메뉴 건너뛰기




Volumn 17, Issue 7, 2008, Pages 1093-1108

Wavelets, ridgelets, and curvelets for poisson noise removal

Author keywords

Curvelets; Filtered Poisson process; Multiscale variance stabilizing transform; Poisson intensity estimation; Ridgelets; Wavelets

Indexed keywords

ASYMPTOTIC ANALYSIS; FILTER BANKS; NORMAL DISTRIBUTION; POISSON DISTRIBUTION; POISSON EQUATION;

EID: 45949089551     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2008.924386     Document Type: Article
Times cited : (333)

References (56)
  • 3
    • 0001243836 scopus 로고
    • The transformation of Poisson, binomial and negative-binomial data
    • F. J. Anscombe, "The transformation of Poisson, binomial and negative-binomial data," Biometrika, vol. 35, pp. 246-254, 1948.
    • (1948) Biometrika , vol.35 , pp. 246-254
    • Anscombe, F.J.1
  • 4
    • 0000370306 scopus 로고
    • Nonlinear wavelet methods for recovery of signals, densities an spectra from indirect and noisy data
    • D. L. Donoho, "Nonlinear wavelet methods for recovery of signals, densities an spectra from indirect and noisy data," in Proc. Symp. Applied Mathematics: Different Perspectives on Wavelets, 1993, vol. 47, pp. 173-205.
    • (1993) Proc. Symp. Applied Mathematics: Different Perspectives on Wavelets , vol.47 , pp. 173-205
    • Donoho, D.L.1
  • 5
    • 0041958932 scopus 로고
    • Ideal spatial adaptation by wavelet shrinkage
    • D. L. Donho, "Ideal spatial adaptation by wavelet shrinkage," Biometrika, vol. 81, pp. 425-455, 1994.
    • (1994) Biometrika , vol.81 , pp. 425-455
    • Donho, D.L.1
  • 6
    • 0029307534 scopus 로고
    • De-noising by soft-thresholding
    • May
    • D. L. Donoho, "De-noising by soft-thresholding" IEEE Trans. Inf. Theory, vol. 41, no. 3, pp. 613-627, May 1995.
    • (1995) IEEE Trans. Inf. Theory , vol.41 , Issue.3 , pp. 613-627
    • Donoho, D.L.1
  • 7
    • 4344601732 scopus 로고    scopus 로고
    • A Haar-Fisz algorithm for Poisson intensity estimation
    • P. Fryźlewicz and G. P. Nason, "A Haar-Fisz algorithm for Poisson intensity estimation," J. Comput. Graph. Statist., vol. 13, pp. 621-638, 2004.
    • (2004) J. Comput. Graph. Statist , vol.13 , pp. 621-638
    • Fryźlewicz, P.1    Nason, G.P.2
  • 8
    • 33846336730 scopus 로고    scopus 로고
    • GOES-8 X-ray sensor variance stabilization using the multiscale data-driven Haar-Fisztransform
    • DD
    • P. Fryzlewicz, V. Delouille and G. P. Nason, "GOES-8 X-ray sensor variance stabilization using the multiscale data-driven Haar-Fisztransform," J. Roy. Statist. Soc. C, vol. 56, no. 1, DD. 99-116, 2007.
    • (2007) J. Roy. Statist. Soc. C , vol.56 , Issue.1 , pp. 99-116
    • Fryzlewicz, P.1    Delouille, V.2    Nason, G.P.3
  • 9
    • 3142759528 scopus 로고
    • The limiting distribution of a function of two independent random variables and its statistical application
    • M. Fisz, "The limiting distribution of a function of two independent random variables and its statistical application," Colloq. Math., vol. 3, pp. 138-146, 1955.
    • (1955) Colloq. Math , vol.3 , pp. 138-146
    • Fisz, M.1
  • 10
    • 33645024708 scopus 로고    scopus 로고
    • Multiscale Poisson data smoothing
    • M. Jansen, "Multiscale Poisson data smoothing," J. Roy. Statist. Soc. B, vol. 68. no. 1. pp. 27-48, 2006.
