메뉴 건너뛰기




Volumn 21, Issue 5, 2012, Pages 2559-2571

Higher degree total variation (HDTV) regularization for image recovery

Author keywords

Higher degree total variation (HDTV); majorize minimize (MM)

Indexed keywords

DIRECTIONAL DERIVATIVE; DIRECTIONAL IMAGES; FUNCTIONALS; IMAGE CHARACTERISTICS; IMAGE DERIVATIVES; IMAGE RECOVERY; IMAGE REGULARIZATION; JOINT SPARSITY; MAJORIZE MINIMIZE (MM); MIXED-NORM; NUMERICAL COMPARISON; OPTIMIZATION PROBLEMS; PERFORMANCE IMPROVEMENTS; PRACTICAL PROBLEMS; REGULARIZER; RINGING ARTIFACTS; TOTAL VARIATION; WAVELET ALGORITHMS;

EID: 84860153628     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2012.2183143     Document Type: Article
Times cited : (193)

References (51)
  • 1
    • 61349108034 scopus 로고    scopus 로고
    • Deblurring from highly incomplete measurements for remote sensing
    • Mar
    • J. Ma and F.-X. Le Dimet, "Deblurring from highly incomplete measurements for remote sensing," IEEE Trans. Geosci. Remote Sens., vol. 47, no. 3, pp. 792-802, Mar. 2009.
    • (2009) IEEE Trans. Geosci. Remote Sens. , vol.47 , Issue.3 , pp. 792-802
    • Ma, J.1    Le Dimet, F.-X.2
  • 3
    • 0032096686 scopus 로고    scopus 로고
    • Fast, robust total variation-based reconstruction of noisy, blurred images
    • Jun
    • C. Vogel and M. Oman, "Fast, robust total variation-based reconstruction of noisy, blurred images," IEEE Trans. Image Process., vol. 7, no. 6, pp. 813-824, Jun. 1998.
    • (1998) IEEE Trans. Image Process. , vol.7 , Issue.6 , pp. 813-824
    • Vogel, C.1    Oman, M.2
  • 4
    • 77951120567 scopus 로고    scopus 로고
    • Nonlinear inverse scale space methods for total variation blind deconvolution
    • Jan
    • A. Marquina, "Nonlinear inverse scale space methods for total variation blind deconvolution," SIAM J. Imag. Sci., vol. 2, no. 1, pp. 64-83, Jan. 2009.
    • (2009) SIAM J. Imag. Sci. , vol.2 , Issue.1 , pp. 64-83
    • Marquina, A.1
  • 5
    • 78651583229 scopus 로고    scopus 로고
    • Deblurring of one dimensional bar codes via total variation energy minimization
    • R. Choksi and Y. van Gennip, "Deblurring of one dimensional bar codes via total variation energy minimization," SIAM J. Imag. Sci., vol. 3, no. 4, pp. 735-764, 2010.
    • (2010) SIAM J. Imag. Sci. , vol.3 , Issue.4 , pp. 735-764
    • Choksi, R.1    Van Gennip, Y.2
  • 6
    • 84859080213 scopus 로고    scopus 로고
    • Total variation as a local filter
    • C. Louchet and L. Moisan, "Total variation as a local filter," SIAM J. Imag. Sci., vol. 4, no. 2, pp. 651-694, 2011.
    • (2011) SIAM J. Imag. Sci. , vol.4 , Issue.2 , pp. 651-694
    • Louchet, C.1    Moisan, L.2
  • 7
    • 84860146005 scopus 로고    scopus 로고
    • A total variation model for retinex
    • M. K. Ng andW.Wang, "A total variation model for retinex," SIAM J. Imag. Sci., vol. 4, no. 1, pp. 345-365, 2011.
