OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 16, Iss. 10 — Oct. 1, 1999
  • pp: 2377–2391

Parametric blind deconvolution: a robust method for the simultaneous estimation of image and blur

Joanne Markham and José-Angel Conchello  »View Author Affiliations

JOSA A, Vol. 16, Issue 10, pp. 2377-2391 (1999)

View Full Text Article

Acrobat PDF (588 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Blind-deconvolution microscopy, the simultaneous estimation of the specimen function and the point-spread function (PSF) of the microscope, is an underdetermined problem with nonunique solutions that are usually avoided by enforcing constraints on the specimen function and the PSF. We derived a maximum-likelihood-based method for blind deconvolution in which we assume a mathematical model for the PSF that depends on a small number of parameters (e.g., less than 20). The algorithm then estimates the unknown parameters together with the specimen function. The mathematical model ensures that all the constraints of the PSF are satisfied, and the maximum-likelihood approach ensures that the specimen is nonnegative. The method successfully estimates the PSF and removes out-of-focus blur. The PSF estimation is robust to aberrations in the PSF and to noise in the image.

© 1999 Optical Society of America

OCIS Codes
(100.1830) Image processing : Deconvolution
(100.3020) Image processing : Image reconstruction-restoration
(100.3190) Image processing : Inverse problems
(100.6890) Image processing : Three-dimensional image processing
(180.6900) Microscopy : Three-dimensional microscopy

