OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 9 — May. 5, 2014
  • pp: 10500–10508

Construction model for total variation regularization parameter

Guanghua Gong, Hongming Zhang, and Minyu Yao  »View Author Affiliations

Optics Express, Vol. 22, Issue 9, pp. 10500-10508 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (841 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Image denoising is important for high-quality imaging in adaptive optics. Richardson-Lucy deconvolution with total variation(TV) regularization is commonly used in image denoising. The selection of TV regularization parameter is an essential issue, yet no systematic approach has been proposed. A construction model for TV regularization parameter is proposed in this paper. It consists of four fundamental elements, the properties of which are analyzed in details. The proposed model bears generality, making it apply to different image recovery scenarios. It can achieve effective spatially adaptive image recovery, which is reflected in both noise suppression and edge preservation. Simulations are provided as validation of recovery and demonstration of convergence speed and relative mean-square error.

© 2014 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(100.2000) Image processing : Digital image processing
(100.2980) Image processing : Image enhancement
(100.1455) Image processing : Blind deconvolution

ToC Category:
Adaptive Optics

Original Manuscript: March 20, 2014
Revised Manuscript: April 15, 2014
Manuscript Accepted: April 15, 2014
Published: April 23, 2014

Guanghua Gong, Hongming Zhang, and Minyu Yao, "Construction model for total variation regularization parameter," Opt. Express 22, 10500-10508 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. V. Oppenheim, R. W. Schafer, T. G. Stockham, “Nonlinear filtering of multiplied and convolved signals,” Audio and Electroacoustics, IEEE Transactions on, 16(3), 437–466 (1968). [CrossRef]
  2. G. R. Ayers, J. C. Dainty, “Iterative blind deconvolution method and its applications,” Opt. Lett. 13(7), 547–549 (1988). [CrossRef] [PubMed]
  3. W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. 62(1), 55–59 (1972). [CrossRef]
  4. L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745 (1974). [CrossRef]
  5. G. Krishnamurthi, C. Y. Wang, G. Steyer, D. L. Wilson, “Removal of subsurface fluorescence in cryo-imaging using deconvolution,” Opt. Expr. 18(21), 22,324–22,338 (2010). [CrossRef]
  6. D. A. Fish, A. M. Brinicombe, E. R. Pike, J. G. Walker, “Blind deconvolution by means of the Richardson-Lucy algorithm,” J. Opt. Soc. Am. A 12(1), 58–65 (1995). [CrossRef]
  7. D. S. C. Biggs, M. Andrews, “Acceleration of iterative image restoration algorithms,” Appl. Opt. 36(8), 1766–1775 (1997). [CrossRef] [PubMed]
  8. D. A. Hope, S. M. Jefferies, “Compact multiframe blind deconvolution,” Opt. Lett. 36(6), 867–869 (2011). [CrossRef] [PubMed]
  9. L. I. Rudin, S. Osher, E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1), 259–268 (1992). [CrossRef]
  10. E. Vera, P. Meza, S. Torres, “Total variation approach for adaptive nonuniformity correction in focal-plane arrays,” Opt. Lett. 36(2), 172–174 (2011). [CrossRef] [PubMed]
  11. M. Freiberger, C. Clason, H. Scharfetter, “Total variation regularization for nonlinear fluorescence tomography with an augmented Lagrangian splitting approach,” Appl. Opt. 49(19), 3741–3747 (2010). [CrossRef] [PubMed]
  12. E. Candes, J. Romberg, T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory 52(2), 489–509 (2006). [CrossRef]
  13. A. Kostenko, K. J. Batenburg, H. Suhonen, S. E. Offerman, L. J. van Vliet, “Phase retrieval in in-line x-ray phase-contrast imaging based on total variation minimization,” Opt. Expr. 21(1), 710–723 (2013). [CrossRef]
  14. E. Y. Sidky, M. A. Anastasio, X. Pan, “Image reconstruction exploiting object sparsity in boundary-enhanced x-ray phase-contrast tomography,” Opt. Expr. 18(10), 10,404–10,422 (2010). [CrossRef]
  15. A. Kostenko, K. J. Batenburg, A. King, S. E. Offerman, L. J. van Vliet, “Total variation minimization approach in in-line x-ray phase-contrast tomography,” Opt. Expr. 21(10), 12,185–12,196 (2013). [CrossRef]
  16. J. I. Sperl, D. Bequé, G. P. Kudielka, K. Mahdi, P. M. Edic, C. Cozzini, “A Fourier-domain algorithm for total-variation regularized phase retrieval in differential X-ray phase contrast imaging,” Opt. Expr. 22(1), 450–462 (2014). [CrossRef]
  17. A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision 20(1–2), 89–97 (2004). [CrossRef]
  18. J. Dahl, P. C. Hansen, S. H. Jensen, T. L. Jensen, “Algorithms and software for total variation image reconstruction via first-order methods,” Num. Alg. 53(1), 67–92 (2010). [CrossRef]
  19. M. Cetin, W. Karl, A. Willsky, “Edge-preserving image reconstruction for coherent imaging applications,” in Proceedings of ICIP 2002 International Conference on Image Processing (Rochester, 2002). [CrossRef]
  20. D. Brady, K. Choi, D. Marks, R. Horisaki, S. Lim, “Compressive holography,” Opt. Expr. 17(15), 13,040–13,049 (2009). [CrossRef]
  21. M. Marim, M. Atlan, E. Angelini, J. Olivo-Marin, “Compressed sensing with off-axis frequency-shifting holography,” Opt. Lett. 35(6), 871–873 (2010). [CrossRef] [PubMed]
  22. A. Bourquard, N. Pavillon, E. Bostan, C. Depeursinge, M. Unser, “A practical inverse-problem approach to digital holographic reconstruction,” Opt. Expr. 21(3), 3417–3433 (2013). [CrossRef]
  23. E. Y. Sidky, X. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53(17), 4777–4807 (2008). [CrossRef] [PubMed]
  24. L. M. Mugnier, J.-M. Conan, T. Fusco, V. Michau, “Joint maximum a posteriori estimation of object and PSF for turbulence-degraded images,” in Bayesian Inference for Inverse Problems, A. Mohammad-Djafari, ed., Proc. SPIE3459, 50–61 (1998). [CrossRef]
  25. N. Dey, L. Blanc-Feraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, J. Zerubia, “Richardson-Lucy Algorithm with Total Variation Regularization for 3D Confocal Microscope Deconvolution,” Microsc. Res. Tech. 69(4), 260–266 (2006). [CrossRef] [PubMed]
  26. H. Tian, H. Cai, J. Lai, X. Xu, “Effective image noise removal based on difference eigenvalue,” in Proceedings of ICIP 2011 International Conference on Image Processing (Brussels, 2011). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited