메뉴 건너뛰기




Volumn 12, Issue 11, 2003, Pages 1338-1351

Image denoising using scale mixtures of Gaussians in the wavelet domain

Author keywords

Bayesian estimation; Gaussian scale mixtures; Hidden Markov model; Natural images; Noise removal; Overcomplete representations; Statistical models; Steerable pyramid

Indexed keywords

COMPUTER SIMULATION; ERRORS; ESTIMATION; GAUSSIAN NOISE (ELECTRONIC); MARKOV PROCESSES; MATHEMATICAL MODELS; PERFORMANCE; STATISTICAL METHODS; VECTORS; WHITE NOISE;

EID: 0242636409     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2003.818640     Document Type: Article
Times cited : (2174)

References (58)
  • 1
    • 0003071947 scopus 로고
    • Scale mixtures of normal distributions
    • D. Andrews and C. Mallows, "Scale mixtures of normal distributions," J. R. Statist. Soc, vol. 36, p. 99, 1974.
    • (1974) J. R. Statist. Soc , vol.36 , pp. 99
    • Andrews, D.1    Mallows, C.2
  • 2
    • 84898965689 scopus 로고    scopus 로고
    • Scale mixtures of Gaussians and the statistics of natural images
    • S. A. Solla, T. K. Leen, and K. R. Müller, Eds. Cambridge, MA: MIT Press
    • M. J. Wainwright and E. P. Simoncelli, "Scale mixtures of Gaussians and the statistics of natural images," in Adv. Neural Information Processing Systems, S. A. Solla, T. K. Leen, and K. R. Müller, Eds. Cambridge, MA: MIT Press, 2000, vol. 12, pp. 855-861.
    • (2000) Adv. Neural Information Processing Systems , vol.12 , pp. 855-861
    • Wainwright, M.J.1    Simoncelli, E.P.2
  • 3
    • 0035391385 scopus 로고    scopus 로고
    • Random cascades on wavelet trees and their use in modeling and analyzing natural imagery
    • July
    • M. J. Wainwright, E. P. Simoncelli, and A. S. Willsky, "Random cascades on wavelet trees and their use in modeling and analyzing natural imagery," Appl. Comput. Harmon. Anal., vol. 11, no. 1, pp. 89-123, July 2001.
    • (2001) Appl. Comput. Harmon. Anal. , vol.11 , Issue.1 , pp. 89-123
    • Wainwright, M.J.1    Simoncelli, E.P.2    Willsky, A.S.3
  • 4
    • 3042609133 scopus 로고    scopus 로고
    • The statistics of natural images
    • D. L. Ruderman, "The statistics of natural images," Network: Comput. Neural Syst., vol. 5, pp. 517-548, 1996.
    • (1996) Network: Comput. Neural Syst. , vol.5 , pp. 517-548
    • Ruderman, D.L.1
  • 5
    • 0023492118 scopus 로고
    • Relations between the statistics of natural images and the response properties of cortical cells
    • D. J. Field, "Relations between the statistics of natural images and the response properties of cortical cells," J. Opt. Soc. Amer. A, vol. 4, no. 12, pp. 2379-2394, 1987.
    • (1987) J. Opt. Soc. Amer. A , vol.4 , Issue.12 , pp. 2379-2394
    • Field, D.J.1
  • 6
    • 0024550990 scopus 로고
    • Entropy reduction and decorrelation in visual coding by oriented neural receptive fields
    • J. G. Daugman, "Entropy reduction and decorrelation in visual coding by oriented neural receptive fields," IEEE Trans. Biomed. Eng., vol. 36, no. 1, pp. 107-114, 1989.
    • (1989) IEEE Trans. Biomed. Eng. , vol.36 , Issue.1 , pp. 107-114
    • Daugman, J.G.1
  • 7
    • 0024700097 scopus 로고
    • A theory for multiresolution signal decomposition: The wavelet representation
    • July
    • S. G. Mallat, "A theory for multiresolution signal decomposition: The wavelet representation," IEEE Pattern Anal. Machine Intell., vol. 11, pp. 674-693, July 1989.