    • (2011) SIAM J. Imag. Sci. , vol.4 , Issue.1 , pp. 345-365
    • Ng, M.K.1    Wang, W.2
  • 8
    • 8744270279 scopus 로고    scopus 로고
    • Decomposition of images by the anisotropic rudin-osher-fatemi model
    • Dec
    • S.Osher and S. Esedoglu, "Decomposition of images by the anisotropic Rudin-Osher-Fatemi model," Commun. Pure Appl. Math., vol. 57, no. 12, pp. 1609-1626, Dec. 2004.
    • (2004) Commun. Pure Appl. Math. , vol.57 , Issue.12 , pp. 1609-1626
    • Osher, S.1    Esedoglu, S.2
  • 9
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • Nov
    • L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Phys. D, Nonlin. Phenom., vol. 60, no. 1-4, pp. 259-268, Nov. 1992.
    • (1992) Phys. D, Nonlin. Phenom. , vol.60 , Issue.1-4 , pp. 259-268
    • Rudin, L.1    Osher, S.2    Fatemi, E.3
  • 11
    • 77954956923 scopus 로고    scopus 로고
    • Total variation regularization for image denoising, ii. Examples
    • Oct
    • W. K. Allard, "Total variation regularization for image denoising, II. Examples," SIAM J. Imag. Sci., vol. 1, no. 4, pp. 400-417, Oct. 2008.
    • (2008) SIAM J. Imag. Sci. , vol.1 , Issue.4 , pp. 400-417
    • Allard, W.K.1
  • 12
    • 84907779428 scopus 로고    scopus 로고
    • A new total variation method for multiplicative noise removal
    • Jan
    • Y.-M. Huang, M. K. Ng, and Y.-W. Wen, "A new total variation method for multiplicative noise removal," SIAM J. Imag. Sci., vol. 2, no. 1, pp. 20-40, Jan. 2009.
    • (2009) SIAM J. Imag. Sci. , vol.2 , Issue.1 , pp. 20-40
    • Huang, Y.-M.1    Ng, M.K.2    Wen, Y.-W.3
  • 13
    • 78651583621 scopus 로고    scopus 로고
    • Improved total variation-type regularization using higher order edge detectors
    • Apr.
    • W. Stefan, R. A. Renaut, and A. Gelb, "Improved total variation-type regularization using higher order edge detectors," SIAM J. Imag. Sci., vol. 3, no. 2, pp. 232-251, Apr. 2010.
    • (2010) SIAM J. Imag. Sci. , vol.3 , Issue.2 , pp. 232-251
    • Stefan, W.1    Renaut, R.A.2    Gelb, A.3
  • 14
    • 79957451716 scopus 로고    scopus 로고
    • An upwind finite-difference method for total variation-based image smoothing
    • A. Chambolle, S. E. Levine, and B. J. Lucier, "An upwind finite-difference method for total variation-based image smoothing," SIAM J. Imag. Sci., vol. 4, no. 1, pp. 277-299, 2011.
    • (2011) SIAM J. Imag. Sci. , vol.4 , Issue.1 , pp. 277-299
    • Chambolle, A.1    Levine, S.E.2    Lucier, B.J.3
  • 15
    • 84860136829 scopus 로고    scopus 로고
    • Contour stencils: Total variation along curves for adaptive image interpolation
    • P. Getreuer, "Contour stencils: Total variation along curves for adaptive image interpolation," SIAM J. Imag. Sci., vol. 4, no. 3, pp. 954-979, 2011.
    • (2011) SIAM J. Imag. Sci. , vol.4 , Issue.3 , pp. 954-979
    • Getreuer, P.1
  • 16
    • 0031333506 scopus 로고    scopus 로고
    • Total variation image restoration: Numerical methods and extensions
    • P. Blomgren, T. F. Chan, P. Mulet, and C. K. Wong, "Total variation image restoration: Numerical methods and extensions," in Proc. IEEE ICIP, 1997, pp. 384-387.
