Complex gaussian scale mixtures of complex wavelet coefficients

IEEE Transactions on Signal Processing

Volumn 58, Issue 7, 2010, Pages 3545-3556

  Rakvongthai, Yothin ^a   Vo, An P N ^b   Oraintara, Soontorn ^a  

^a University of Texas at Arlington   (United States)

^b FEINSTEIN INSTITUTE FOR MEDICAL RESEARCH   (United States)

Author keywords

Complex Gaussian scale mixtures (CGSMs); Complex wavelets; Magnitude; Phase

Indexed keywords

CLOSED FORM; COMPLEX GAUSSIAN; COMPLEX RANDOM VARIABLES; COMPLEX WAVELETS; GAUSSIAN SCALE MIXTURES; GENERALIZED GAUSSIAN DISTRIBUTIONS; IMAGE DE-NOISING; LEAST-SQUARE ESTIMATORS; PROBABILITY DENSITY FUNCTION (PDF); RELATIVE PHASE; TRANSFORM DOMAIN;

GAUSSIAN DISTRIBUTION; IMAGE PROCESSING; MIXTURES; PARTIAL DISCHARGES; RANDOM VARIABLES; REAL VARIABLES; WAVELET TRANSFORMS;

PROBABILITY DENSITY FUNCTION;

EID: 77953731101     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2010.2046698     Document Type: Article

References (49)

