104
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Simultaneous cartoon and texture reconstruction for image restoration by bivariate function

, &
Pages 1275-1289 | Received 05 Jan 2010, Accepted 16 Mar 2010, Published online: 22 Sep 2010

References

  • Osher , S , Rudin , LI and Fatem , E . 1992 . Nonlinear total variation based noise removal algorithms . Physics D , 60 : 259 – 268 .
  • Y. Meyer, Oscillating patterns in some nonlinear evolution equations, in Mathematical foundation of turbulent viscous flows, Vol. 1871 of Lecture Notes in Math., Springer, Berlin, 2006, pp. 101–187.
  • Vese , L and Osher , S . 2002 . Modeling textures with total variation minimization and oscillating patterns in image Process . J. Sci. Comput. , 19 ( 1–3 ) : 553 – 572 .
  • Osher , S , Sole , A and Vese , L . 2003 . Image decomposition and restoration using total variation minimization and the H −1 norm . Multiscale Model. Simul. , 1 ( 3 ) : 349 – 370 .
  • Aujol , J , Aubert , G , Blanc-Feraud , L and Chambolle , A . 2003 . Image decomposition application to SAR images . Lecture Notes in Comput. Sci. , 2695 : 297 – 312 .
  • Daubechies , I and Teschkeb , G . 2005 . Variational image restoration by means of wavelets: Simultaneous decomposition, deblurring, and denoising . Appl. Comput. Harmonic Anal. , 19 : 1 – 16 .
  • Aujol , J and Chambolle , A . 2005 . Dual norms and image decomposition models . Int. J. Comput. Vision , 63 ( 1 ) : 85 – 104 .
  • Meyer , F , Averbuch , A and Coifman , R . 2002 . Multilayered image representation: Application to image compression . IEEE Trans. Image Process. , 11 ( 9 ) : 1072 – 1080 .
  • C. Guo, S. Zhu, and Y. Wu. Towards a mathematical theory of primal sketch and sketchability, in Proceedings of the Ninth IEEE International Conference on Computer Vision, S.C. Zhu, ed., Nice, France, 2003, pp. 1228–1235.
  • Mallat , S and Zhang , Z . 1993 . Matching pursuits with time-frequency dictionaries . IEEE Trans. Signal Process. , 41 ( 12 ) : 3397 – 3415 .
  • Elad , M , Starck , J , Querre , P and Donoho , D . 2005 . Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA) . Appl. Comput. Harmonic Anal. , 19 ( 3 ) : 340 – 358 .
  • Fadili , M , Starck , J and Murtagh , F . 2009 . Inpainting and zooming using sparse represntations . Comput. J. , 52 ( 1 ) : 64 – 79 .
  • Starck , J , Elad , M and Donoho , D . 2005 . Image decomposition via the combination of sparse representations and a variational approach . IEEE Trans. Image Process. , 14 ( 10 ) : 1570 – 1582 .
  • Candès , E and Donoho , D . 1999 . Curvelets: A surprisingly effective nonadaptive representation of objects with edges , CA : Technical Report, Stanford University .
  • Candès , E and Donoho , D . 2004 . New tight frames of curvelets and optimal representation of objects with piecewise C2 singularities . Commun. Pure Appl. Math. , 57 : 219 – 266 .
  • Daubechies , I . 1992 . Ten Lectures on Wavelets , Philadelphia, PA : SIAM .
  • Ron , A and Shen , Z . 1997 . Affine systems in L 2(R d ): The analysis of the analysis operator . J. Funct. Anal. , 148 ( 2 ) : 408 – 447 .
  • Mallat , S . 1999 . A Wavelet Tour of Signal Process, , 2nd , San Diego : Academic Press .
  • Davis , G , Mallat , S and Avellaneda , M . 1997 . Adaptive greedy approximations . Constructive Approx. , 13 ( 1 ) : 57 – 98 .
  • Natarajan , B . 1995 . Sparse approximate solutions to linear systems . SIAM J. Comput. , 24 : 227 – 234 .
  • Chen , S , Donoho , D and Saunders , M . 1999 . Atomic decomposition by basis pursuit . SIAM J. Sci. Comput. , 20 ( 1 ) : 33 – 61 .
  • Donoho , D , Elad , M and Temlyakov , V . 2006 . Stable recovery of sparse over complete representations in the presence of noise . IEEE Trans. Inform. Theory , 52 ( 1 ) : 6 – 18 .
