OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 17 — Aug. 16, 2010
  • pp: 17819–17833

Tensor factorization for model-free space-variant blind deconvolution of the single- and multi-frame multi-spectral image

Ivica Kopriva  »View Author Affiliations

Optics Express, Vol. 18, Issue 17, pp. 17819-17833 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (5423 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The higher order orthogonal iteration (HOOI) is used for a single-frame and multi-frame space-variant blind deconvolution (BD) performed by factorization of the tensor of blurred multi-spectral image (MSI). This is achieved by conversion of BD into blind source separation (BSS), whereupon sources represent the original image and its spatial derivatives. The HOOI-based factorization enables an essentially unique solution of the related BSS problem with orthogonality constraints imposed on factors and the core tensor of the Tucker3 model of the image tensor. In contrast, the matrix factorization-based unique solution of the same BSS problem demands sources to be statistically independent or sparse which is not true. The consequence of such an approach to BD is that it virtually does not require a priori information about the possibly space-variant point spread function (PSF): neither its model nor size of its support. For the space-variant BD problem, MSI is divided into blocks whereupon the PSF is assumed to be a space-invariant within the blocks. The success of proposed concept is demonstrated in experimentally degraded images: defocused single-frame gray scale and red-green-blue (RGB) images, single-frame gray scale and RGB images blurred by atmospheric turbulence, and a single-frame RGB image blurred by a grating (photon sieve). A comparable or better performance is demonstrated in relation to the blind Richardson-Lucy algorithm which, however, requires a priori information about parametric model of the blur.

© 2010 OSA

OCIS Codes
(100.1830) Image processing : Deconvolution
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems
(100.6640) Image processing : Superresolution
(100.6890) Image processing : Three-dimensional image processing

ToC Category:
Image Processing

Original Manuscript: June 21, 2010
Revised Manuscript: July 23, 2010
Manuscript Accepted: July 24, 2010
Published: August 3, 2010