Joanne Markham and José-Angel Conchello, "Parametric blind deconvolution: a robust method for the simultaneous estimation of image and blur," J. Opt. Soc. Am. A 16, 2377-2391 (1999)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. S. C. Gens, J. G. McNally, and B. G. Pickard, “Resolution of binding sites for antibodies to integrin, vitronection and fibronectin on onion epidermis protoplasts and depectinated walls,” ASGSB Bull. 7, 42 (1993).
  2. J. S. Gens, K. W. Doolittle, J. G. McNally, and B. G. Pickard, “Binding sites for antibodies to animal integrin, vitronectin and fibronectin in a plant model for mechanosensing,” Biophys. J. 66, A169 (1994).
  3. Z. Kam, J. S. Minden, D. A. Agard, J. W. Sedat, and M. Leptin, “Drosophila gastrulation: analysis of cell shape changes in living embryos by three-dimensional fluorescence microscopy,” Development (Cambridge, UK) 112, 365–370 (1991).
  4. J. G. McNally, “Computational optical-sectioning microscopy for 3D quantization of cell motion: results and challenges,” in Image Reconstruction and Restoration, T. J. Schulz and D. L. Snyder, eds., Proc. SPIE 2302, 342–351 (1994).
  5. B. G. Pickard, “Contemplating the plasmalemmal control center model,” Protoplasma 182, 1–9 (1994).
  6. B. G. Pickard, C. Reuzeau, K. W. Doolittle, and J. G. McNally, “High resolution visualization in onion of distribution patterns of spectrin, talin and vinculin antigenicities,” ASGSB Bull. 8, 54 (1994).
  7. J. A. Conchello, “Fluorescence photobleaching correction for expectation maximization algorithm,” in Three-Dimensional Microscopy: Image Acquisition and Processing II, T. Wilson and C. J. Cogswell, eds., Proc. SPIE 2412, 138–146 (1995).
  8. J.-A. Conchello, J. J. Kim, and E. W. Hansen, “Enhanced 3-D reconstruction from confocal scanning microscope im-ages. 2: depth discrimination vs. signal-to-noise ratio in partially confocal images,” Appl. Opt. 33, 3740–3750 (1994).
  9. J. A. Conchello and E. W. Hansen, “Enhanced 3-D reconstruction from confocal scanning microscope images. 1: Deterministic and maximum likelihood reconstructions,” Appl. Opt. 29, 3795–3804 (1990).
  10. J. A. Conchello and J. G. McNally, “Fast regularization technique for expectation maximization algorithm for computational optical sectioning microscopy,” in Three-Dimensional Microscopy: Image Acquisition and Processing III, C. J. Cogswell, G. Kino, and T. Wilson, eds., Proc. SPIE 2655, 199–208 (1996).
  11. C. Preza, M. I. Miller, L. J. Thomas, Jr., and J. G. McNally, “Regularized method for reconstruction of three-dimensional microscopic objects from optical sections,” J. Opt. Soc. Am. A 9, 219–228 (1992).
  12. S. Joshi and M. I. Miller, “Maximum a posteriori estimation with Good’s roughness for optical sectioning microscopy,” J. Opt. Soc. Am. A 10, 1078–1085 (1993).
  13. D. A. Agard, “Optical sectioning microscopy,” Annu. Rev. Biophys. Bioeng. 13, 191–219 (1984).
  14. W. A. Carrington, K. E. Fogarty, and F. S. Fay, “3D fluorescence imaging of single cells using image restoration,” in Noninvasive Techniques in Cell Biology, J. K. Fosket and S. Grinstein, eds. (Wiley-Liss, New York, 1990).
  15. A. Erhardt, G. Zinser, D. Komitowski, and J. Bille, “Reconstructing 3-D light-microscopic images by digital image processing,” Appl. Opt. 24, 194–200 (1985).
  16. T. J. Holmes, “Expectation-maximization restoration of band limited, truncated point-process intensities with application in microscopy,” J. Opt. Soc. Am. A 6, 1006–1014 (1989).
  17. T. J. Holmes, “Maximum-likelihood image restoration adapted for noncoherent optical imaging,” J. Opt. Soc. Am. A 5, 666–673 (1988).
  18. D. L. Snyder, A. M. Hammoud, and R. L. White, “Image recovery from data acquired with a charge-coupled-device camera,” J. Opt. Soc. Am. A 10, 1014–1023 (1993).
  19. F. S. Gibson and F. Lanni, “Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy,” J. Opt. Soc. Am. A 8, 1601–1613 (1991).
  20. J. A. Conchello and Q. Yu, “Parametric blind deconvolution of fluorescence microscopy images: preliminary results,” in Three-Dimensional Microscopy: Image Acquisition and Processing III, C. J. Cogswell, G. Kino, and T. Wilson, eds., Proc. SPIE 2655, 164–174 (1996).
  21. J. Markham and J. A. Conchello, “Parametric blind deconvolution of microscopic images: further results,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing V, C. J. Cogswell, J. A. Conchello, and T. Wilson, chairs/eds., Proc. SPIE 3261, 38–49 (1998).
  22. T. J. Schulz, “Multiframe blind deconvolution of astronomical images,” J. Opt. Soc. Am. A 10, 1064–1073 (1993).
  23. V. Krishnamurthi, Y.-H. Liu, S. Bhattacharyya, J. N. Turner, and T. J. Holmes, “Blind deconvolution of fluorescence micrographs by maximum-likelihood estimation,” Appl. Opt. 34, 6633–6647 (1995).
  24. T. J. Holmes, “Blind deconvolution of quantum-limited incoherent imagery,” J. Opt. Soc. Am. A 9, 1052–1061 (1992).