    • (2006) J. Roy. Statist. Soc. B , vol.68 , Issue.1 , pp. 27-48
    • Jansen, M.1
  • 11
    • 0032634507 scopus 로고    scopus 로고
    • Wavelet-domain filtering for photon imaging systems
    • May
    • R. D. Nowak and R. G. Baraniuk, "Wavelet-domain filtering for photon imaging systems," IEEE Trans. Image Process., vol. 8, no. 5, pp. 666-678, May 1999.
    • (1999) IEEE Trans. Image Process , vol.8 , Issue.5 , pp. 666-678
    • Nowak, R.D.1    Baraniuk, R.G.2
  • 12
    • 3042674778 scopus 로고    scopus 로고
    • Wavelet shrinkage for natural exponential families with quadratic variance functions
    • A. Antoniadis and T. Sapatinas, "Wavelet shrinkage for natural exponential families with quadratic variance functions," Biometrika vol. 88, pp. 805-820, 2001.
    • (2001) Biometrika , vol.88 , pp. 805-820
    • Antoniadis, A.1    Sapatinas, T.2
  • 13
    • 0034179316 scopus 로고    scopus 로고
    • Nonparametric estimation of intensity maps using Haar wavelets and Poisson noise characteristics
    • E. D. Kolaczyk, "Nonparametric estimation of intensity maps using Haar wavelets and Poisson noise characteristics," Astrophys. J., vol. 534, pp. 490-505, 2000.
    • (2000) Astrophys. J , vol.534 , pp. 490-505
    • Kolaczyk, E.D.1
  • 14
    • 45949100866 scopus 로고    scopus 로고
    • B. Zhang, M. J. Fadili, J.-L. Starck, and S. W. Digel, Fast Poisson noise removal by biorthogonal Haar domain hypothesis testing, Statsit, Method., 2007.
    • B. Zhang, M. J. Fadili, J.-L. Starck, and S. W. Digel, "Fast Poisson noise removal by biorthogonal Haar domain hypothesis testing," Statsit, Method., 2007.
  • 15
    • 0035452167 scopus 로고    scopus 로고
    • On the distribution of the wavelet coefficient for a Poisson noise
    • A. Bijaoui and G. Jammal, "On the distribution of the wavelet coefficient for a Poisson noise," Signal Process., vol. 81, pp. 1789-1800, 2001.
    • (2001) Signal Process , vol.81 , pp. 1789-1800
    • Bijaoui, A.1    Jammal, G.2
  • 16
    • 0033410025 scopus 로고    scopus 로고
    • Wavelet shrinkage estimation of certain Poisson intentsity signals using corrected thresholds
    • E. D. Kolaczyk, "Wavelet shrinkage estimation of certain Poisson intentsity signals using corrected thresholds," Statist. Sinica, vol. 9, pp. 119-135, 1999.
    • (1999) Statist. Sinica , vol.9 , pp. 119-135
    • Kolaczyk, E.D.1
  • 17
    • 45949095469 scopus 로고    scopus 로고
    • Bayesian multiscale models for Poisson processes
    • Apr
    • E. D. Kolaczyk, "Bayesian multiscale models for Poisson processes," IEEE Trans. Inf. Theory, vol. 45, no. 3, pp. 846-862, Apr. 1999.
    • (1999) IEEE Trans. Inf. Theory , vol.45 , Issue.3 , pp. 846-862
    • Kolaczyk, E.D.1
  • 18
    • 0032628620 scopus 로고    scopus 로고
    • Multiscal modeling and estimation of Poisson processes with application to photon-limited imaging
    • Apr
    • K. E. Timmermann and R. D. Nowak, "Multiscal modeling and estimation of Poisson processes with application to photon-limited imaging," IEEE Trans. Inf. Theory, vol. 45, no. 3, pp. 846-862, Apr. 1999.
