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Efficient Recursive Multichannel Blind Image Restoration


This paper presents a novel multichannel recursive filtering (MRF) technique to address blind image restoration. The primary motivation for developing the MRF algorithm to solve multichannel restoration is due to its fast convergence in joint blur identification and image restoration. The estimated image is recursively updated from its previous estimates using a regularization framework. The multichannel blurs are identified iteratively using conjugate gradient optimization. The proposed algorithm incorporates a forgetting factor to discard the old unreliable estimates, hence achieving better convergence performance. A key feature of the method is its computational simplicity and efficiency. This allows the method to be adopted readily in real-life applications. Experimental results show that it is effective in performing blind multichannel blind restoration.


  1. 1.

    Kundur D, Hatzinakos D: Blind image deconvolution. IEEE Signal Processing Magazine 1996,13(3):43–64. 10.1109/79.489268

    Article  Google Scholar 

  2. 2.

    Hunt BR, Kuebler O: Karhunen-Loeve multispectral image restoration, part I: theory. IEEE Transactions on Acoustics, Speech, and Signal Processing 1984,32(3):592–600. 10.1109/TASSP.1984.1164363

    Article  Google Scholar 

  3. 3.

    Pillai SU, Liang B: Blind image restoration using a robust GCD approach. IEEE Transactions on Image Processing 1999,8(2):295–301. 10.1109/83.743863

    Article  Google Scholar 

  4. 4.

    Harikumar G, Bresler Y: Perfect blind restoration of images blurred by multiple filters: theory and efficient algorithms. IEEE Transactions on Image Processing 1999,8(2):202–219. 10.1109/83.743855

    Article  Google Scholar 

  5. 5.

    Giannakis GB, Heath RW Jr.: Blind identification of multichannel FIR blurs and perfect image restoration. IEEE Transactions on Image Processing 2000,9(11):1877–1896. 10.1109/83.877210

    MathSciNet  Article  Google Scholar 

  6. 6.

    Pai H-T, Bovik AC: On eigenstructure-based direct multichannel blind image restoration. IEEE Transactions on Image Processing 2001,10(10):1434–1446. 10.1109/83.951530

    Article  Google Scholar 

  7. 7.

    Galatsanos NP, Katsaggelos AK, Chin RT, Hillery AD: Least squares restoration of multichannel images. IEEE Transactions on Signal Processing 1991,39(10):2222–2236. 10.1109/78.91180

    Article  Google Scholar 

  8. 8.

    Kang MG, Katsaggelos AK: Simultaneous multichannel image restoration and estimation of the regularization parameters. IEEE Transactions on Image Processing 1997,6(5):774–778. 10.1109/83.568936

    Article  Google Scholar 

  9. 9.

    Yang Y, Galatsanos NP, Stark H: Projection-based blind deconvolution. Journal of the Optical Society of America A 1994,11(9):2401–2409. 10.1364/JOSAA.11.002401

    Article  Google Scholar 

  10. 10.

    You Y-L, Kaveh M: Regularization approach to joint blur identification and image restoration. IEEE Transactions on Image Processing 1996,5(3):416–428. 10.1109/83.491316

    Article  Google Scholar 

  11. 11.

    Chan TF, Wong CK: Convergence of the alternating minimization algorithm for blind deconvolution. Linear Algebra and Its Applications 2000,316(1–3):259–285.

    MathSciNet  Article  Google Scholar 

  12. 12.

    Chow TWS, Li X-D, Ng K-T: Double-regularization approach for blind restoration of multichannel imagery. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 2001,48(9):1075–1085. 10.1109/81.948435

    Article  Google Scholar 

  13. 13.

    Molina R, Mateos J, Katsaggelos AK, Vega M: Bayesian multichannel image restoration using compound Gauss-Markov random fields. IEEE Transactions on Image Processing 2003,12(12):1642–1654. 10.1109/TIP.2003.818015

    Article  Google Scholar 

  14. 14.

    Sroubek F, Flusser J: Multichannel blind iterative image restoration. IEEE Transactions on Image Processing 2003,12(9):1094–1106. 10.1109/TIP.2003.815260

    MathSciNet  Article  Google Scholar 

  15. 15.

    Panci G, Campisi P, Colonnese S, Scarano G: Multichannel blind image deconvolution using the Bussgang algorithm: spatial and multiresolution approaches. IEEE Transactions on Image Processing 2003,12(11):1324–1337. 10.1109/TIP.2003.818022

    MathSciNet  Article  Google Scholar 

  16. 16.

    Haykin S: Adaptive Filter Theory. 4th edition. Prentice-Hall, Upper Saddle River, NJ, USA; 2002.

    Google Scholar 

  17. 17.

    Chen L, Yap K-H: A soft double regularization approach to parametric blind image deconvolution. IEEE Transactions on Image Processing 2005,14(5):624–633.

    Article  Google Scholar 

  18. 18.

    Chen L, Yap K-H: Efficient discrete spatial techniques for blur support identification in blind image deconvolution. IEEE Transactions on Signal Processing 2006,54(4):1557–1562.

    Article  Google Scholar 

  19. 19.

    Galatsanos NP, Katsaggelos AK: Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation. IEEE Transactions on Image Processing 1992,1(3):322–336. 10.1109/83.148606

    Article  Google Scholar 

  20. 20.

    Andrews HC, Hunt BR: Digital Image Restoration. Prentice-Hall, Upper Saddle River, NJ, USA; 1977.

    Google Scholar 

  21. 21.

    Golub GH, Van Loan CF: Matrix Computations. 3rd edition. John Hopkins University Press, New York. NY, USA; 1996.

    Google Scholar 

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Correspondence to Li Chen.

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Chen, L., Yap, K. & He, Y. Efficient Recursive Multichannel Blind Image Restoration. EURASIP J. Adv. Signal Process. 2007, 019675 (2006).

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  • Information Technology
  • Quantum Information
  • Conjugate Gradient
  • Primary Motivation
  • Fast Convergence