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Volumn 46, Issue 5, 2000, Pages 1811-1825

A Statistical Multiscale Framework for Poisson Inverse Problems

Author keywords

Imaging; Inverse problems; Multiscale analysis; Poisson processes

Indexed keywords

ALGORITHMS; COMPUTERIZED TOMOGRAPHY; CONVERGENCE OF NUMERICAL METHODS; INVERSE PROBLEMS; MATHEMATICAL MODELS; MATRIX ALGEBRA; MAXIMUM LIKELIHOOD ESTIMATION; POISSON DISTRIBUTION; SPECTRUM ANALYSIS; STATISTICAL METHODS;

EID: 0034246021     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.857793     Document Type: Article
Times cited : (122)

References (56)
  • 2
    • 0020194763 scopus 로고    scopus 로고
    • Maximum likelihood reconstruction for emission tomography
    • 113-122, Jan. 1982
    • L. A. Shepp and Y. Vardi, "Maximum likelihood reconstruction for emission tomography," IEEE Trans. Med. Imag., pp. 113-122, Jan. 1982.
    • IEEE Trans. Med. Imag., Pp.
    • Shepp, L.A.1    Vardi, Y.2
  • 3
    • 84972545853 scopus 로고    scopus 로고
    • A statistical perspective on ill-posed inverse problems
    • vol. 1, no. 4, pp. 502-527, 1986
    • F. O'Sullivan, "A statistical perspective on ill-posed inverse problems," Statist. Sei., vol. 1, no. 4, pp. 502-527, 1986.
    • Statist. Sei.
    • O'Sullivan, F.1
  • 5
    • 0041958932 scopus 로고    scopus 로고
    • Ideal adaptation via wavelet shrinkage
    • vol. 81, pp. 425-455, 1994
    • D. Donoho and I. Johnstone, "Ideal adaptation via wavelet shrinkage," Biometrika, vol. 81, pp. 425-455, 1994.
    • Biometrika
    • Donoho, D.1    Johnstone, I.2
  • 6
    • 0032628620 scopus 로고    scopus 로고
    • Multiscale modeling and estimation of Poisson processes with application to photon-limited imaging
    • vol. 45, pp. 846-862, Apr. 1999
    • K. Timmermann and R. Nowak, "Multiscale modeling and estimation of Poisson processes with application to photon-limited imaging," IEEE Trans. Inform. Theory, vol. 45, pp. 846-862, Apr. 1999.
    • IEEE Trans. Inform. Theory
    • Timmermann, K.1    Nowak, R.2
  • 7
    • 0032628798 scopus 로고    scopus 로고
    • Minmax description length for signal denoising and optimal representation
    • vol. 45, pp. 898-908, Apr. 1999
    • H. Krim and I. Schick, "Minmax description length for signal denoising and optimal representation," IEEE Trans. Inform. Theory, vol. 45, pp. 898-908, Apr. 1999.
    • IEEE Trans. Inform. Theory
    • Krim, H.1    Schick, I.2
  • 11
    • 0029288068 scopus 로고    scopus 로고
    • Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition
    • vol. 2, pp. 101-126, 1995
    • D. L. Donoho, "Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition," Appl. and Comput. Harmonic Anal., vol. 2, pp. 101-126, 1995.
    • Appl. and Comput. Harmonic Anal.
    • Donoho, D.L.1
  • 12
    • 0000521350 scopus 로고    scopus 로고
    • Wavelet decomposition approaches to statistical inverse problems
    • vol. 85, pp. 115-129, 1998
    • F. Abramovich and B. W. Silverman, "Wavelet decomposition approaches to statistical inverse problems," Biometrika, vol. 85, pp. 115-129, 1998.
    • Biometrika
    • Abramovich, F.1    Silverman, B.W.2
  • 13
    • 0030126684 scopus 로고    scopus 로고
    • Spatially adaptive wavelet-based multiscale image restoration
    • vol. 5, pp. 619-634, Apr. 1996
    • M. R. Banham and A. K. Katsaggelos, "Spatially adaptive wavelet-based multiscale image restoration," IEEE Trans. Image Processing, vol. 5, pp. 619-634, Apr. 1996.
    • IEEE Trans. Image Processing
    • Banham, M.R.1    Katsaggelos, A.K.2
  • 14
    • 0029306397 scopus 로고    scopus 로고
    • Solution of inverse problem in image processing by wavelet expansion
    • vol. 4, pp. 579-593, May 1995
    • J. Z. G. Wang and G.-W. Pan, "Solution of inverse problem in image processing by wavelet expansion," IEEE Trans. Image Processing, vol. 4, pp. 579-593, May 1995.
    • IEEE Trans. Image Processing
    • Wang, J.Z.G.1    Pan, G.-W.2
  • 15