    • (1989) IEEE Pattern Anal. Machine Intell. , vol.11 , pp. 674-693
    • Mallat, S.G.1
  • 8
    • 0029938380 scopus 로고    scopus 로고
    • Emergence of simple-cell receptive field properties by learning a sparse code for natural images
    • B. A. Olshausen and D. J. Field, "Emergence of simple-cell receptive field properties by learning a sparse code for natural images," Nature, vol. 381, pp. 607-609, 1996.
    • (1996) Nature , vol.381 , pp. 607-609
    • Olshausen, B.A.1    Field, D.J.2
  • 9
    • 0030832881 scopus 로고    scopus 로고
    • The 'independent components' of natural scenes are edge filters
    • A. J. Bell and T. J. Sejnowski, "The 'independent components' of natural scenes are edge filters," Vis. Res., vol. 37, no. 23, pp. 3327-3338, 1997.
    • (1997) Vis. Res. , vol.37 , Issue.23 , pp. 3327-3338
    • Bell, A.J.1    Sejnowski, T.J.2
  • 10
    • 0017944026 scopus 로고
    • Digital techniques for reducing television noise
    • J. P. Rossi, "Digital techniques for reducing television noise," JSMPTE, vol. 87, pp. 134-140, 1978.
    • (1978) JSMPTE , vol.87 , pp. 134-140
    • Rossi, J.P.1
  • 11
    • 0041958932 scopus 로고
    • Ideal spatial adaptation by wavelet shrinkage
    • D. L. Donoho and I. M. Johnstone, "Ideal spatial adaptation by wavelet shrinkage," Biometrika, vol. 81, no. 3, pp. 425-455, 1994.
    • (1994) Biometrika , vol.81 , Issue.3 , pp. 425-455
    • Donoho, D.L.1    Johnstone, I.M.2
  • 16
    • 0000446730 scopus 로고    scopus 로고
    • Bayesian denoising of visual images in the wavelet domain
    • P. Müller and B. Vidakovic, Eds. New York: Springer-Verlag; ch. 18
    • E. P. Simoncelli, "Bayesian denoising of visual images in the wavelet domain," in Bayesian Inference in Wavelet Based Models, P. Müller and B. Vidakovic, Eds. New York: Springer-Verlag, 1999, vol. 141, ch. 18, pp. 291-308.
    • (1999) Bayesian Inference in Wavelet Based Models , vol.141 , pp. 291-308
    • Simoncelli, E.P.1
  • 17
    • 0032662774 scopus 로고    scopus 로고
    • Analysis of multiresolution image denoising schemes using a generalized Gaussian and complexity priors
    • P. Moulin and J. Liu, "Analysis of multiresolution image denoising schemes using a generalized Gaussian and complexity priors," IEEE Trans. Inform. Theory, vol. 45, pp. 909-919, 1999.
    • (1999) IEEE Trans. Inform. Theory , vol.45 , pp. 909-919
    • Moulin, P.1    Liu, J.2
  • 18
    • 0348223982 scopus 로고    scopus 로고
    • Sparse code shrinkage: Denoising of non-Gaussian data by maximum likelihood estimation
    • A. Hyvarinen, "Sparse code shrinkage: Denoising of non-Gaussian data by maximum likelihood estimation," Neural Comput., vol. 11, no. 7, pp. 1739-1768, 1999.
    • (1999) Neural Comput. , vol.11 , Issue.7 , pp. 1739-1768
    • Hyvarinen, A.1
  • 20
    • 17944388697 scopus 로고
    • Statistical dependence between orientation filter outputs used in an human vision based image code
    • Lausanne, Switzerland
    • B. Wegmann and C. Zetzsche, "Statistical dependence between orientation filter outputs used in an human vision based image code," in Proc. Visual Comm. Image Processing, vol. 1360, Lausanne, Switzerland, 1990, pp. 909-922.
    • (1990) Proc. Visual Comm. Image Processing , vol.1360 , pp. 909-922
    • Wegmann, B.1    Zetzsche, C.2
  • 21
    • 0031674414 scopus 로고    scopus 로고
    • Statistical models for images: Compression, restoration and synthesis
    • [Online]
    • E. P. Simoncelli. Statistical models for images: Compression, restoration and synthesis. presented at Proc. 31st Asilomar Conf. on Signals, Systems and Computers. [Online]. Available: http://www.cns.nyu.edu/~eero/publications.html
    • Proc. 31st Asilomar Conf. on Signals, Systems and Computers
    • Simoncelli, E.P.1
  • 22
    • 0033338289 scopus 로고    scopus 로고
    • Image compression via joint statistical characterization in the wavelet domain
    • Dec.
