메뉴 건너뛰기




Volumn 4, Issue 2, 2010, Pages 288-297

A fast alternating direction method for TVL1-L2 signal reconstruction from partial Fourier data

Author keywords

Alternating direction method; Compressed sensing; Compressive sensing (CS); Discrete cosine transform (DCT); Fast Fourier transform (FFT); Magnetic resonance imaging (MRI); MRI reconstruction; Total variation

Indexed keywords

ALTERNATING DIRECTION METHODS; COMPRESSED SENSING; COMPRESSIVE SENSING (CS); MRI RECONSTRUCTION; TOTAL VARIATION;

EID: 77949723995     PISSN: 19324553     EISSN: None     Source Type: Journal    
DOI: 10.1109/JSTSP.2010.2042333     Document Type: Article
Times cited : (602)

References (47)
  • 2
    • 55649115527 scopus 로고    scopus 로고
    • A simple proof of the restricted isometry property for random matrices
    • R. Baraniuk, M. Davenport, R. DeVore, and M.Wakin, "A simple proof of the restricted isometry property for random matrices," Constructive Approx., vol.28, pp. 253-263, 2008.
    • (2008) Constructive Approx. , vol.28 , pp. 253-263
    • Baraniuk, R.1    Davenport, M.2    Devore, R.3    Wakin, M.4
  • 5
    • 85014561619 scopus 로고    scopus 로고
    • A fast iterative shrinkage-thresholding algorithm for linear inverse problems
    • A. Beck and M. Teboulle, "A fast iterative shrinkage-thresholding algorithm for linear inverse problems," SIAM J. Imag. Sci., vol.2, no.1, pp. 183-202, 2009.
    • (2009) SIAM J. Imag. Sci. , vol.2 , Issue.1 , pp. 183-202
    • Beck, A.1    Teboulle, M.2
  • 6
    • 36749005582 scopus 로고    scopus 로고
    • A new TwIST: Two-step iterative thresholding algorithm for image restoration
    • Dec.
    • J. Bioucas-Dias and M. Figueiredo, "A new TwIST: Two-step iterative thresholding algorithm for image restoration," IEEE Trans. Imag. Process., vol.16, no.12, pp. 2992-3004, Dec. 2007.
    • (2007) IEEE Trans. Imag. Process , vol.16 , Issue.12 , pp. 2992-3004
    • Bioucas-Dias, J.1    Figueiredo, M.2
  • 7
    • 69949177588 scopus 로고    scopus 로고
    • An iterative algorithm for linear inverse problems with compound regularizers
    • San Diego, CA
    • J. M. Bioucas-Dias and M. Figueiredo, "An iterative algorithm for linear inverse problems with compound regularizers," in Proc. IEEE Int. Conf. Image Process., San Diego, CA, 2008, pp. 685-688.
    • (2008) Proc. IEEE Int. Conf. Image Process , pp. 685-688
    • Bioucas-Dias, J.M.1    Figueiredo, M.2
  • 8
    • 69049120308 scopus 로고    scopus 로고
    • Near-ideal model selection by L1 minimization
    • E. Candés and Y. Plan, "Near-ideal model selection by L1 minimization," Ann. Statist., vol. 37, no. 5A, pp. 2145-2177.
    • Ann. Statist. , vol.37 , Issue.5 A , pp. 2145-2177
    • Candés, E.1    Plan, Y.2
  • 10
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate information
    • E. Candés, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate information," Commun. Pure Appl. Math., vol.59, pp. 1207-1233, 2005.
    • (2005) Commun. Pure Appl. Math. , vol.59 , pp. 1207-1233
    • Candés, E.1    Romberg, J.2    Tao, T.3
  • 11
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • E. Candés, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Info. Theory, vol.52, no.2, pp. 489-509, 2006.
    • (2006) IEEE Trans. Info. Theory , vol.52 , Issue.2 , pp. 489-509
    • Candés, E.1    Romberg, J.2    Tao, T.3
  • 12
    • 34249687049 scopus 로고    scopus 로고
    • Sparsity and incoherence in compressive sampling
    • E. Candés and J. Romberg, "Sparsity and incoherence in compressive sampling," Inverse Problems, vol.23, pp. 969-985, 2006.
    • (2006) Inverse Problems , vol.23 , pp. 969-985
    • Candés, E.1    Romberg, J.2
  • 13
    • 29144439194 scopus 로고    scopus 로고
