Abstract

We develop a novel multivariate Bayesian wavelet estimator of a simple analytical form that is computationally effective for the image denoising problem. The estimator is derived from the multivariate Laplacian model by using the maximum a posteriori rule. We find the multivariate estimator produces restoration results of high quality, both visually and in terms of peak signal-to-noise ratio.

© 2007 Optical Society of America

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References

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  1. E. P. Simoncelli, in Proceedings of the 31st Asilomar Conference on Signals, Systems and Computers (IEEE, 1997), pp. 673-678.
  2. J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, IEEE Trans. Image Process. 12, 1338 (2003).
    [CrossRef]
  3. S. Tan and L. C. Jiao, "Multivariate statistical models for image denoising in the wavelet domain," Int. J. Comput. Vis. (to be published).
  4. L. Sendur and I. W. Selesnick, IEEE Trans. Signal Process. 50, 2744 (2002).
    [CrossRef]
  5. L. Sendur and I. W. Selesnick, IEEE Signal Process. Lett. 9, 438 (2002).
    [CrossRef]
  6. D. N. Anderson, Stat. Probab. Lett. 14, 333 (1992).
  7. T. Eltoft, T. Kim, and T. Lee, IEEE Signal Process. Lett. 13, 300 (2006).
  8. M.Abramowitz and C.A.Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972), pp. 925-964.
  9. T. T. Cai and B. W. Silverman, Sankhya, Ser. B 63, 127 (2001).
  10. M. Elad and M. Aharon, IEEE Trans. Image Process. 15, 3736 (2006).
    [CrossRef]
  11. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, Proc. SPIE 6064, 6064A-30 (2006).
  12. S. Tan and L. C. Jiao, J. Opt. Soc. Am. A 23, 2449 (2006).
  13. D. D.-Y. Po and M. N. Do, IEEE Trans. Image Process. 15, 610 (2006).

2006 (5)

M. Elad and M. Aharon, IEEE Trans. Image Process. 15, 3736 (2006).
[CrossRef]

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, Proc. SPIE 6064, 6064A-30 (2006).

D. D.-Y. Po and M. N. Do, IEEE Trans. Image Process. 15, 610 (2006).

S. Tan and L. C. Jiao, J. Opt. Soc. Am. A 23, 2449 (2006).

T. Eltoft, T. Kim, and T. Lee, IEEE Signal Process. Lett. 13, 300 (2006).

2003 (1)

J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, IEEE Trans. Image Process. 12, 1338 (2003).
[CrossRef]

2002 (2)

L. Sendur and I. W. Selesnick, IEEE Trans. Signal Process. 50, 2744 (2002).
[CrossRef]

L. Sendur and I. W. Selesnick, IEEE Signal Process. Lett. 9, 438 (2002).
[CrossRef]

2001 (1)

T. T. Cai and B. W. Silverman, Sankhya, Ser. B 63, 127 (2001).

1992 (1)

D. N. Anderson, Stat. Probab. Lett. 14, 333 (1992).

IEEE Signal Process. Lett. (2)

L. Sendur and I. W. Selesnick, IEEE Signal Process. Lett. 9, 438 (2002).
[CrossRef]

T. Eltoft, T. Kim, and T. Lee, IEEE Signal Process. Lett. 13, 300 (2006).

IEEE Trans. Image Process. (3)

J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, IEEE Trans. Image Process. 12, 1338 (2003).
[CrossRef]

M. Elad and M. Aharon, IEEE Trans. Image Process. 15, 3736 (2006).
[CrossRef]

D. D.-Y. Po and M. N. Do, IEEE Trans. Image Process. 15, 610 (2006).

IEEE Trans. Signal Process. (1)

L. Sendur and I. W. Selesnick, IEEE Trans. Signal Process. 50, 2744 (2002).
[CrossRef]

Int. J. Comput. Vis. (1)

S. Tan and L. C. Jiao, "Multivariate statistical models for image denoising in the wavelet domain," Int. J. Comput. Vis. (to be published).

J. Opt. Soc. Am. A (1)

Proc. SPIE (1)

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, Proc. SPIE 6064, 6064A-30 (2006).

Sankhya, Ser. B (1)

T. T. Cai and B. W. Silverman, Sankhya, Ser. B 63, 127 (2001).

Stat. Probab. Lett. (1)

D. N. Anderson, Stat. Probab. Lett. 14, 333 (1992).

Other (2)

M.Abramowitz and C.A.Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972), pp. 925-964.

E. P. Simoncelli, in Proceedings of the 31st Asilomar Conference on Signals, Systems and Computers (IEEE, 1997), pp. 673-678.

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