    • R. W. Buccigrossi and E. P. Simoncelli, "Image compression via joint statistical characterization in the wavelet domain," IEEE Trans. Image Processing, vol. 8, pp. 1688-1701, Dec. 1999.
    • (1999) IEEE Trans. Image Processing , vol.8 , pp. 1688-1701
    • Buccigrossi, R.W.1    Simoncelli, E.P.2
  • 23
    • 0023313586 scopus 로고
    • Description and generation of spherically invariant speech-model signals
    • H. Brehm and W. Stammler, "Description and generation of spherically invariant speech-model signals," Signal Process., vol. 12, pp. 119-141, 1987.
    • (1987) Signal Process , vol.12 , pp. 119-141
    • Brehm, H.1    Stammler, W.2
  • 25
    • 33747727601 scopus 로고    scopus 로고
    • Wavelet-based statistical signal processing using hidden Markov models
    • Apr.
    • M. S. Crouse, R. D. Nowak, and R. G. Baraniuk, "Wavelet-based statistical signal processing using hidden Markov models," IEEE Trans. Signal Processing, vol. 46, pp. 886-902, Apr. 1998.
    • (1998) IEEE Trans. Signal Processing , vol.46 , pp. 886-902
    • Crouse, M.S.1    Nowak, R.D.2    Baraniuk, R.G.3
  • 26
    • 0035398091 scopus 로고    scopus 로고
    • Bayesian tree-structured image modeling using wavelet-domain hidden Markov models
    • July
    • J. Romberg, H. Choi, and R. Baraniuk, "Bayesian tree-structured image modeling using Wavelet-domain hidden Markov models," IEEE Trans. Image Processing, vol. 10, July 2001.
    • (2001) IEEE Trans. Image Processing , vol.10
    • Romberg, J.1    Choi, H.2    Baraniuk, R.3
  • 28
    • 0342647438 scopus 로고    scopus 로고
    • Low-complexity image denoising based on statistical modeling of wavelet coefficients
    • Dec.
    • M. K. Mihçak, I. Kozintsev, K. Ramchandran, and P. Moulin, "Low-complexity image denoising based on statistical modeling of wavelet coefficients," IEEE Trans. Signal Processing, vol. 6, pp. 300-303, Dec. 1999.
    • (1999) IEEE Trans. Signal Processing , vol.6 , pp. 300-303
    • Mihçak, M.K.1    Kozintsev, I.2    Ramchandran, K.3    Moulin, P.4
  • 29
    • 0018998148 scopus 로고
    • Digital image enhancement and noise filtering by use of local statistics
    • Mar.
    • J. S. Lee, "Digital image enhancement and noise filtering by use of local statistics," IEEE Pattern Anal. Machine Intell., vol. PAMI-2, pp. 165-168, Mar. 1980.
    • (1980) IEEE Pattern Anal. Machine Intell. , vol.PAMI-2 , pp. 165-168
    • Lee, J.S.1
  • 30
    • 0002533801 scopus 로고
    • The empirical Bayes approach to statistical decision problems
    • H. Robbins, "The empirical Bayes approach to statistical decision problems," Ann. Math. Statist., vol. 35, pp. 1-20, 1964.
    • (1964) Ann. Math. Statist. , vol.35 , pp. 1-20
    • Robbins, H.1
  • 31
    • 0031117537 scopus 로고    scopus 로고
    • Wavelet-based image denoising using a Markov random field a priori model
    • Apr.
    • M. Malfait and D. Roose, "Wavelet-based image denoising using a Markov random field a priori model," IEEE Trans. Image Processing, vol. 6, pp. 549-565, Apr. 1997.
    • (1997) IEEE Trans. Image Processing , vol.6 , pp. 549-565
    • Malfait, M.1    Roose, D.2
  • 33
    • 0037189287 scopus 로고    scopus 로고
    • Empirical bayes approach to block wavelet function estimation
    • F. Abramovich, T. Besbeas, and T. Sapatinas, "Empirical Bayes approach to block wavelet function estimation," Comput. Statist. Data Anal., vol. 39, pp. 435-451, 2002.