    • (1997) Proc. IEEE ICIP , pp. 384-387
    • Blomgren, P.1    Chan, T.F.2    Mulet, P.3    Wong, C.K.4
  • 17
    • 0035074671 scopus 로고    scopus 로고
    • Higher-order total variation-based image restoration
    • Jul
    • T. Chan, A.Marqina, and P. Mulet, "Higher-order total variation-based image restoration," SIAM J. Sci. Comput., vol. 22, no. 2, pp. 503-516, Jul. 2000.
    • (2000) SIAM J. Sci. Comput. , vol.22 , Issue.2 , pp. 503-516
    • Chan, T.1    Marqina, A.2    Mulet, P.3
  • 18
    • 24644476589 scopus 로고    scopus 로고
    • Relations between higher order tv regularization and support vector regression
    • Jan
    • G. Steidl, S. Didas, and J. Neumann, "Relations between higher order TV regularization and support vector regression," Scale-Space, PDE Methods Comput. Vis., vol. 3459, pp. 515-527, Jan. 2005.
    • (2005) Scale-Space, PDE Methods Comput. Vis. , vol.3459 , pp. 515-527
    • Steidl, G.1    Didas, S.2    Neumann, J.3
  • 19
    • 34249819922 scopus 로고    scopus 로고
    • Recent developments in total variation image restoration
    • Berlin, Germany: Springer-Verlag
    • T. Chan, S. Esedoglu, F. Park, and A. Yip, "Recent developments in total variation image restoration," in Mathematics Models Computer Vision. Berlin, Germany: Springer-Verlag, 2005.
    • (2005) Mathematics Models Computer Vision
    • Chan, T.1    Esedoglu, S.2    Park, F.3    Yip, A.4
  • 20
    • 33746456398 scopus 로고    scopus 로고
    • Splines in higher order tv regularization
    • Dec
    • G. Steidl, S. Didas, and J. Neumann, "Splines in higher order TV regularization," Int. J. Comput. Vis., vol. 70, no. 3, pp. 241-255, Dec. 2006.
    • (2006) Int. J. Comput. Vis. , vol.70 , Issue.3 , pp. 241-255
    • Steidl, G.1    Didas, S.2    Neumann, J.3
  • 21
    • 0034298888 scopus 로고    scopus 로고
    • Fourth-order partial differential equations for noise removal
    • Oct
    • Y. You and M. Kaveh, "Fourth-order partial differential equations for noise removal," IEEE Trans. Image Process., vol. 9, no. 10, pp. 1723-1730, Oct. 2000.
    • (2000) IEEE Trans. Image Process. , vol.9 , Issue.10 , pp. 1723-1730
    • You, Y.1    Kaveh, M.2
  • 22
    • 4544278119 scopus 로고    scopus 로고
    • Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time
    • Dec
    • M. Lysaker, A. Lundervold, and X.-C. Tai, "Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time," IEEE Trans. Image Process., vol. 12, no. 12, pp. 1579-1590, Dec. 2003.
    • (2003) IEEE Trans. Image Process. , vol.12 , Issue.12 , pp. 1579-1590
    • Lysaker, M.1    Lundervold, A.2    Tai, X.-C.3
  • 23
    • 0036685493 scopus 로고    scopus 로고
    • Generalized sampling: A variational approach, part i
    • Aug
    • J. Kybic, T. Blu, and M. Unser, "Generalized sampling: A variational approach, part I," IEEE Trans. Signal Process., vol. 50, no. 8, pp. 1965-1976, Aug. 2002.
    • (2002) IEEE Trans. Signal Process. , vol.50 , Issue.8 , pp. 1965-1976
    • Kybic, J.1    Blu, T.2    Unser, M.3
  • 24
    • 78651078998 scopus 로고    scopus 로고
    • A fourth order dual method for staircase reduction in texture extraction and image restoration problems
    • T. F. Chan, S. Esedoglu, and F. E. Park, "A fourth order dual method for staircase reduction in texture extraction and image restoration problems," in Proc. IEEE Int. Conf. Image Process., 2010, pp. 4137-4140.