    • (1999) IEEE Trans. Inf. Theory , vol.45 , Issue.3 , pp. 846-862
    • Timmermann, K.E.1    Nowak, R.D.2
  • 19
    • 0034246021 scopus 로고    scopus 로고
    • A statistical multiscale framework for Poisson inverse problems
    • Aug
    • R. D. Nowak and E. D. Kolaczyk, "A statistical multiscale framework for Poisson inverse problems," IEEE Trans. Inf. Theory, vol. 46, no. 8, pp. 1811-1825, Aug. 2000.
    • (2000) IEEE Trans. Inf. Theory , vol.46 , Issue.8 , pp. 1811-1825
    • Nowak, R.D.1    Kolaczyk, E.D.2
  • 20
    • 3142756370 scopus 로고    scopus 로고
    • A comparative simulation study of wavelet shrinkage estimators for Poisson counts
    • P. Besbeas, I. D. Feis, and T. Sapatinas, "A comparative simulation study of wavelet shrinkage estimators for Poisson counts," Int. Statist. Rev., vol. 72, no. 2, pp. 209-237, 2004.
    • (2004) Int. Statist. Rev , vol.72 , Issue.2 , pp. 209-237
    • Besbeas, P.1    Feis, I.D.2    Sapatinas, T.3
  • 21
    • 2142732992 scopus 로고    scopus 로고
    • Automatic smoothing with wavelets for a wide class of distributions
    • Jun
    • S. Sardy, A. Antoniadis, and P. Tseng, "Automatic smoothing with wavelets for a wide class of distributions," J. Comput. Graph. Statist., vol. 13, no. 2, pp. 399-421, Jun. 2004.
    • (2004) J. Comput. Graph. Statist , vol.13 , Issue.2 , pp. 399-421
    • Sardy, S.1    Antoniadis, A.2    Tseng, P.3
  • 22
    • 45949103558 scopus 로고    scopus 로고
    • R. M. Willett and R. D. Nowak, Fast, near-optimal, multiresolution estimation of Poisson signals and images, presented at the EUSIPCO, San Diego, CA, 2004.
    • R. M. Willett and R. D. Nowak, "Fast, near-optimal, multiresolution estimation of Poisson signals and images," presented at the EUSIPCO, San Diego, CA, 2004.
  • 23
    • 34547544849 scopus 로고    scopus 로고
    • Multiscale Poisson intensity and density estimation,
    • Tech. Rep, Duke Univ, Durham, NC
    • R. M. Willett and R. D. Nowak, "Multiscale Poisson intensity and density estimation," Tech. Rep., Duke Univ., Durham, NC, 2005.
    • (2005)
    • Willett, R.M.1    Nowak, R.D.2
  • 24
    • 78651561977 scopus 로고    scopus 로고
    • Multiscale analysis of photon-limited astronomical images
    • presented at the
    • R. Willett, "Multiscale analysis of photon-limited astronomical images," presented at the Statistical Challenges in Modern Astronomy IV, 2006.
    • (2006) Statistical Challenges in Modern Astronomy IV
    • Willett, R.1
  • 26
    • 0346727379 scopus 로고    scopus 로고
    • Ridgelets: The key to high dimensional intermittency?
    • E. Candès and D. Donoho, "Ridgelets: The key to high dimensional intermittency?," Philosoph. Trans. Roy. Soc. Lond. A, vol. 357, pp. 2495-2509, 1999.
    • (1999) Philosoph. Trans. Roy. Soc. Lond. A , vol.357 , pp. 2495-2509
    • Candès, E.1    Donoho, D.2
  • 27
    • 0003306887 scopus 로고    scopus 로고
    • Curvelets - A surprisingly effective nonadaptive representation for objects with edges
    • A. Cohen, C. Rabut, and L. Schumaker, Eds. Nashville, TN: Vanderbilt Univ. Press
    • E. J. Candès and D. L. Donoho, "Curvelets - A surprisingly effective nonadaptive representation for objects with edges," in Curve and Surface Fitting, A. Cohen, C. Rabut, and L. Schumaker, Eds. Nashville, TN: Vanderbilt Univ. Press, 1999.
    • (1999) Curve and Surface Fitting
    • Candès, E.J.1    Donoho, D.L.2
  • 28
    • 0036612499 scopus 로고    scopus 로고
    • The curvelet transform for image denoising
    • Jun
    • J.-L. Starck, E. Candès, and D. Donoho, "The curvelet transform for image denoising," IEEE Trans. Image Process., vol. 11, no. 6, pp. 131-141, Jun. 2002.
