The BKF Bayesian wavelet estimator

Signal Processing

Volumn 87, Issue 9, 2007, Pages 2268-2271

  Nadarajah, Saralees ^a   Kotz, Samuel ^b  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b GEORGE WASHINGTON UNIVERSITY   (United States)

Author keywords

Bessel K forms; Error function; Modified Bessel function of the first kind; Posterior conditional mean; Wavelets; Whittaker function

Indexed keywords

APPROXIMATION THEORY; COMPUTER PROGRAMMING; ERROR ANALYSIS; IMAGE PROCESSING; PATTERN RECOGNITION; WAVELET ANALYSIS;

BESSEL K FORM; MODIFIED BESSEL FUNCTION OF THE FIRST KIND; POSTERIOR CONDITIONAL MEAN; WHITTAKER FUNCTION;

BAYESIAN NETWORKS;

EID: 34247590200     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2007.02.013     Document Type: Article

References (17)

1. Boubchir L., and Fadili J.M. A closed-form nonparametric Bayesian estimator in the wavelet domain of images using an approximate alpha-stable prior. Pattern Recognition Lett. 271 (September 2006) 1370-1382
2. Fadili J.M., and Boubchir L. Analytical form for a Bayesian wavelet estimator of images using the Bessel K form densities. IEEE Trans. Image Process. 14 (February 2005) 231-240
3. E.P. Simoncelli, E.H. Adelson, Noise removal via Bayesian wavelet coring, in: Proceedings of the Third International Conference on Image Processing, vol. 1, Lausanne, Switzerland, 1996, pp. 379-382.
4. Chipman H.A., Kolaczyk E.D., and McCulloch R.E. Adaptive Bayesian wavelet shrinkage. J. Am. Stat. Assoc. 92 (1997) 1413-1421
5. Abramovich F., Sapatinas T., and Silverman B. Wavelet thresholding via a Bayesian approach. J. R. Stat. Soc. B 60 (1998) 725-749
6. Crouse M., Nowak R., and Baraniuk R. Wavelet-based statistical signal processing using hidden Markov models. IEEE Trans. Signal Process. 46 (April 1998) 886-902
7. Johnstone I.M., and Silverman B.W. Needles and straw in haystacks: empirical Bayes estimates of possibly sparse sequences. Ann. Stat. 32 (2004) 1594-1649
8. Johnstone I.M., and Silverman B.W. Empirical Bayes selection of wavelet thresholds. Ann. Stat. 33 (2005) 1700-1752
9. Vidakovic B. Nonlinear wavelet shrinkage with Bayes rules and Bayes factors. J. Am. Stat. Assoc. 93 (1998) 173-179
10. M.A. Clyde, E.I. George, Empirical Bayes estimation in wavelet nonparametric regression, in: P. Muller, B. Vidakovic (Eds.), Bayesian Inference in Wavelet Based Models, Springer, New York, NY, 1999, pp. 309-322.
11. Clyde M., and George E. Flexible empirical Bayes estimation for wavelets. J. R. Stat. Soc. B 62 (2000) 681-698
12. Vannucci M., and Corradi F. Covariance structure of wavelet coefficients: theory and models in a Bayesian perspective. J. R. Stat. Soc. B 61 (1999) 971-986
13. Huang S., and Lu H. Bayesian wavelet shrinkage for nonparametric mixed effects models. Stat. Sin. 10 (2000) 1021-1040
14. Chang S., Yu B., and Vetterli M. Adaptive wavelet thresholding for image denoising and compression. IEEE Trans. Image Process. 9 (September 2000) 1522-1523
15. A. Achim, A. Bezerianos, P. Tsakalides, Novel Bayesian multiscale method for speckle removal in medical ultrasound images, IEEE Trans. Med. Imaging 20 (May 2001) 772-783.
16. Prudnikov A.P., Brychkov Y.A., and Marichev O.I. Integrals and Series vol. 2 (1986), Gordon and Breach Science Publishers, Amsterdam
17. Gradshteyn I.S., and Ryzhik I.M. Table of Integrals, Series, and Products. sixth ed. (2000), Academic Press, San Diego, CA