    • (2002) Comput. Statist. Data Anal. , vol.39 , pp. 435-451
    • Abramovich, F.1    Besbeas, T.2    Sapatinas, T.3
  • 37
    • 0002001578 scopus 로고
    • Translation-invariant de-noising
    • A. Antoniadis and G. Oppenheim, Eds. San Diego, CA: Springer-Verlag; Lecture notes
    • R. R. Coifman and D. L. Donoho, "Translation-invariant de-noising," in Wavelets and Statistics, A. Antoniadis and G. Oppenheim, Eds. San Diego, CA: Springer-Verlag, 1995, Lecture notes.
    • (1995) Wavelets and Statistics
    • Coifman, R.R.1    Donoho, D.L.2
  • 40
    • 0023422157 scopus 로고
    • The cortex transform: Rapid computation of simulated neural images
    • A. B. Watson, "The cortex transform: Rapid computation of simulated neural images," Comput. Vis. Graphics Image Process., vol. 39, pp. 311-327, 1987.
    • (1987) Comput. Vis. Graphics Image Process. , vol.39 , pp. 311-327
    • Watson, A.B.1
  • 41
    • 0346727379 scopus 로고    scopus 로고
    • Ridgelets: A key to higher-dimensional intermittency?
    • E. J. Candes and D. L. Donoho, "Ridgelets: A key to higher-dimensional intermittency?," Phil. Trans. R. Soc. Lond A, vol. 357, pp. 2495-2509, 1999.
    • (1999) Phil. Trans. R. Soc. Lond A , vol.357 , pp. 2495-2509
    • Candes, E.J.1    Donoho, D.L.2
  • 42
    • 0035331869 scopus 로고    scopus 로고
    • Complex wavelets for shift invariant analysis and filtering of signals
    • May
    • N. Kingsbury, "Complex wavelets for shift invariant analysis and filtering of signals," Appl. Comput. Harmon. Anal., vol. 10, no. 3, pp. 234-253, May 2001.
    • (2001) Appl. Comput. Harmon. Anal. , vol.10 , Issue.3 , pp. 234-253
    • Kingsbury, N.1
  • 45
    • 0035442514 scopus 로고    scopus 로고
    • Wavelet-based image estimation: An empirical Bayes approach using Jeffrey's noninformative prior
    • Sept.
    • M. Figueiredo and R. Nowak, "Wavelet-based image estimation: An empirical Bayes approach using Jeffrey's noninformative prior," IEEE Trans. Image Processing, vol. 10, pp. 1322-1331, Sept. 2001.
    • (2001) IEEE Trans. Image Processing , vol.10 , pp. 1322-1331
    • Figueiredo, M.1    Nowak, R.2
  • 46
    • 0027798110 scopus 로고
    • Embedded image coding using zerotrees of wavelet coefficients
    • Dec.
    • J. Shapiro, "Embedded image coding using zerotrees of wavelet coefficients," IEEE Trans. Signal Processing, vol. 41, pp. 3445-3462, Dec. 1993.
    • (1993) IEEE Trans. Signal Processing , vol.41 , pp. 3445-3462
    • Shapiro, J.1
  • 47
    • 0030817745 scopus 로고    scopus 로고
    • Origins of scaling in natural images
    • D. L. Ruderman, "Origins of scaling in natural images," Vis. Res., vol. 37, pp. 3385-3398, 1997.
    • (1997) Vis. Res. , vol.37 , pp. 3385-3398
    • Ruderman, D.L.1
  • 48
    • 0032689866 scopus 로고    scopus 로고
    • Duality of log-polar image representations in the space and the spatial-frequency domains
    • Sept.
    • A. Tabernero, J. Portilla, and R. Navarro, "Duality of log-polar image representations in the space and the spatial-frequency domains," IEEE Trans. Signal Processing, vol. 47, pp. 2469-2479, Sept. 1999.
    • (1999) IEEE Trans. Signal Processing , vol.47 , pp. 2469-2479
    • Tabernero, A.1    Portilla, J.2    Navarro, R.3
  • 49
    • 0036844073 scopus 로고    scopus 로고
    • Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency
    • Nov.
    • L. Sendur and I. W. Selesnick, "Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency," IEEE Trans. Signal Processing, vol. 50, pp. 2744-2756, Nov. 2002.