    • (2002) IEEE Trans. Image Process , vol.11 , Issue.6 , pp. 131-141
    • Starck, J.-L.1    Candès, E.2    Donoho, D.3
  • 29
    • 0001259658 scopus 로고
    • The stationary wavelet transform and some statistical applications
    • New York: Springer-Verlag
    • G. P. Nason and B. W. Silverman, "The stationary wavelet transform and some statistical applications," in Lecture Notes in Statistics. New York: Springer-Verlag, 1995, vol. 103, pp. 281-299.
    • (1995) Lecture Notes in Statistics , vol.103 , pp. 281-299
    • Nason, G.P.1    Silverman, B.W.2
  • 30
    • 0002001578 scopus 로고
    • Translation-invariant de-noising
    • New York: Springer-Verlag
    • R. R. Coifman and D. L. Donoho, "Translation-invariant de-noising," in Lecture Notes in Statistics. New York: Springer-Verlag, 1995, vol. 103, pp. 125-150.
    • (1995) Lecture Notes in Statistics , vol.103 , pp. 125-150
    • Coifman, R.R.1    Donoho, D.L.2
  • 32
    • 0026938667 scopus 로고
    • Discrete wavelet transforms: Wedding theà trous and mallat algorithms
    • Oct
    • M. J. Shensa, "Discrete wavelet transforms: Wedding theà trous and mallat algorithms," IEEE Trans. Signal Process., vol. 40, no. 10, pp. 2464-2482, Oct. 1992.
    • (1992) IEEE Trans. Signal Process , vol.40 , Issue.10 , pp. 2464-2482
    • Shensa, M.J.1
  • 33
    • 33847702157 scopus 로고    scopus 로고
    • The undecimated wavelet decomposition and its reconstruction
    • Feb
    • J.-L. Starck, M. Fadili, and F. Murtagh, "The undecimated wavelet decomposition and its reconstruction," IEEE Trans. Image Process. vol. 16, no. 2, pp. 297-309, Feb. 2007.
    • (2007) IEEE Trans. Image Process , vol.16 , Issue.2 , pp. 297-309
    • Starck, J.-L.1    Fadili, M.2    Murtagh, F.3
  • 34
    • 0036721668 scopus 로고    scopus 로고
    • Extraction of spots in biological images using multiscale products
    • J. C. Olivo-Marin, "Extraction of spots in biological images using multiscale products," Pattern Recognit., vol. 35, no. 9, pp. 1989-1996, 2002.
    • (2002) Pattern Recognit , vol.35 , Issue.9 , pp. 1989-1996
    • Olivo-Marin, J.C.1
  • 35
    • 0012780893 scopus 로고    scopus 로고
    • Wavelet estimators in nonparametric regression: A comparative simulation study
    • A. Antoniadis, J. Bigot, and T. Sapatinas, "Wavelet estimators in nonparametric regression: A comparative simulation study," J. Statist. Softw., vol. 6, no. 6, 2001.
    • (2001) J. Statist. Softw , vol.6 , Issue.6
    • Antoniadis, A.1    Bigot, J.2    Sapatinas, T.3
  • 36
    • 0001677717 scopus 로고
    • Controlling the false discovery rate: A practical and powerful approach to multiple testing
    • Y. Benjamini and Y. Hochberg, "Controlling the false discovery rate: A practical and powerful approach to multiple testing," J. Roy. Statist. Soc. B, vol. 57, no. 1, pp. 289-300, 1995.
    • (1995) J. Roy. Statist. Soc. B , vol.57 , Issue.1 , pp. 289-300
    • Benjamini, Y.1    Hochberg, Y.2
  • 37
    • 0035733108 scopus 로고    scopus 로고
    • The control of the false discovery rate in multiple testing under dependency
    • Y. Benjamini and Y. Yekutieli, "The control of the false discovery rate in multiple testing under dependency," Ann. Statist., vol. 29, no. 4, pp. 1165-1188, 2001.