Ivica Kopriva, "Tensor factorization for model-free space-variant blind deconvolution of the single- and multi-frame multi-spectral image," Opt. Express 18, 17819-17833 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. L. Lagendijk, and J. Biemond, Iterative Identification and Restoration of Images (KAP, 1991).
  2. M. R. Banham and A. K. Katsaggelos, “Digital Image Restoration,” IEEE Signal Process. Mag. 14(2), 24–41 (1997). [CrossRef]
  3. D. Kundur and D. Hatzinakos, “Blind Image Deconvolution,” IEEE Signal Process. Mag. 13(3), 43–64 (1996). [CrossRef]
  4. P. Campisi and K. Egiazarian, eds., Blind Image Deconvolution (CRC Press, Boca Raton, 2007).
  5. I. Kopriva, “Single-frame multichannel blind deconvolution by nonnegative matrix factorization with sparseness constraints,” Opt. Lett. 30(23), 3135–3137 (2005). [CrossRef] [PubMed]
  6. I. Kopriva, “3D tensor factorization approach to single-frame model-free blind-image deconvolution,” Opt. Lett. 34(18), 2835–2837 (2009). [CrossRef] [PubMed]
  7. F. Li, X. Jia, and D. Fraser, “Superresolution Reconstruction of Multispectral Data for Improved Image Classification,” IEEE Geosci. Remote Sens. Lett. 6(4), 689–693 (2009). [CrossRef]
  8. H. Ji and C. Fermüller, “Robust wavelet-based super-resolution reconstruction: theory and algorithm,” IEEE Trans. Pattern Anal. Mach. Intell. 31(4), 649–660 (2009). [CrossRef] [PubMed]
  9. T. J. Schulz, “Multiframe blind deconvolution of astronomical images,” J. Opt. Soc. Am. A 10(5), 1064–1073 (1993). [CrossRef]
  10. R. Fergus, B. Singh, A. Hertzmann, S. T. Roweis, and W. T. Freeman, “Removing Camera Shake from a Single Photograph,” ACM Trans. Graph. 25(3), 787–794 (2006). [CrossRef]
  11. Q. Shan, J. Jia, and A. Agarwala, “High-quality Motion Deblurring from a Single Image,” ACM Trans. Graph. 27(3), 1 (2008). [CrossRef]
  12. S. Cho and S. Lee, “Fast Motion Deblurring,” ACM Trans. Graph. 28(5), 1 (2009). [CrossRef]
  13. J. Miskin and D. J. C. MacKay, “Ensemble Learning for Blind Image Separation and Deconvolution,” in: Advances in Independent Component Analysis (Springer, London, 2000).
  14. M. Šorel and J. Flusser, “Space-variant restoration of images degraded by camera motion blur,” IEEE Trans. Image Process. 17(2), 105–116 (2008). [CrossRef] [PubMed]
  15. J. Bardsley, S. Jefferies, J. Nagy, and R. Plemmons, “A computational method for the restoration of images with an unknown, spatially-varying blur,” Opt. Express 14(5), 1767–1782 (2006). [CrossRef] [PubMed]
  16. E. F. Y. Hom, F. Marchis, T. K. Lee, S. Haase, D. A. Agard, and J. W. Sedat, “AIDA: an adaptive image deconvolution algorithm with application to multi-frame and three-dimensional data,” J. Opt. Soc. Am. A 24(6), 1580–1600 (2007). [CrossRef]
  17. I. Kopriva, “Approach to blind image deconvolution by multiscale subband decomposition and independent component analysis,” J. Opt. Soc. Am. A 24(4), 973–983 (2007). [CrossRef]
  18. L. De Lathauwer, B. De Moor, and J. Vandewalle, “A multilinear singular value decomposition,” SIAM J. Matrix Anal. Appl. 21(4), 1253–1278 (2000). [CrossRef]
  19. L. De Lathauwer, B. De Moor, and J. Vandewalle, “On the best rank-1 and rank-(R1,R2,…,RN) approximation of higher-order tensors,” SIAM J. Matrix Anal. Appl. 21(4), 1324–1342 (2000). [CrossRef]
  20. S. Umeyama, “Blind deconvolution of blurred images by use of ICA,” Electron Commun. Jpn 84(12), 1–9 (2001).
  21. J. G. Daugman, ““Complete Discrete 2-D Gabor Transforms by Neural Networks for Image Analysis and Compression,” IEEE Trans. Acoust. Speech Signal Process. 36(7), 1169–1179 (1988). [CrossRef]
  22. J. Lin and A. Zhang, “Fault feature separation using wavelet-ICA filter,” NDT Int. 38(6), 421–427 (2005). [CrossRef]
  23. M. E. Davies and C. J. James, “Source separation using single channel ICA,” Signal Process. 87(8), 1819–1832 (2007). [CrossRef]
  24. H. G. Ma, Q. B. Jiang, Z. Q. Liu, G. Liu, and Z. Y. Ma, “A novel blind source separation method for single-channel signal,” Signal Process. 90(12), 3232–3241 (2010). [CrossRef]
  25. D. A. Fish, A. M. Brinicombe, E. R. Pike, and J. G. Walker, “Blind deconvolution by means of the Richardson-Lucy algorithm,” J. Opt. Soc. Am. A 12(1), 58–65 (1995). [CrossRef]
  26. D. S. C. Biggs and M. Andrews, “Acceleration of iterative image restoration algorithms,” Appl. Opt. 36(8), 1766–1775 (1997). [CrossRef] [PubMed]
  27. A. Cichocki, R. Zdunek, A. H. Phan, and S. I. Amari, Nonnegative Matrix and Tensor Factorization (John Wiley & Sons, 2009).
  28. A. Cichocki and S. Amari, Adaptive Blind Signal and Image Processing (John Wiley, New York, 2002).
  29. H. A. L. Kiers, “Towards a standardized notation and terminology in multiway analysis,” J. Chemometr. 14(3), 105–122 (2000). [CrossRef]
  30. L. R. Tucker, “Some mathematical notes on three-mode factor analysis,” Psychometrika 31(3), 279–311 (1966). [CrossRef] [PubMed]
  31. A. Cichocki, and A. H. Phan. Fast Local Algorithms for Large Scale Nonnegative Matrix and Tensor Factorizations. IEICE Trans Fundamentals 2009; E92-A(3): 708–721.
  32. B. W. Bader and T. G. Kolda, MATLAB Tensor Toolbox version 2.2. http://csmr.ca.sandia.gov/~tkolda/TensorToolbox .
  33. I. Kopriva, Q. Du, H. Szu, and W. Wasylkiwskyj, “Independent Component Analysis Approach to Image Sharpening in the Presence of Atmospheric Turbulence,” Opt. Commun. 233(1-3), 7–14 (2004). [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