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Volumn 20, Issue 11, 2013, Pages 1054-1057

A direct algorithm for 1-D total variation denoising

Author keywords

Convex nonsmooth optimization; denoising; fused lasso; nonlinear smoothing; nonparametric regression; regularized least squares; taut string; total variation

Indexed keywords

DE-NOISING; FUSED LASSOS; LEAST SQUARE; NON-LINEAR SMOOTHING; NON-PARAMETRIC REGRESSION; NONSMOOTH OPTIMIZATION; TAUT-STRING; TOTAL VARIATION;

EID: 84884390219     PISSN: 10709908     EISSN: None     Source Type: Journal    
DOI: 10.1109/LSP.2013.2278339     Document Type: Article
Times cited : (336)

References (38)
  • 1
    • 80755182306 scopus 로고    scopus 로고
    • Generalized methods and solvers for noise removal from piecewise constant signals. I. Background theory & II. New methods
    • M. A. Little and N. S. Jones, "Generalized methods and solvers for noise removal from piecewise constant signals. I. Background theory & II. New methods," Proc. R. Soc. A, vol. 467, 2011.
    • (2011) Proc. R. Soc. A , vol.467
    • Little, M.A.1    Jones, N.S.2
  • 3
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D, vol. 60, no. 1-4, pp. 259-268, 1992.
    • (1992) Physica D , vol.60 , Issue.1-4 , pp. 259-268
    • Rudin, L.1    Osher, S.2    Fatemi, E.3
  • 5
    • 79954564965 scopus 로고    scopus 로고
    • Should penalized least squares regression be interpreted as maximum a posteriori estimation?
    • May
    • R.Gribonval, "Should penalized least squares regression be interpreted as maximum a posteriori estimation?," IEEE Trans. Signal Process., vol. 59, no. 5, pp. 2405-2410, May 2011.
    • (2011) IEEE Trans. Signal Process , vol.59 , Issue.5 , pp. 2405-2410
    • Gribonval, R.1
  • 6
    • 84897584361 scopus 로고    scopus 로고
    • MMSE estimation of sparse Lévy processes
    • Jan.
    • U. S. Kamilov, P. Pad, A. Amini, and M. Unser, "MMSE estimation of sparse Lévy processes," IEEE Trans. Signal Process., vol. 61, no. 1, pp. 137-147, Jan. 2013.
    • (2013) IEEE Trans. Signal Process , vol.61 , Issue.1 , pp. 137-147
    • Kamilov, U.S.1    Pad, P.2    Amini, A.3    Unser, M.4
  • 8
    • 37249032736 scopus 로고    scopus 로고
    • Spatial smoothing and hot spot detection for CGH data using the fused lasso
    • DOI 10.1093/biostatistics/kxm013
    • R. Tibshirani and P. Wang, "Spatial smoothing and hot spot detection for CGH data using the fused lasso," Biostatistics, vol. 9, pp. 18-29, 2008. (Pubitemid 350274579)
    • (2008) Biostatistics , vol.9 , Issue.1 , pp. 18-29
    • Tibshirani, R.1    Wang, P.2
  • 10
    • 84884379155 scopus 로고    scopus 로고
    • The group fused lasso for multiple changepoint detection
    • Jun to be published
    • K. Bleakley and J.-P. Vert, "The group fused lasso for multiple changepoint detection," PUBLICATION NAME?, Jun. 2011, to be published.
    • (2011) Publication Name?
    • Bleakley, K.1    Vert, J.-P.2
  • 12
    • 0001556589 scopus 로고    scopus 로고
    • Iterative methods for total variation denoising
    • C. R. Vogel and M. E. Oman, "Iterative methods for total variation denoising," SIAM J. Sci. Comput., vol. 17, pp. 227-238, 1996. (Pubitemid 126621162)
    • (1996) SIAM Journal of Scientific Computing , vol.17 , Issue.1 , pp. 227-238
    • Vogel, C.R.1    Oman, M.E.2
  • 13
    • 0035250066 scopus 로고    scopus 로고
    • The digital TV filter and nonlinear denoising
    • PII S105771490100817X
    • T. F. Chan, S. Osher, and J. Shen, "The digital TV filter and nonlinear denoising," IEEE Trans. Image Process., vol. 10, no. 2, pp. 231-241, Feb. 2001. (Pubitemid 33777271)
    • (2001) IEEE Transactions on Image Processing , vol.10 , Issue.2 , pp. 231-241
    • Chan, T.F.1    Osher, S.2    Shen, J.3
  • 15
    • 34249819922 scopus 로고    scopus 로고
    • Recent developments in total variation image restoration
    • N. Paragios, Y. Chen, and O. Faugeras, Eds. Berlin, Germany: Springer Verlag