    • (2001) Ann. Statist , vol.29 , Issue.4 , pp. 1165-1188
    • Benjamini, Y.1    Yekutieli, Y.2
  • 38
    • 33746242092 scopus 로고    scopus 로고
    • Adapting to unknown sparsity by controlling the false discovery rate
    • F. Abramovich, Y. Benjamini, D. Donoho, and I. Johnstone, "Adapting to unknown sparsity by controlling the false discovery rate," Ann. Statist., vol. 34, no. 2, pp. 584-653, 2006.
    • (2006) Ann. Statist , vol.34 , Issue.2 , pp. 584-653
    • Abramovich, F.1    Benjamini, Y.2    Donoho, D.3    Johnstone, I.4
  • 39
    • 34547291918 scopus 로고    scopus 로고
    • Asymptotic minimaxity of false discovery rate thresholding for sparse exponential data
    • D. L. Donoho and J. Jin, "Asymptotic minimaxity of false discovery rate thresholding for sparse exponential data," Ann. Statist., vol. 34, no. 6, pp. 2980-3018, 2006.
    • (2006) Ann. Statist , vol.34 , Issue.6 , pp. 2980-3018
    • Donoho, D.L.1    Jin, J.2
  • 40
    • 0029502270 scopus 로고
    • Multiresolution support applied to image filtering and deconvolution
    • Sep
    • J. L. Starck, A. Bijaoui, and F. Murtagh, "Multiresolution support applied to image filtering and deconvolution," CVIP: Graphical Models and Image Processing, vol. 57, no. 5, pp. 420-431, Sep. 1995.
    • (1995) CVIP: Graphical Models and Image Processing , vol.57 , Issue.5 , pp. 420-431
    • Starck, J.L.1    Bijaoui, A.2    Murtagh, F.3
  • 41
    • 0037418225 scopus 로고    scopus 로고
    • 1 minimization
    • 1 minimization," PNAS, vol. 100, no. 5, pp. 2197-2202, 2003.
    • (2003) PNAS , vol.100 , Issue.5 , pp. 2197-2202
    • Donoho, D.L.1    Elad, M.2
  • 42
    • 33646365077 scopus 로고    scopus 로고
    • 1 -norm solution is also the sparsest solution
    • 1 -norm solution is also the sparsest solution," Commun. Pure Appl. Math., vol. 59, no. 6, pp. 797-829, 2006.
    • (2006) Commun. Pure Appl. Math , vol.59 , Issue.6 , pp. 797-829
    • Donoho, D.L.1
  • 43
    • 0000769685 scopus 로고    scopus 로고
    • The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings
    • New York: Elsevier
    • I. Yamada, "The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings," in Inherently Parallel Algorithm in Feasibility and Optimization and their Applications. New York: Elsevier, 2001.
    • (2001) Inherently Parallel Algorithm in Feasibility and Optimization and their Applications
    • Yamada, I.1
  • 44
    • 34247535092 scopus 로고    scopus 로고
    • Gaussian approximations of fluorescence microscope point-spread function models
    • B. Zhang, J. Zerubia, and J.-C. Olivo-Marin, "Gaussian approximations of fluorescence microscope point-spread function models," Appl. Opt. vol. 46, no. 10, pp. 1819-1829, 2007.
    • (2007) Appl. Opt , vol.46 , Issue.10 , pp. 1819-1829
    • Zhang, B.1    Zerubia, J.2    Olivo-Marin, J.-C.3
  • 45
    • 0038321621 scopus 로고    scopus 로고
    • Platelets: A multiscale approach for recovering edges and surfaces in photon-limited medical imaging
    • Mar
    • R. M. Willett and R. D. Nowak, "Platelets: A multiscale approach for recovering edges and surfaces in photon-limited medical imaging," IEEE Trans. Med. Imag., vol. 22, no. 3, pp. 332-350, Mar. 2003.