1. I. W. Selesnick, R. G. Baraniuk, and N. G. Kingsbury, "The dual-tree complex wavelet transform," IEEE Signal Process. Mag., vol.22, no.6, pp. 123-151, Nov. 2005.
2. A. V. Oppenheim and J. S. Lim, "The importance of phase in signals," Proc. IEEE, vol.PROC-69, no.5, pp. 529-541, May 1981.
3. R. Anderson, N. Kingsbury, and J. Fauqueur, "Determining multiscale image feature angles from complex wavelet phases," presented at the ICIAR, Toronto, ON, Canada, Sep. 2005.
4. P. D. Kovesi, "Image features from phase congruency," J. Comput. Vis. Res., vol.16, no.3, Summer 1999.
5. Z.Wang and E. P. Simoncelli, "Local phase coherence and the perception of blur," Adv. Neural Inform. Process. Syst., vol.16, 2004.
6. A. P. N. Vo and S. Oraintara, "A study of relative phase in complex wavelet domain: Property, statistics and applications in texture image retrieval and segmentation," Signal Process.: Image Commun., vol.25, no.1, pp. 28-46, Jan. 2010.
7. A. P. N. Vo, S. Oraintara, and T. T. Nguyen, "Statistical image modeling using distribution of relative phase in the complex wavelet domain," presented at the EUSIPCO, Lausanne, Switzerland, Aug. 2008.
8. R. A.Wooding, "The multivariate distribution of complex normal variables," Biometrika, vol.4, no.1-2, pp. 212-215, 1956.
9. N. R. Goodman, "Statistics analysis based on certain multivariate complex distribution (an introduction)," Ann. Math. Stat., vol.34, no.1, pp. 152-177, 1963.
10. K. S. Miller, "Complex Gaussian processes," SIAM Rev., vol.11, no.4, pp. 544-567, Oct. 1969.
11. H. Choi, J. K. Romberg, R. G. Baraniuk, and N. G. Kingsbury, "Hidden Markov tree modeling of complex wavelet transforms," in Proc. IEEE ICASSP, Jun. 2000, vol.1, pp. 133-136.
12. N. G. Kingsbury, "Complex wavelets for shift invariant analysis and filtering of signals," Appl. Computat. Harm. Anal., vol.10, no.3, pp. 234-253, May 2001.
13. L. Şendur and I. W. Selesnick, "Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency," IEEE Trans. Signal Process., vol.50, no.11, pp. 2744-2756, Nov. 2002.
14. A. Achim and E. E. Kuruǒglu, "Image denoising using bivariate α-stable distributions in the complex wavelet domain," IEEE Signal Process. Lett., vol.12, no.1, pp. 17-20, Jan. 2005.
15. S. M. M. Rahman, M. O. Ahmad, and M. N. S. Swamy, "Statistics of 2-DDT-CWT coefficients for a Gaussian distributed signal," IEEE Trans. Circuits Syst. I, Reg. Papers, vol.55, no.7, pp. 2013-2025, Aug. 2008.
16. Y. Rakvongthai and S. Oraintara, "Statistical image modeling with the magnitude probability density function of complex wavelet coefficients," in Proc. IEEE ISCAS, Taipei, Taiwan, May 2009, pp. 1879-1882.
17. D. F. Andrews and C. L. Mallows, "Scale mixtures of normal distributions," J. Roy. Stat. Soc. B, vol.36, no.1, pp. 99-102, 1974.
18. M. J. Wainwright, E. P. Simoncelli, and A. S. Willsky, "Random cascades on wavelet trees and their use in analying and modeling natural images," Appl. Comput. Harm. Anal., vol.11, pp. 89-123, 2001.
19. M. J. Wainwright and E. P. Simoncelli, "Scale mixtures of Gaussians and the statistics of natural images," Adv. Neural Inform. Process. Syst., vol.12, pp. 855-861, 2000.
20. S. G. Mallat, "A theory for multiresolution signal decomposition: The wavelet representation," IEEE Trans. Pattern Anal. Mach. Intell., vol.11, no.7, pp. 674-693, Jul. 1989.
21. M. S. Crouse, R. D. Nowak, and R. G. Baraniuk, "Wavelet-based statistical signal processing using hidden Markov models," IEEE Trans. Signal Process., vol.46, no.4, pp. 886-902, Apr. 1998.
22. J. M. Fadili and L. Boubchir, "Analytical form for a Bayesian wavelet estimator of images using the Bessel K form densities," IEEE Trans. Image Process., vol.14, no.2, pp. 231-240, Feb. 2005.
23. D. Cho and T. D. Bui, "Multivariate statistical modeling for image denoising using wavelet transforms," Signal Proces.: Image Commun., vol.20, no.1, pp. 77-89, Jan. 2005.
24. I. W. Selesnick, "The estimation of Laplace random vectors in addtive white Gaussian noise," IEEE Trans. Signal Process., vol.56, no.8, pp. 3482-3496, Aug. 2008.
25. S. Tan, L. Jiao, and I. A. Kakadiaris, "Wavelet-based Bayesian image estimation: From marginal and bivariate prior models to multivariate prior models," IEEE Trans. Image Process., vol.17, no.4, pp. 469-481, Apr. 2008.
26. J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, "Image denoising using scale mixtures of Gaussians in the wavelet domain," IEEE Trans. Image Process., vol.12, no.11, pp. 1338-1351, Nov. 2003.
27. J. A. Guerrero-Colón, L. Mancera, and J. Portilla, "Image restoration using space-variant Gaussian scale mixture in overcomplete pyramids," IEEE Trans. Image Process., vol.17, no.1, pp. 27-41, Jan. 2008.
28. D. K. Hammond and E. P. Simoncelli, "Image modeling and denoising with orientation-adapted Gaussian scale mixtures," IEEE Trans. Image Process., vol.17, no.11, pp. 2089-2101, Nov. 2008.
29. M. Miller and N. Kingsbury, "Image denoising using derotated complex wavelet coefficients," IEEE Trans. Image Process., vol.19, no.9, pp. 1500-1511, Sep. 2008.
30. E. J. Candès, D. L. Donoho, and L. Ying, "Fast discrete curvelet transform," Multiscale Model. Simul., vol.5, no.3, pp. 861-899, Sep. 2006.
31. T. T. Nguyen and S. Oraintara, "The shiftable complex directional pyramid-Part I: Theoretical aspects," IEEE Trans. Signal Process., vol.56, no.10, pp. 4651-4660, Oct. 2008.
32. T. T. Nguyen and H. Chauris, "Uniform discrete curvelet transform for seismic processing," presented at the EAGE Conf. and Tech. Exhibit., Rome, Italy, Jun. 2008.
33. A. P. N. Vo, T. T. Nguyen, and S. Oraintara, "Image denoising using shiftable directional pyramid and scale mixtures of complex Gaussians," in Proc. IEEE ISCAS, New Orleans, LA, May 2007, pp. 4000-4003.
34. S. Lyu and E. P. Simoncelli, "Nonlinear image representation using divisive normalization," in Proc. IEEE CVPR, Anchorage, AK, Jun. 2008, pp. 1-8.
35. G. H. Granlund and H. Knutsson, Signal Processing for Computer Vision. Dordrecht, The Netherlands: Kluwer, 1995.
36. A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes. New York: McGraw-Hill, 2002.
37. B. Picinbono, "Second-order complex random vectors and normal distributions," IEEE Trans. Signal Process., vol.44, no.10, pp. 2637-2640, Oct. 1996.
38. F. D. Neeser and J. L. Massey, "Proper complex random processes with applications to information theory," IEEE Trans. Inf. Theory, vol.39, no.4, pp. 1293-1302, Jul. 1997.
39. P. J. Schreier, "Bounds on the degree of impropriety of complex random vectors," IEEE Signal Process. Lett., vol.15, pp. 190-193, 2008.
40. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Upper Saddle River, NJ: Prentice-Hall, 1993.
41. H. Hamden, "Characterizing and approximating infinite scale mixtures of normals," Commun. Stat.-Theory Meth., vol.35, no.3, pp. 407-413, 2006.
42. P. Moulin and J. Liu, "Analysis of multiresolution image denoising schemes using generalized Gaussian and complexity priors," IEEE Trans. Inf. Theory, vol.45, no.3, pp. 909-919, Apr. 1999.
43. M. S. Davis, P. Bidigare, and D. Chang, "Statistical modeling and ML parameter estimation of complex SAR imagery," in Proc. Asilomar Conf. Signals, Syst., Comput, Nov. 2007, pp. 500-502.
44. S. Kotz, T. J. Kozubowski, and K. Podgórski, The Laplace Distribution and Generalizations: A Revisit With Applications to Communications, Economics, Engineering, and Finance. Boston, MA: Birkhäuser, 2001.
45. A. P. N. Vo, S. Oraintara, and T. T. Nguyen, "Using phase and magnitude information of the complex directional filter bank for texture image retrieval," in Proc. IEEE ICIP, San Antonio, TX, Sep. 2007, vol.4, pp. IV-61-IV-64.
46. G. E. P. Box and G. C. Tiao, Bayesian Inference in Statistical Analysis. Reading, MA: Addison-Wesley, 1973.
47. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, "Image quality assessment: From error visibility to structural similarity," IEEE Trans. Image Process., vol.13, no.4, pp. 600-612, Apr. 2004.
48. P. J. Schreier and L. L. Scharf, "Second-order analysis of improper complex random vectors and processes," IEEE Trans. Signal Process., vol.51, no.3, pp. 714-725, Mar. 2003.
49. L. Şendur and I. W. Selesnick, "Bivariate shrinkage with local variance estimation," IEEE Signal Process. Lett., vol.9, no.12, pp. 438-441, Dec. 2002.