    • Decoding by linear programming
    • Dec.
    • E. Candés and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol.51, no.12, pp. 4203-4215, Dec. 2005.
    • (2005) IEEE Trans. Inf. Theory , vol.51 , Issue.12 , pp. 4203-4215
    • Candés, E.1    Tao, T.2
  • 14
    • 33947416035 scopus 로고    scopus 로고
    • Near optimal signal recovery from random projections: Universal encoding strategies
    • Dec.
    • E. Candés and T. Tao, "Near optimal signal recovery from random projections: Universal encoding strategies," IEEE Trans. Inf. Theory, vol.52, no.12, pp. 5406-5425, Dec. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.12 , pp. 5406-5425
    • Candés, E.1    Tao, T.2
  • 15
    • 1242352408 scopus 로고    scopus 로고
    • An algorithm for total variation minimization and applications
    • A. Chambolle, "An algorithm for total variation minimization and applications," J. Math. Imag. Vis., vol.20, pp. 89-97, 2004.
    • (2004) J. Math. Imag. Vis. , vol.20 , pp. 89-97
    • Chambolle, A.1
  • 16
    • 70449490591 scopus 로고    scopus 로고
    • Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data
    • R. Chartrand, "Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data," in Proc. IEEE Int. Symp. Biomed. Imag. (ISBI), 2009.
    • (2009) Proc. IEEE Int. Symp. Biomed. Imag. (ISBI)
    • Chartrand, R.1
  • 18
    • 62649171652 scopus 로고    scopus 로고
    • A proximal decomposition method for solving convex variational inverse problems
    • P. L. Combettes and J.-C. Pesquet, "A proximal decomposition method for solving convex variational inverse problems," Inverse Problems, vol.24, no.6, 2008, Article ID 065014.
    • (2008) Inverse Problems , vol.24 , Issue.6
    • Combettes, P.L.1    Pesquet, J.-C.2
  • 19
    • 34548674463 scopus 로고    scopus 로고
    • A note on wavelet-based inversion algorithms
    • C. De Mol and M. Defrise, "A note on wavelet-based inversion algorithms," Contemp. Math., vol.313, pp. 85-96, 2002.
    • (2002) Contemp. Math. , vol.313 , pp. 85-96
    • De Mol, C.1    Defrise, M.2
  • 20
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • Apr.
    • D. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol.52, no.4, pp. 1289-1306, Apr. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.4 , pp. 1289-1306
    • Donoho, D.1
  • 21
    • 33744552752 scopus 로고    scopus 로고
    • For most large underdetermined systems of linear equations, the minimal l1-norm solution is also the sparsest solution
    • D. Donoho, "For most large underdetermined systems of linear equations, the minimal l1-norm solution is also the sparsest solution," Commun. Pure Appl. Math., vol.59, no.7, pp. 907-934, 2006.
    • (2006) Commun. Pure Appl. Math. , vol.59 , Issue.7 , pp. 907-934
    • Donoho, D.1
  • 22
    • 84967782959 scopus 로고
    • On the numerical solution of heat conduction problems in two and three space variables
    • J. Douglas and H. Rachford, "On the numerical solution of heat conduction problems in two and three space variables," Trans. Amer. Math. Soc., vol.82, pp. 421-439, 1956.
    • (1956) Trans. Amer. Math. Soc. , vol.82 , pp. 421-439
    • Douglas, J.1    Rachford, H.2
  • 23
    • 0027113845 scopus 로고
    • On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
    • North-Holland
    • J. Eckstein and D. Bertsekas, "On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators," Mathematical Programming, vol.55, 1992, North-Holland.
    • (1992) Mathematical Programming , vol.55
    • Eckstein, J.1    Bertsekas, D.2
  • 24
    • 79551532991 scopus 로고    scopus 로고
    • Applications of Lagrangian-based alternating direction methods and connections to split Bregman
