vol.41 , Issue.1 , pp. 83-92
    • Censor, Y.1    Eggermont, P.P.B.2    Gordon, D.3
  • 3
    • 0031567810 scopus 로고    scopus 로고
    • The rate of convergence for the method of alternating projections
    • Deutsch, F., Hundal, H.: The rate of convergence for the method of alternating projections. J. Math. Anal. Appl. 205(2), 381-405 (1997).
    • (1997) J. Math. Anal. Appl. , vol.205 , Issue.2 , pp. 381-405
    • Deutsch, F.1    Hundal, H.2
  • 5
    • 78651472693 scopus 로고    scopus 로고
    • Semi-convergence and relaxation parameters for a class of SIRT algorithms
    • Elfving, T., Nikazad, T., Hansen, P. C.: Semi-convergence and relaxation parameters for a class of SIRT algorithms. Electron. Trans. Numer. Anal. 37, 321-336 (2010).
    • (2010) Electron. Trans. Numer. Anal. , vol.37 , pp. 321-336
    • Elfving, T.1    Nikazad, T.2    Hansen, P.C.3
  • 6
    • 0039891923 scopus 로고
    • A Kaczmarz-based approach to nonperiodic sampling on unions of rectangular lattices
    • Feichtinger, H. G., Strohmer, T.: A Kaczmarz-based approach to nonperiodic sampling on unions of rectangular lattices. In: Proc. Conf. SampTA-95, pp. 32-37 (1995).
    • (1995) Proc. Conf. SampTA-95 , pp. 32-37
    • Feichtinger, H.G.1    Strohmer, T.2
  • 7
    • 23844486226 scopus 로고    scopus 로고
    • On the rate of convergence of the alternating projection method in finite dimensional spaces
    • Galàntai, A.: On the rate of convergence of the alternating projection method in finite dimensional spaces. J. Math. Anal. Appl. 310(1), 30-44 (2005).
    • (2005) J. Math. Anal. Appl. , vol.310 , Issue.1 , pp. 30-44
    • Galàntai, A.1
  • 8
    • 0039081637 scopus 로고
    • On the acceleration of Kaczmarz's method for inconsistent linear systems
    • Hanke, M., Niethammer, W.: On the acceleration of Kaczmarz's method for inconsistent linear systems. Linear Algebra Appl. 130, 83-98 (1990).
    • (1990) Linear Algebra Appl. , vol.130 , pp. 83-98
    • Hanke, M.1    Niethammer, W.2
  • 9
    • 0027659444 scopus 로고
    • Algebraic reconstruction techniques can be made computationally efficient
    • Herman, G. T., Meyer, L. B.: Algebraic reconstruction techniques can be made computationally efficient. IEEE Trans. Med. Imaging 12(3), 600-609 (1993).
    • (1993) IEEE Trans. Med. Imaging , vol.12 , Issue.3 , pp. 600-609
    • Herman, G.T.1    Meyer, L.B.2
  • 10
    • 0001554939 scopus 로고
    • Angenäherte Auflösung von Systemen linearer Gleichungen
    • Kaczmarz, S.: Angenäherte Auflösung von Systemen linearer Gleichungen. Bull. Int. Acad. Polon. Sci. Lett. A A35, 335-357 (1937).
    • (1937) Bull. Int. Acad. Polon. Sci. Lett. A , vol.A35 , pp. 335-357
    • Kaczmarz, S.1
  • 11
    • 77956625417 scopus 로고    scopus 로고
    • Randomized methods for linear constraints: convergence rates and conditioning
    • Leventhal, D., Lewis, A. S.: Randomized methods for linear constraints: convergence rates and conditioning. Math. Oper. Res. 35(3), 641-654 (2010).
    • (2010) Math. Oper. Res. , vol.35 , Issue.3 , pp. 641-654
    • Leventhal, D.1    Lewis, A.S.2
  • 13
    • 77952012306 scopus 로고    scopus 로고
    • Randomized Kaczmarz solver for noisy linear systems
    • Needell, D.: Randomized Kaczmarz solver for noisy linear systems. BIT Numer. Math. 50(2), 395-403 (2010).
    • (2010) BIT Numer. Math. , vol.50 , Issue.2 , pp. 395-403
    • Needell, D.1
  • 15
    • 84875401473 scopus 로고    scopus 로고
    • Two-subspace projection method for coherent overdetermined systems
    • Claremont McKenna College
    • Needell, D., Ward, R.: Two-subspace projection method for coherent overdetermined systems. Technical report, Claremont McKenna College (2012).
    • (2012) Technical report
    • Needell, D.1    Ward, R.2
  • 16
    • 84875407177 scopus 로고    scopus 로고
    • Almost sure convergence for the Kaczmarz algorithm with random measurements
    • (to appear)
    • Powell, A., Chen, X.: Almost sure convergence for the Kaczmarz algorithm with random measurements. J. Fourier Anal. Appl. (to appear).
    • J. Fourier Anal. Appl.
    • Powell, A.1    Chen, X.2
  • 17
    • 84919829481 scopus 로고    scopus 로고
    • Beneath the valley of the noncommutative arithmetic-geometric mean inequality: conjectures, case studies, and consequences
    • Recht, B., Re, C.: Beneath the valley of the noncommutative arithmetic-geometric mean inequality: conjectures, case studies, and consequences. In: Proc. of COLT (2012).
    • (2012) Proc. Of COLT
    • Recht, B.1    Re, C.2
  • 18
    • 0003388852 scopus 로고
    • Applications of convex projection theory to image recovery in tomography and related areas
    • H. Stark (Ed.), San Diego: Academic Press
    • Sezan, K. M., Stark, H.: Applications of convex projection theory to image recovery in tomography and related areas. In: Stark, H. (ed.) Image Recovery: Theory and Application, pp. 415-462. Academic Press, San Diego (1987).
    • (1987) Image Recovery: Theory and Application , pp. 415-462
    • Sezan, K.M.1    Stark, H.2
  • 19
    • 33750060286 scopus 로고    scopus 로고
    • A randomized solver for linear systems with exponential convergence
    • Lecture Notes in Computer Science, Berlin: Springer
    • Strohmer, T., Vershynin, R.: A randomized solver for linear systems with exponential convergence. In: RANDOM 2006 (10th International Workshop on Randomization and Computation). Lecture Notes in Computer Science, vol. number 4110, pp. 499-507. Springer, Berlin (2006).
    • (2006) RANDOM 2006 (10th International Workshop on Randomization and Computation) , vol.4110 , pp. 499-507
    • Strohmer, T.1    Vershynin, R.2
  • 20
    • 67349206945 scopus 로고    scopus 로고
    • A randomized Kaczmarz algorithm with exponential convergence
    • Strohmer, T., Vershynin, R.: A randomized Kaczmarz algorithm with exponential convergence. J. Fourier Anal. Appl. 15, 262-278 (2009).
    • (2009) J. Fourier Anal. Appl. , vol.15 , pp. 262-278
    • Strohmer, T.1    Vershynin, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.