    • T. Chan, S. Esedoglu, F. Park, and M. Yip, "Recent developments in total variation image restoration," in Mathematical Models of Computer Vision, N. Paragios, Y. Chen, and O. Faugeras, Eds. Berlin, Germany: Springer Verlag, 2005.
    • (2005) Mathematical Models of Computer Vision
    • Chan, T.1    Esedoglu, S.2    Park, F.3    Yip, M.4
  • 16
    • 36749031147 scopus 로고    scopus 로고
    • An iteratively reweighted norm algorithm for minimization of total variation functionals
    • DOI 10.1109/LSP.2007.906221
    • 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, 2007. (Pubitemid 350201251)
    • (2007) IEEE Signal Processing Letters , vol.14 , Issue.12 , pp. 948-951
    • Wohlberg, B.1    Rodriguez, P.2
  • 17
    • 85032751460 scopus 로고    scopus 로고
    • L1-L2 optimization in signal and image processing
    • M. Zibulevsky and M. Elad, "L1-L2 optimization in signal and image processing," IEEE Signal Process. Mag., vol. 27, no. 3, pp. 76-88, 2010.
    • (2010) IEEE Signal Process. Mag , vol.27 , Issue.3 , pp. 76-88
    • Zibulevsky, M.1    Elad, M.2
  • 19
    • 70350593691 scopus 로고    scopus 로고
    • Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems
    • Nov
    • A. Beck and M. Teboulle, "Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems," IEEE Trans. Image Process., vol. 18, no. 11, pp. 2419-2434, Nov. 2009.
    • (2009) IEEE Trans. Image Process , vol.18 , Issue.11 , pp. 2419-2434
    • Beck, A.1    Teboulle, M.2
  • 20
    • 79953201848 scopus 로고    scopus 로고
    • A first-order primal-dual algorithm for convex problems with applications to imaging
    • A. Chambolle and T. Pock, "A first-order primal-dual algorithm for convex problems with applications to imaging," J. Math. Imag. Vis., vol. 40, no. 1, pp. 120-145, 2011.
    • (2011) J. Math. Imag. Vis , vol.40 , Issue.1 , pp. 120-145
    • Chambolle, A.1    Pock, T.2
  • 21
    • 84881083126 scopus 로고    scopus 로고
    • A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms
    • L. Condat, "A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms," J. Optim. Theory Applicat., vol. 158, no. 2, pp. 460-479, 2013.
    • (2013) J. Optim. Theory Applicat , vol.158 , Issue.2 , pp. 460-479
    • Condat, L.1
  • 22
    • 67349189437 scopus 로고    scopus 로고
    • On total variation minimization and surface evolution using parametric maximal flows
    • A. Chambolle and J. Darbon, "On total variation minimization and surface evolution using parametric maximal flows," Int. J. Comput. Vis., vol. 84, no. 3, 2009.
    • (2009) Int. J. Comput. Vis , vol.84 , Issue.3
    • Chambolle, A.1    Darbon, J.2
  • 23
    • 84937928741 scopus 로고    scopus 로고
    • A parametric maximum flow approach for discrete total variation regularization
    • R. Lukac, Ed. Boca Raton, FL, USA: CRC/Taylor and Francis Digital Imaging and Computer Vision
    • A. Chambolle and J. Darbon, "A parametric maximum flow approach for discrete total variation regularization," in Image Processing and Analysis With Graphs: Theory and Practice, R. Lukac, Ed. Boca Raton, FL, USA: CRC/Taylor and Francis, 2012, Digital Imaging and Computer Vision.
    • (2012) Image Processing and Analysis with Graphs: Theory and Practice
    • Chambolle, A.1    Darbon, J.2
  • 24
    • 84855691417 scopus 로고    scopus 로고
    • An efficient and effective tool for image segmentation, total variations and regularization
    • Proc. Int. Conf. Scale Space and Variational Methods in Computer Vision (SSVM)
    • D. S. Hochbaum, "An efficient and effective tool for image segmentation, total variations and regularization," in Proc. Int. Conf. Scale Space and VariationalMethods in Computer Vision (SSVM), 2011, vol. LNCS 6667, pp. 338-349.
    • (2011) LNCS , vol.6667 , pp. 338-349
    • Hochbaum, D.S.1
  • 25
    • 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
  • 26
    • 0035608644 scopus 로고    scopus 로고
    • Local extremes, runs, strings and multiresolution
    • P. L. Davies and A. Kovac, "Local extremes, runs, strings and multiresolution," Ann. Statist., vol. 29, no. 1, pp. 1-65, 2001.