    • E. Esser, "Applications of Lagrangian-based alternating direction methods and connections to split Bregman," UCLA, Los Angeles, CAM Rep. 09-31, 2009.
    • (2009) UCLA, Los Angeles, CAM Rep. , pp. 09-31
    • Esser, E.1
  • 26
    • 0142200827 scopus 로고    scopus 로고
    • An em algorithm for wavelet-based image restoration
    • Dec.
    • M. Figueiredo and R. Nowak, "An EM algorithm for wavelet-based image restoration," IEEE Trans. Image Process., vol.12, no.8, pp. 906-916, Dec. 2003.
    • (2003) IEEE Trans. Image Process , vol.12 , Issue.8 , pp. 906-916
    • Figueiredo, M.1    Nowak, R.2
  • 27
    • 0002211517 scopus 로고
    • A dual algorithm for the solution of nonlinear variational problems via finite-element approximations
    • D. Gabay and B. Mercier, "A dual algorithm for the solution of nonlinear variational problems via finite-element approximations," Comp. Math. Appl., vol.2, pp. 17-40, 1976.
    • (1976) Comp. Math. Appl. , vol.2 , pp. 17-40
    • Gabay, D.1    Mercier, B.2
  • 28
    • 0016536442 scopus 로고
    • Sur lapproximation par elements finis dordre un, et la resolution par penalisation-dualite dune classe de problemes de Dirichlet nonlineaires
    • R. Glowinski and A. Marrocco, "Sur lapproximation par elements finis dordre un, et la resolution par penalisation-dualite dune classe de problemes de Dirichlet nonlineaires," Rev. Francaise dAut. Inf. Rech. Oper., vol.R-2, pp. 41-76, 1975.
    • (1975) Rev. Francaise DAut. Inf. Rech. Oper. , vol.R-2 , pp. 41-76
    • Glowinski, R.1    Marrocco, A.2
  • 30
    • 0003200255 scopus 로고
    • Augmented Lagrangian and operatorsplitting methods in nonlinear mechanics
    • Philadelphia, PA: SIAM
    • R. Glowinski and P. Le Tallec, "Augmented Lagrangian and operatorsplitting methods in nonlinear mechanics," in SIAM Studies in Applied Mathematics. Philadelphia, PA: SIAM, 1989.
    • (1989) SIAM Studies in Applied Mathematics
    • Glowinski, R.1    Le Tallec, P.2
  • 31
    • 69949140539 scopus 로고    scopus 로고
    • The split Bregman method for l1 regularized problems
    • T. Goldstein and S. Osher, "The split Bregman method for l1 regularized problems," UCLA, Los Angeles, CAM Rep. 08-29, 2008.
    • (2008) UCLA, Los Angeles, CAM Rep. , pp. 08-29
    • Goldstein, T.1    Osher, S.2
  • 32
    • 38149131932 scopus 로고    scopus 로고
    • MR image reconstruction by using the iterative refinement method and nonlinear inverse scale space methods
    • L. He, T.-C. Chang, S. Osher, T. Fang, and P. Speier, "MR image reconstruction by using the iterative refinement method and nonlinear inverse scale space methods," UCLA, Los Angeles, CAM Rep. 06-35, 2006.
    • (2006) UCLA, Los Angeles, CAM Rep. , pp. 06-35
    • He, L.1    Chang, T.-C.2    Osher, S.3    Fang, T.4    Speier, P.5
  • 33
    • 0242462717 scopus 로고    scopus 로고
    • A new inexact alternating directions method for monotone variational inequalities
    • B. S. He, L. Z. Liao, D. Han, and H. Yang, "A new inexact alternating directions method for monotone variational inequalities," Math. Progam. Ser. A, vol.92, pp. 103-118, 2002.
    • (2002) Math. Progam. Ser. A , vol.92 , pp. 103-118
    • He, B.S.1    Liao, L.Z.2    Han, D.3    Yang, H.4
  • 34
    • 36849088522 scopus 로고    scopus 로고
    • Sparse MRI: The application of compressed sensing for rapid MR imaging
    • M. Lustig, D. Donoho, and J. Pauly, "Sparse MRI: The application of compressed sensing for rapidMRimaging," Magn. Resonance in Med., vol.58, no.6, pp. 1182-1195, 2007.
    • (2007) Magn. Resonance in Med. , vol.58 , Issue.6 , pp. 1182-1195
    • Lustig, M.1    Donoho, D.2    Pauly, J.3
  • 35
    • 51949114453 scopus 로고    scopus 로고
    • An efficient algorithm for compressed MR imaging using total variation and wavelets