    • (2002) IEEE Trans. Signal Processing , vol.50 , pp. 2744-2756
    • Sendur, L.1    Selesnick, I.W.2
  • 50
    • 0036959297 scopus 로고    scopus 로고
    • Bivariate shrinkage with local variance estimation
    • Dec.
    • ____, "Bivariate shrinkage with local variance estimation," IEEE Signal Processing Lett., vol. 9, pp. 438-441, Dec. 2002.
    • (2002) IEEE Signal Processing Lett. , vol.9 , pp. 438-441
    • Sendur, L.1    Selesnick, I.W.2
  • 51
    • 0036563492 scopus 로고    scopus 로고
    • A joint inter- and intrascale statistical model for Bayesian wavelet based image denoising
    • May
    • A. Pižurica, W. Philips, I. Lemahieu, and M. Acheroy, "A joint inter- and intrascale statistical model for Bayesian wavelet based image denoising," IEEE Trans. Image Processing, vol. 11, pp. 545-557, May 2002.
    • (2002) IEEE Trans. Image Processing , vol.11 , pp. 545-557
    • Pižurica, A.1    Philips, W.2    Lemahieu, I.3    Acheroy, M.4
  • 52
    • 0035767715 scopus 로고    scopus 로고
    • Very high quality image restoration
    • August
    • J. L. Starck, D. L. Donoho, and E. Candes, "Very high quality image restoration," Proc. SPIE, vol. 4478, pp. 9-19, August 2001.
    • (2001) Proc. SPIE , vol.4478 , pp. 9-19
    • Starck, J.L.1    Donoho, D.L.2    Candes, E.3
  • 53
    • 0242639742 scopus 로고    scopus 로고
    • Image denoising using gaussian scale mixtures in the wavelet domain
    • Courant Inst. of Math. Sci., New York University, Tech. Rep. TR2002-831
    • J. Portilla, V. Strela, M. Wainwright, and E. Simoncelli, "Image Denoising Using Gaussian Scale Mixtures in the Wavelet Domain," Courant Inst. of Math. Sci., New York University, Tech. Rep. TR2002-831, 2002.
    • (2002)
    • Portilla, J.1    Strela, V.2    Wainwright, M.3    Simoncelli, E.4
  • 55
    • 0006420689 scopus 로고    scopus 로고
    • Image features from phase congruency
    • Summer
    • P. D. Kovesi, "Image features from phase congruency," J. Comput. Vis. Res., vol. 1, no. 3, Summer 1999.
    • (1999) J. Comput. Vis. Res. , vol.1 , Issue.3
    • Kovesi, P.D.1
  • 56
    • 0034291204 scopus 로고    scopus 로고
    • A parametric texture model based on joint statistics of complex wavelet coefficients
    • J. Portilla and E. P. Simoncelli, "A parametric texture model based on joint statistics of complex wavelet coefficients," Int. J. Comput. Vis., vol. 40, no. 1, pp. 49-71, 2000.
    • (2000) Int. J. Comput. Vis. , vol.40 , Issue.1 , pp. 49-71
    • Portilla, J.1    Simoncelli, E.P.2
  • 57
    • 0032022704 scopus 로고    scopus 로고
    • Nonlinear wavelet image processing: Variational problems, compression, and noise removal through wavelet shrinkage
    • Mar.
    • A. Chambolle, R. A. DeVore, N. Lee, and B. J. Lucier, "Nonlinear wavelet image processing: Variational problems, compression, and noise removal through wavelet shrinkage," IEEE Trans. Image Processing, vol. 7, pp. 319-335, Mar. 1998.
    • (1998) IEEE Trans. Image Processing , vol.7 , pp. 319-335
    • Chambolle, A.1    DeVore, R.A.2    Lee, N.3    Lucier, B.J.4
  • 58
    • 0032349461 scopus 로고    scopus 로고
    • Nonlinear wavelet shrinkage with Bayes rules and Bayes factors
    • B. Vidakovic, "Nonlinear wavelet shrinkage with Bayes rules and Bayes factors," J. Amer. Statist. Assoc., vol. 93, pp. 173-179, 1998.
    • (1998) J. Amer. Statist. Assoc. , vol.93 , pp. 173-179
    • Vidakovic, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.