    • (2003) IEEE Trans. Med. Imag , vol.22 , Issue.3 , pp. 332-350
    • Willett, R.M.1    Nowak, R.D.2
  • 46
    • 3142656055 scopus 로고    scopus 로고
    • Redundant multiscale transforms and their application for morphological component analysis
    • J.-L. Starck, M. Elad, and D. Donoho, "Redundant multiscale transforms and their application for morphological component analysis," Adv. Imag. Electron. Phys., vol. 132, 2004.
    • (2004) Adv. Imag. Electron. Phys , vol.132
    • Starck, J.-L.1    Elad, M.2    Donoho, D.3
  • 47
    • 45949103389 scopus 로고    scopus 로고
    • Fast Slant Stack: A notion of Radon transform for data in a cartesian grid which is rapidly computible, algebraically exact, geometrically faithful and invertible
    • to be published
    • A. Averbuch, R. R. Coifman, D. L. Donoho, M. Israeli, and J.Waldén, "Fast Slant Stack: A notion of Radon transform for data in a cartesian grid which is rapidly computible, algebraically exact, geometrically faithful and invertible," SIAM J. Sci. Comput., 2001, to be published.
    • (2001) SIAM J. Sci. Comput
    • Averbuch, A.1    Coifman, R.R.2    Donoho, D.L.3    Israeli, M.4    Waldén, J.5
  • 48
    • 20444478110 scopus 로고    scopus 로고
    • Digital ridgelet transform based on true ridge functions
    • J. Schmeidler and G. Well, Eds. New York: Academic
    • D. Donoho and A. G. Flesia, "Digital ridgelet transform based on true ridge functions," in Beyond Wavelets, J. Schmeidler and G. Well, Eds. New York: Academic, 2002.
    • (2002) Beyond Wavelets
    • Donoho, D.1    Flesia, A.G.2
  • 49
    • 0033716552 scopus 로고    scopus 로고
    • Digital curvelet transform: Strategy, implementation and experiments
    • H. H. Szu, M. Vetterli, W. Campbell, and J. R. Buss, Eds
    • D. L. Donoho and M. R. Duncan, "Digital curvelet transform: Strategy, implementation and experiments," in Proc. Aerosense, Wavelet Applications VII, H. H. Szu, M. Vetterli, W. Campbell, and J. R. Buss, Eds., vol. 4056, pp. 12-29.
    • Proc. Aerosense, Wavelet Applications VII , vol.4056 , pp. 12-29
    • Donoho, D.L.1    Duncan, M.R.2
  • 50
    • 0037316980 scopus 로고    scopus 로고
    • Astronomical image representation by the curvelet tansform
    • J.-L. Starck, E. Candes, and D. Donoho, "Astronomical image representation by the curvelet tansform," Astron. Astrophysics, vol. 398, pp. 785-800, 2003.
    • (2003) Astron. Astrophysics , vol.398 , pp. 785-800
    • Starck, J.-L.1    Candes, E.2    Donoho, D.3
  • 52
    • 35148877210 scopus 로고    scopus 로고
    • Wave atoms and sparsity of oscillatory patterns
    • to be published
    • L. Demanet and L. Ying, "Wave atoms and sparsity of oscillatory patterns," Appl. Comput. Harmon. Anal, 2007, to be published.
    • (2007) Appl. Comput. Harmon. Anal
    • Demanet, L.1    Ying, L.2
  • 53
    • 0035767715 scopus 로고    scopus 로고
    • Very high quality image restoration by combining wavelets and curvelets
    • Dec
    • J. L. Starck, "Very high quality image restoration by combining wavelets and curvelets," Proc. SPIE, vol. 4478, pp. 9-19, Dec. 2001.
    • (2001) Proc. SPIE , vol.4478 , pp. 9-19
    • Starck, J.L.1
  • 56
    • 0030246542 scopus 로고    scopus 로고
    • On projection algorithms for solving convex feasibility problems
    • H. H. Bauschke and J. M. Borwein, "On projection algorithms for solving convex feasibility problems," SIAM Rev., vol. 38, no. 3, pp. 367-426, 1996.
    • (1996) SIAM Rev , vol.38 , Issue.3 , pp. 367-426
    • Bauschke, H.H.1    Borwein, J.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.