    • S. Ma,W. Yin, Y. Zhang, and A. Chakraborty, "An efficient algorithm for compressed MR imaging using total variation and wavelets," in Proc.IEEE Conf. CVPR, 2008, pp. 1-8.
    • (2008) Proc.IEEE Conf. CVPR , pp. 1-8
    • Maw. Yin, S.1    Zhang, Y.2    Chakraborty, A.3
  • 36
    • 19844370110 scopus 로고    scopus 로고
    • An iterated regularization method for total variation-based image restoration
    • S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, "An iterated regularization method for total variation-based image restoration," Multiscale Model. Simul., vol.4, pp. 460-489, 2005.
    • (2005) Multiscale Model. Simul. , vol.4 , pp. 460-489
    • Osher, S.1    Burger, M.2    Goldfarb, D.3    Xu, J.4    Yin, W.5
  • 37
    • 84892206732 scopus 로고    scopus 로고
    • [Online]. Available
    • Rice Wavelet Toolbox, [Online]. Available: http://www.dsp.rice.edu/ software/rwt.shtml
    • Rice Wavelet Toolbox
  • 38
    • 77949675954 scopus 로고    scopus 로고
    • Douglas-rachford splitting and frame shrinkage
    • Proc. 2nd Int. Conf. Scale Space Methods and Variational Methods in Comput. Vis. Split Bregman Algorithm
    • S. Setzer, "Douglas-rachford splitting and frame shrinkage," in Proc. 2nd Int. Conf. Scale Space Methods and Variational Methods in Comput. Vis., Lecture Notes in Computer Science, 2009, Split Bregman Algorithm.
    • (2009) Lecture Notes in Computer Science
    • Setzer, S.1
  • 39
    • 64649083745 scopus 로고    scopus 로고
    • Signal recovery from random measurements via orthogonal matching pursuit
    • J. A. Tropp and A. C. Gilbert, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Trans. Inf. Theory, vol.53, no.12, pp. 4655-4666, 2007.
    • (2007) IEEE Trans. Inf. Theory , vol.53 , Issue.12 , pp. 4655-4666
    • Tropp, J.A.1    Gilbert, A.C.2
  • 41
    • 85012251675 scopus 로고    scopus 로고
    • A new alternating minimization algorithm for total variation image reconstruction
    • Y. Wang, J.-F. Yang, W. Yin, and Y. Zhang, "A new alternating minimization algorithm for total variation image reconstruction," SIAM J. Imag. Sci., vol.1, no.3, pp. 248-272, 2008.
    • (2008) SIAM J. Imag. Sci. , vol.1 , Issue.3 , pp. 248-272
    • Wang, Y.1    Yang, J.-F.2    Yin, W.3    Zhang, Y.4
  • 43
    • 85024122496 scopus 로고    scopus 로고
    • A fast algorithm for edgepreserving variational multichannel image restoration
    • J.-F.Yang, W. Yin, Y. Zhang, and Y.Wang, "A fast algorithm for edgepreserving variational multichannel image restoration," SIAM J. Imag. Sci., vol.2, no.2, pp. 569-592, 2009.
    • (2009) SIAM J. Imag. Sci. , vol.2 , Issue.2 , pp. 569-592
    • Yang, J.-F.1    Yin, W.2    Zhang, Y.3    Wang, Y.4
  • 44
    • 76149100480 scopus 로고    scopus 로고
    • An efficient TVL1 algorithm for deblurring of multichannel images corrupted by impulsive noise
    • J.-F.Yang, Y. Zhang, and W.Yin, "An efficient TVL1 algorithm for deblurring of multichannel images corrupted by impulsive noise," SIAM J. Sci. Comput., vol.31, no.4, pp. 2842-2865, 2009.
    • (2009) SIAM J. Sci. Comput. , vol.31 , Issue.4 , pp. 2842-2865
    • Yang, J.-F.1    Zhang, Y.2    Yin, W.3
  • 46
    • 84977895355 scopus 로고    scopus 로고
    • Bregman iterative algorithms for L1-minimization with applications to compressed sensing
    • W. Yin, S. Osher, D. Goldfarb, and J. Darbon, "Bregman iterative algorithms for L1-minimization with applications to compressed sensing," SIAM J. Imag. Sci., vol.1, no.1, pp. 143-168, 2008.
    • (2008) SIAM J. Imag. Sci. , vol.1 , Issue.1 , pp. 143-168
    • Yin, W.1    Osher, S.2    Goldfarb, D.3    Darbon, J.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.