    • (2010) Proc. IEEE Int. Conf. Image Process. , pp. 4137-4140
    • Chan, T.F.1    Esedoglu, S.2    Park, F.E.3
  • 25
    • 29344446686 scopus 로고    scopus 로고
    • Iterative image restoration combining total variationminimization and a second order functional
    • M. Lysaker, "Iterative image restoration combining total variationminimization and a second order functional," Int. J. Comput. Vis., vol. 66, no. 1, pp. 5-18, 2006.
    • (2006) Int. J. Comput. Vis. , vol.66 , Issue.1 , pp. 5-18
    • Lysaker, M.1
  • 26
    • 0031492191 scopus 로고    scopus 로고
    • Image recovery via total variation minimization and related problems
    • Apr
    • A. Chambolle and P. Lions, "Image recovery via total variation minimization and related problems," Numerische Mathematik, vol. 76, no. 2, pp. 167-188, Apr. 1997.
    • (1997) Numerische Mathematik , vol.76 , Issue.2 , pp. 167-188
    • Chambolle, A.1    Lions, P.2
  • 27
    • 78651543709 scopus 로고    scopus 로고
    • Total generalized variation
    • K. Bredies, K. Kunisch, and T. Pock, "Total generalized variation," SIAM J. Imag. Sci., vol. 3, no. 3, pp. 492-526, 2010.
    • (2010) SIAM J. Imag. Sci. , vol.3 , Issue.3 , pp. 492-526
    • Bredies, K.1    Kunisch, K.2    Pock, T.3
  • 28
    • 79251548920 scopus 로고    scopus 로고
    • Second order total generalized variation (tgv) for mri
    • Feb.
    • F. Knoll, K. Bredies, T. Pock, and R. Stollberger, "Second order total generalized variation (TGV) for MRI," Magn. Reson. Med., vol. 65, no. 2, pp. 480-491, Feb. 2011.
    • (2011) Magn. Reson. Med. , vol.65 , Issue.2 , pp. 480-491
    • Knoll, F.1    Bredies, K.2    Pock, T.3    Stollberger, R.4
  • 29
    • 36749019495 scopus 로고    scopus 로고
    • Recovery algorithms for vector valued data with joint sparsity constraints
    • Mar
    • M. Fornasier and H. Rauhut, "Recovery algorithms for vector valued data with joint sparsity constraints," SIAM J. Numer. Anal., vol. 46, no. 2, pp. 577-613, Mar. 2008.
    • (2008) SIAM J. Numer. Anal. , vol.46 , Issue.2 , pp. 577-613
    • Fornasier, M.1    Rauhut, H.2
  • 30
    • 67349190935 scopus 로고    scopus 로고
    • The application of joint sparsity and total variation minimization algorithms to a real-life art restoration problem
    • M. Fornasier, R. Ramlau, and G. Teschke, "The application of joint sparsity and total variation minimization algorithms to a real-life art restoration problem," Adv. Comput. Math., vol. 31, no. 1, pp. 157-184, 2009.
    • (2009) Adv. Comput. Math. , vol.31 , Issue.1 , pp. 157-184
    • Fornasier, M.1    Ramlau, R.2    Teschke, G.3
  • 32
    • 36749031147 scopus 로고    scopus 로고
    • An iteratively reweighted norm algorithm for minimization of total variation functionals
    • Dec
    • B. Wohlberg and P. Rodriguez, "An iteratively reweighted norm algorithm for minimization of total variation functionals," IEEE Signal Process. Lett., vol. 14, no. 12, pp. 948-951, Dec. 2007.
    • (2007) IEEE Signal Process. Lett. , vol.14 , Issue.12 , pp. 948-951
    • Wohlberg, B.1    Rodriguez, P.2
  • 33
    • 0001556589 scopus 로고    scopus 로고
    • Iterative methods for total variation de-noising
    • C. Vogel and M. Oman, "Iterative methods for total variation de-noising," SIAM J. Sci. Comput., vol. 17, no. 1, pp. 227-238, 1996.