    • (2001) Ann. Statist , vol.29 , Issue.1 , pp. 1-65
    • Davies, P.L.1    Kovac, A.2
  • 27
    • 0031514745 scopus 로고    scopus 로고
    • Locally adaptive regression splines
    • E. Mammen and S. van de Geer, "Locally adaptive regression splines," Ann. Statist., vol. 25, no. 1, pp. 387-413, 1997.
    • (1997) Ann. Statist , vol.25 , Issue.1 , pp. 387-413
    • Mammen, E.1    Geer De S.Van2
  • 28
    • 33846270363 scopus 로고    scopus 로고
    • The equivalence of the taut string algorithm and BV-regularization
    • DOI 10.1007/s10851-006-9796-4
    • M. Grasmair, "The equivalence of the taut string algorithm and BV-regularization," J. Math. Imag. Vis., vol. 27, no. 1, pp. 59-66, 2007. (Pubitemid 46122369)
    • (2007) Journal of Mathematical Imaging and Vision , vol.27 , Issue.1 , pp. 59-66
    • Grasmair, M.1
  • 30
    • 13244274395 scopus 로고    scopus 로고
    • On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization, and SIDEs
    • DOI 10.1137/S0036142903422429
    • G. Steidl, J.Weickert, T. Brox, P.Mrazek, andM.Welk, "On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization, and SIDEs," SIAM J. Numer. Anal., vol. 42, no. 2, pp. 686-713, 2004. (Pubitemid 40645211)
    • (2004) SIAM Journal on Numerical Analysis , vol.42 , Issue.2 , pp. 686-713
    • Steidl, G.1    Weickert, J.2    Brox, T.3    Mrazek, P.4    Welk, M.5
  • 31
    • 84976641351 scopus 로고    scopus 로고
    • Extensions of smoothing via taut strings
    • L. Dümbgen and A. Kovac, "Extensions of smoothing via taut strings," Electron. J. Statist., vol. 3, pp. 41-75, 2009.
    • (2009) Electron. J. Statist , vol.3 , pp. 41-75
    • Dümbgen, L.1    Kovac, A.2
  • 32
    • 77956206508 scopus 로고    scopus 로고
    • An efficient algorithm for a class of fused lasso problems
    • J. Liu, L. Yuan, and J. Ye, "An efficient algorithm for a class of fused lasso problems," in Proc. ACM SIGKDD, 2010, pp. 323-332.
    • (2010) Proc ACM SIGKDD , pp. 323-332
    • Liu, J.1    Yuan, L.2    Ye, J.3
  • 33
    • 80053439604 scopus 로고    scopus 로고
    • Fast Newton-type methods for total variation regularization
    • Jun
    • A. Barbero and S. Sra, "Fast Newton-type methods for total variation regularization," in Proc. Int. Conf. Mach. Learning (ICML), Jun. 2011, pp. 313-320.
    • (2011) Proc. Int. Conf. Mach. Learning (ICML) , pp. 313-320
    • Barbero, A.1    Sra, S.2
  • 35
    • 79952801173 scopus 로고    scopus 로고
    • A path algorithm for the fused lasso signal approximator
    • H. Höfling, "A path algorithm for the fused lasso signal approximator," J. Computat. Graphical Statist., vol. 19, no. 4, pp. 984-1006, 2010.
    • (2010) J. Computat. Graphical Statist , vol.19 , Issue.4 , pp. 984-1006
    • Höfling, H.1
  • 36
    • 79954994522 scopus 로고    scopus 로고
    • The solution path of the generalized lasso
    • R. J. Tibshirani and J. Taylor, "The solution path of the generalized lasso," Ann. Statist., vol. 39, no. 3, pp. 1335-1371, 2011.
    • (2011) Ann. Statist , vol.39 , Issue.3 , pp. 1335-1371
    • Tibshirani, R.J.1    Taylor, J.2
  • 37
    • 84884363386 scopus 로고    scopus 로고
    • A path algorithm for constrained estimation
    • H. Zhou and K. Lange, "A path algorithm for constrained estimation," J. Comput. Graph. Statist., vol. 22, no. 2, pp. 261-283, 2013.
    • (2013) J. Comput. Graph. Statist , vol.22 , Issue.2 , pp. 261-283
    • Zhou, H.1    Lange, K.2
  • 38
    • 13244257017 scopus 로고    scopus 로고
    • Nonlinear evolution equations as fast and exact solvers of estimation problems
    • DOI 10.1109/TSP.2004.840786
    • I. Pollak, A. S.Willsky, and Y. Huang, "Nonlinear evolution equations as fast and exact solvers of estimation problems," IEEE Trans. Signal Process., vol. 53, no. 2, pp. 484-498, Feb. 2005. (Pubitemid 40181745)
    • (2005) IEEE Transactions on Signal Processing , vol.53 , Issue.2 , pp. 484-498
    • Pollak, I.1    Willsky, A.S.2    Huang, Y.3


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