  • Cai , J , Osher , S and Shen , Z . 2009 . Split Bregman methods and frame based image restoration . Multiscal Model. Simul. , 8 ( 2 ) : 337 – 369 .
  • Candès , E and Tao , T . 2006 . Near-optimal signal recovery from random projections: universal encoding strategies . IEEE Trans. Inform. Theory , 52 ( 12 ) : 5406 – 5425 .
  • Donoho , D . 1995 . Denoising by soft-thresholding . IEEE Trans. Information Theory , 41 : 613 – 627 .
  • Blu , T and Luisier , F . 2007 . The sure-let approach to image denoising . IEEE Trans. Image Process. , 16 ( 11 ) : 2778 – 2786 .
  • Da Cunha , A , Zhou , J and Do , M . 2006 . The nonsubsampled contourlet transform: Theory, design, and applications . IEEE Trans. Image Process. , 15 ( 10 ) : 3089 – 3101 .
  • Do , M and Vetterli , M . 2002 . Rotation invariant texture characterization and retrieval using steerable wavelet-domain hidden markov models . IEEE Trans. Multimedia , 4 ( 4 ) : 517 – 527 .
  • Do , M and Vetterli , M . 2003 . The finite ridgelet transform for image representation . IEEE Trans. Image Process. , 12 ( 1 ) : 16 – 28 .
  • Do , M and Vetterli , M . 2003 . Framing pyramids . IEEE Trans. Signal Process. , 51 ( 9 ) : 2329 – 2342 .
  • Eslami , R and Radha , H . 2006 . Translation-invariant contourlet transform and its application to image denoising . IEEE Trans. Image Process. , 15 ( 11 ) : 3362 – 3374 .
  • Lang , M , Guo , H , Odegard , J , Burrus , C and Wells , R . 1996 . Noise reduction using an undecimated discrete wavelet transform . IEEE Signal Process. Lett. , 3 ( 1 ) : 10 – 12 .
  • Starck , J , Candes , E and Donoho , D . 2002 . The curvelet transform for image denoising . IEEE Trans. Image Process. , 11 ( 6 ) : 670 – 684 .
  • Elad , M . 2006 . Why simple shrinkage is still relevant for redundant representation . IEEE Trans. Inform. Theory , 52 ( 12 ) : 5559 – 5569 .
  • Bruce , A , Sardy , S and Tseng , P . 1998 . Block coordinate relaxation methods for nonparametric signal de-noising . Proc. SPIE , 3391 : 75 – 86 .
  • Krishnan , D , Lin , P and Tai , X . 2006 . An efficient operator splitting method for noise removal in images . Commun. Comput. Phys. , 1 : 847 – 858 .
  • Lysaker , M and Tai , X . 2004 . Noise removal using smoothed normals and surface fitting . IEEE Trans. Image Process. , 13 : 1345 – 1357 .
  • Vogel , C and Oman , M . 1996 . Iterative method for total variation denoising . SIAM J. Sci. Comput. , 17 : 227 – 238 .
  • J. Bioucas-Dias, M. Figueiredo, and R. Nowak. Total variation-based image deconvolution: A majorization–minimization approach, IEEE International Conference on Acoustics, Speech, and Signal Processing – ICASSP'2006,2:II-II, 2006.
  • Chan , T and Mulet , P . 1999 . On the convergence of the lagged diffusivity fixed point method in total variation image restoration . SIAM J. Numer. Anal. , 36 : 354 – 367 .
  • Chan , R and Jin , X . 2007 . An Introduction to Iterative Toeplitz Solvers , Philadelphia, PA : SIAM .
  • Ng , M . 2004 . Iterative Methods for Toeplitz Systems , Oxford : Oxford University Press .
  • Ng , M , Chan , R and Tang , W . 2000 . A fast algorithm for deblurring models with Neumann boundary conditions . SIAM J. Sci. Comput. , 21 ( 3 ) : 851 – 866 .
  • Opial , Z . 1967 . Weak convergence of the sequence of successive approximations for nonexpansive mappings . Bull. Am. Math. Soc. , 73 : 591 – 597 .
  • Combettes , P . 2004 . Solving monotone inclusions via compositions of nonexpansive averaged operators . Optimization , 53 ( 5–6 ) : 475 – 504 .
  • Combettes , P and Wajs , V . 2005 . Signal recovery by proximal forward-backward splitting . SIAM J. Multiscale Model. Simul. , 4 ( 4 ) : 1168 – 1200 .
  • Bertsekas , D , Nedic , A and Ozdaglar , E . 2003 . Convex Analysis and Optimization , Nashua, NH : Athena Scientific .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.