    • (1996) SIAM J. Sci. Comput. , vol.17 , Issue.1 , pp. 227-238
    • Vogel, C.1    Oman, M.2
  • 34
    • 0000668458 scopus 로고    scopus 로고
    • On the convergence of the lagged diffusivity fixed point method in total variation image restoration
    • T. 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.1    Mulet, P.2
  • 35
    • 78649843367 scopus 로고    scopus 로고
    • On total variation denoising: A new majorization-minimization algorithm and an experimental comparison with wavelet denoising
    • M. Figueiredo, J. Dias, J. Oliveira, and R. Nowak, "On total variation denoising: A new majorization-minimization algorithm and an experimental comparison with wavelet denoising," in Proc. IEEE Int. Conf. Image Process., 2006, pp. 2633-2636.
    • (2006) Proc. IEEE Int. Conf. Image Process. , pp. 2633-2636
    • Figueiredo, M.1    Dias, J.2    Oliveira, J.3    Nowak, R.4
  • 36
    • 0000418073 scopus 로고
    • On the stability of inverse problems
    • A. Tychonoff, "On the stability of inverse problems," Doklady Akademii Nauk SSSR, vol. 39, no. 5, pp. 195-198, 1943.
    • (1943) Doklady Akademii Nauk SSSR , vol.39 , Issue.5 , pp. 195-198
    • Tychonoff, A.1
  • 37
    • 61349142394 scopus 로고    scopus 로고
    • A fast multilevel algorithm for waveletregularized image restoration
    • Mar
    • C. Vonesch and M. Unser, "A fast multilevel algorithm for waveletregularized image restoration," IEEE Trans. Image Process., vol. 18, no. 3, pp. 509-523, Mar. 2009.
    • (2009) IEEE Trans. Image Process. , vol.18 , Issue.3 , pp. 509-523
    • Vonesch, C.1    Unser, M.2
  • 38
    • 36749072615 scopus 로고    scopus 로고
    • Majorization-minimization algorithms forwavelet-based image restoration
    • Dec
    • M. Figueiredo, J. Bioucas-Dias, and R. Nowak, "Majorization- minimization algorithms forwavelet-based image restoration," IEEE Trans. Image Process., vol. 16, no. 12, pp. 2980-2991, Dec. 2007.
    • (2007) IEEE Trans. Image Process. , vol.16 , Issue.12 , pp. 2980-2991
    • Figueiredo, M.1    Bioucas-Dias, J.2    Nowak, R.3
  • 39
    • 1242308449 scopus 로고    scopus 로고
    • Video denoising using 2-d and 3-d dual-tree complex wavelet transforms
    • Jan
    • I. Selesnick and K. Li, "Video denoising using 2-D and 3-D dual-tree complex wavelet transforms," in Proc. SPIE, Jan. 2003, pp. 607-618.
    • (2003) Proc. SPIE , pp. 607-618
    • Selesnick, I.1    Li, K.2
  • 40
    • 0029487233 scopus 로고
    • The steerable pyramid: A flexible architecture for multi-scale derivative computation
    • Oct
    • E. Simoncelli and W. Freeman, "The steerable pyramid: A flexible architecture for multi-scale derivative computation," in Proc. IEEE Int. Conf. Image Process., Oct. 1995, vol. III, pp. 444-447.
    • (1995) Proc. IEEE Int. Conf. Image Process. , vol.3 , pp. 444-447
    • Simoncelli, E.1    Freeman, W.2
  • 41
  • 42
    • 17144426986 scopus 로고    scopus 로고
    • Vector-valued image regularization with pdes: A common framework for different applications
    • Apr
    • D. Tschumperle and R. Deriche, "Vector-valued image regularization with PDEs: A common framework for different applications," IEEE Trans. Pattern Anal. Mach. Intell., vol. 27, no. 4, pp. 506-517, Apr. 2005.