  25. R. G. Lane, “Blind deconvolution of speckle images,” J. Opt. Soc. Am. A 9, 1508–1514 (1992).
  26. Y. Yang, N. P. Galatsanos, and H. Stark, “Projection-based blind deconvolution,” J. Opt. Soc. Am. A 11, 2401–2409 (1994).
  27. R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9, 1072–1085 (1992).
  28. E. Thiébaut and J.-M. Conan, “Strict a priori constraints for maximum-likelihood blind deconvolution,” J. Opt. Soc. Am. A 12, 485–492 (1995).
  29. G. B. Avinash, “Simultaneous blur and image restoration in 3D optical microscopy,” Zoological Studies 34 Suppl. I, 184–185 (1995).
  30. B. C. McCallum, “Blind deconvolution by simulated annealing,” Opt. Commun. 75, 101–105 (1990).
  31. A. K. Katsaggelos and K. T. Lay, “Maximum likelihood blur identification and image restoration using the EM algorithm,” IEEE Trans. Signal Process. 39, 729–733 (1991).
  32. D. Snyder and M. I. Miller, Random Point Processes in Time and Space (Springer-Verlag, New York, 1991).
  33. M. H. DeGroot, Probability and Statistics, 2nd ed. (Addison Wesley, Reading, Mass., 1984), pp. 348–349.
  34. A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Statist. Soc. B 39, 1–38 (1977).
  35. R. Fletcher, Practical Methods of Optimization, 2nd ed. (Wiley, New York, 1987), p. 22.
  36. See Subsection 4.1 of Ref. 35.
  37. G. A. Seber and C. J. Wild, Nonlinear Regression (Wiley, New York, 1989), pp. 605–609.
  38. C. G. Broyden, “Quasi-Newton methods and their application to function maximization,” Math. Comput. 21, 368–381 (1967).
  39. C. G. Broyden, “The convergence of a class of double-rank minimization algorithms. Part I,” J. Inst. Math. Appl. 6, 76–90 (1970); “Part II,” 222–231 (1970).
  40. R. Fletcher, “A new approach to variable metric algorithms,” Comput. J. 13, 317–322 (1970).
  41. D. Goldfarb, “A family of variable metric methods derived by variational means,” Math. Comput. 24, 23–26 (1970).
  42. D. F. Shanno, “Conditioning of quasi-Newton methods for function minimization,” Math. Comput. 24, 647–657 (1970).
  43. See pp. 21–23 of Ref. 35.
  44. The netlib routines are available from the University of Tennessee, Knoxville, URL http://netlib2.cs.utk.edu.
  45. J. G. McNally, C. Preza, J. A. Conchello, and L. J. Thomas, Jr., “Artifacts in computational optical-sectioning microscopy,” J. Opt. Soc. Am. A 11, 1056–1067 (1994).
  46. The XCOSM deconvolution package is available from URL http://www.ibc.wustl.edu/bcl/xcosm/xcosm.html.
  47. 40×/1.0 NA is notation used widely to give the magnification and the numerical aperture of an objective. In this case the objective magnifies 40 times and has a numerical aperture of 1.0.
  48. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 436.
  49. S. T. Buckland, K. P. Burnham, and N. H. Augustin, “Model selection: an integral part of inference,” Biometrics 53, 603–618 (1997).
  50. A. C. Atkinson, “A note on the generalized information criterion for choice of a model,” Biometrika 67, 413–418 (1980).
  51. C. R. Rao and Y. Wu, “A strongly consistent procedure for model selection in a regression problem,” Biometrika 76, 369–374 (1989).
  52. H. Akaike, “Fitting autoregressive models for prediction,” Ann. Inst. Statist. Math. 21, 243–247 (1969).
  53. H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Autom. Control. 19, 716–723 (1974).
  54. G. Schwarz, “Estimating the dimension of a model,” Ann. Statist. 6, 461–464 (1978).
  55. J. Rissanen, “Modeling by shortest data description,” Automatica 12, 94–104 (1991).
  56. S. Konishi and G. Kitagawa, “Generalised information criteria in model selection,” Biometrika 83, 875–890 (1996).
  57. Z. Liang, J. R. MacFall, and D. P. Harrington, “Parameter estimation and tissue segmentation from multispectral MR images,” IEEE Trans. Med. Imaging 13, 441–449 (1994).
  58. N. Merhav, “The estimation of model order in exponen-tial families,” IEEE Trans. Inf. Theory 35, 1109–1114 (1989).
  59. D. Hirshberg and N. Merhav, “Robust methods for model order estimation,” IEEE Trans. Signal Process. 44, 620–628 (1996).
  60. G. Qian and H. R. Künsch, “Some notes on Rissanen’s stochastic complexity,” IEEE Trans. Inf. Theory 44, 782–786 (1998).
  61. J. J. Rissanen, “Fisher information and stochastic complexity,” IEEE Trans. Inf. Theory 42, 40–47 (1996).
  62. H. L. Van, Trees Detection, Estimation, and Modulation Theory (Wiley, New York, 1968), p. 80.
  63. See Example 3.3.5, p. 141 of Ref. 32.
  64. A. J. M. Spencer, D. F. Parker, D. S. Berry, A. H. England, T. R. Faulkner, W. A. Green, J. T. Holden, D. Middleton, and T. G. Rogers, Engineering Mathematics (Van Nostrand Reinhold, New York, 1977), Vol. 2, Chap. 8.
  65. L. Kaufman, “Implementing and accelerating the EM algorithm for positron emission tomography,” IEEE Trans. Med. Imaging 6, 37–51 (1987).

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