    • (2005) IEEE Trans. Pattern Anal. Mach. Intell. , vol.27 , Issue.4 , pp. 506-517
    • Tschumperle, D.1    Deriche, R.2
  • 44
    • 36348943666 scopus 로고    scopus 로고
    • The sure-let approach to image denoising
    • Nov
    • T. Blu and F. Luisier, "The sure-let approach to image denoising," IEEE Trans. Image Process., vol. 16, no. 11, pp. 2778-2786, Nov. 2007.
    • (2007) IEEE Trans. Image Process. , vol.16 , Issue.11 , pp. 2778-2786
    • Blu, T.1    Luisier, F.2
  • 46
    • 33749009570 scopus 로고    scopus 로고
    • Robust generalized cross-validation for choosing the regularization parameter
    • Oct. [Online]. Available:
    • M. A. Lukas, "Robust generalized cross-validation for choosing the regularization parameter," Inverse Probl. vol. 22, no. 5, pp. 1883-1902, Oct. 2006 [Online]. Available: http://stacks.iop.org/0266-5611/22/i=5/ a=021
    • (2006) Inverse Probl. , vol.22 , Issue.5 , pp. 1883-1902
    • Lukas, M.A.1
  • 47
    • 50549090016 scopus 로고    scopus 로고
    • Monte-carlo sure: A black-box optimization of regularization parameters for general denoising algorithms
    • Sep. [Online]. Available:
    • S. Ramani, T. Blu, and M. Unser, "Monte-Carlo sure: a black-box optimization of regularization parameters for general denoising algorithms," IEEE Trans. Image Process.-Publ. IEEE Signal Process. Soc. vol. 17, no. 9, pp. 1540-1554, Sep. 2008 [Online]. Available: http:// www.ncbi.nlm.nih.gov/pubmed/18701393
    • (2008) IEEE Trans. Image Process.-Publ. IEEE Signal Process. Soc. , vol.17 , Issue.9 , pp. 1540-1554
    • Ramani, S.1    Blu, T.2    Unser, M.3
  • 48
    • 70449473857 scopus 로고    scopus 로고
    • A sure approach for digital signal/image deconvolution problems
    • Dec. [Online]. Available
    • J.-C. Pesquet, A. Benazza-Benyahia, and C. Chaux, "A SURE approach for digital signal/image deconvolution problems," IEEE Trans. Signal Process. vol. 57, no. 12, pp. 4616-4632, Dec. 2009 [Online]. Available: http://ieeexplore.ieee.org/xpl/freeabs-all.jsp?arnumber= 5109706
    • (2009) IEEE Trans. Signal Process. , vol.57 , Issue.12 , pp. 4616-4632
    • Pesquet, J.-C.1    Benazza-Benyahia, A.2    Chaux, C.3
  • 49
    • 80055053462 scopus 로고    scopus 로고
    • Regularized parallel mri reconstruction using an alternating direction method of multipliers
    • S. Ramani and J. A. Fessler, "Regularized parallel MRI reconstruction using an alternating direction method of multipliers," in Proc. IEEE Int. Symp. Biomed. Imag.-From Nano to Macro, 2011, pp. 385-388.
    • (2011) Proc. IEEE Int. Symp. Biomed. Imag.-From Nano to Macro , pp. 385-388
    • Ramani, S.1    Fessler, J.A.2
  • 50
    • 85012251675 scopus 로고    scopus 로고
    • A new alternating minimization algorithm for total variation image reconstruction
    • Y. Wang, J. 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.2    Yin, W.3    Zhang, Y.4
  • 51
    • 78650834156 scopus 로고    scopus 로고
    • Augmented lagragian method, dual methods and split bregman iteration for rof, vectorial tv, and higher order models
    • Jul.
    • C. Wu and X.-C. Tai, "Augmented Lagragian method, dual methods and split Bregman iteration for ROF, vectorial TV, and higher order models," SIAM J. Imag. Sci., vol. 3, no. 3, pp. 300-339, Jul. 2010.
    • (2010) SIAM J. Imag. Sci. , vol.3 , Issue.3 , pp. 300-339
    • Wu, C.1    Tai, X.-C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.