    • 0030327273 scopus 로고    scopus 로고
    • A wavelet shrinkage approach to tomographic image reconstruction
    • vol. 91, pp. 1079-1990, 1996
    • E. Kolaczyk, "A wavelet shrinkage approach to tomographic image reconstruction," J. Amer. Statist. Assoc., vol. 91, pp. 1079-1990, 1996.
    • J. Amer. Statist. Assoc.
    • Kolaczyk, E.1
  • 21
    • 0010293907 scopus 로고    scopus 로고
    • A statistical model for positron emission tomography
    • vol. 80, pp. 8-37, 1985
    • Y Vardi, L. A. Shepp, and L. Kaufman, "A statistical model for positron emission tomography," J. Amer. Statist. Assoc., vol. 80, pp. 8-37, 1985.
    • J. Amer. Statist. Assoc.
    • Vardi, Y.1    Shepp, L.A.2    Kaufman, L.3
  • 22
    • 0024683826 scopus 로고    scopus 로고
    • Feasible images and practical stopping rules for iterative algorithms in emission tomography
    • vol. 8, pp. 186-193, 1989
    • J. Llacer and E. Veklerov, "Feasible images and practical stopping rules for iterative algorithms in emission tomography," IEEE Trans. Med. Imag., vol. 8, pp. 186-193, 1989.
    • IEEE Trans. Med. Imag.
    • Llacer, J.1    Veklerov, E.2
  • 23
    • 0023363121 scopus 로고    scopus 로고
    • A theoretical study of some maximum likelihood algorithms for emission and transmission tomography
    • vol. 6, pp. 106-114, 1987
    • K. Lange, M. Bahn, and R. Little, "A theoretical study of some maximum likelihood algorithms for emission and transmission tomography," IEEE Trans. Med. Imag., vol. 6, pp. 106-114, 1987.
    • IEEE Trans. Med. Imag.
    • Lange, K.1    Bahn, M.2    Little, R.3
  • 24
    • 0024681039 scopus 로고    scopus 로고
    • A generalized em algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors
    • vol. 8, pp. 194-202, Feb. 1989
    • T. Hebert and R. Leahy, "A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors," IEEE Trans. Med. Imag., vol. 8, pp. 194-202, Feb. 1989.
    • IEEE Trans. Med. Imag.
    • Hebert, T.1    Leahy, R.2
  • 25
    • 0025404969 scopus 로고    scopus 로고
    • Bayesian reconstruction from emission tomography data using a modified em algorithm
    • vol. 9, pp. 84-93, Jan. 1990
    • P. J. Green, "Bayesian reconstruction from emission tomography data using a modified EM algorithm," IEEE Trans. Med. Imag., vol. 9, pp. 84-93, Jan. 1990.
    • IEEE Trans. Med. Imag.
    • Green, P.J.1
  • 26
    • 0029392038 scopus 로고    scopus 로고
    • Penalized maximum-likelihood image reconstruction using space-alternating generalized em algorithms
    • vol. 4, pp. 1417-1429, Oct. 1995
    • J. A. Fessier and A. O. Hero, "Penalized maximum-likelihood image reconstruction using space-alternating generalized EM algorithms," IEEE Trans. Image Processing, vol. 4, pp. 1417-1429, Oct. 1995.
    • IEEE Trans. Image Processing
    • Fessier, J.A.1    Hero, A.O.2
  • 27
    • 33747159565 scopus 로고    scopus 로고
    • A unified approach to statistical tomography
    • vol. 5, pp. 480192, 1996
    • C. A. Bouman and K. Sauer, "A unified approach to statistical tomography," IEEE Trans. Image Processing, vol. 5, pp. 480192, 1996.
    • IEEE Trans. Image Processing
    • Bouman, C.A.1    Sauer, K.2
  • 28
    • 0026870457 scopus 로고    scopus 로고
    • Simulation evaluation of Gibbs prior distributions for use in maximum a posteriori SPECT reconstructions
    • vol. 11, pp. 267-275, 1992
    • D. S. Lalush and B. M. W. Tsui, "Simulation evaluation of Gibbs prior distributions for use in maximum a posteriori SPECT reconstructions," IEEE Trans. Med. Imag., vol. 11, pp. 267-275, 1992.
    • IEEE Trans. Med. Imag.
    • Lalush, D.S.1    Tsui, B.M.W.2
  • 29
    • 0030081110 scopus 로고    scopus 로고
    • A wavelet-based method for multiscale tomographic reconstruction
    • vol. 15, pp. 92-101, Jan. 1996
    • M. Bhatia, W. C. Karl, and A. S. Willsky, "A wavelet-based method for multiscale tomographic reconstruction," IEEE Trans. Med. Imag., vol. 15, pp. 92-101, Jan. 1996.
    • IEEE Trans. Med. Imag.
    • Bhatia, M.1    Karl, W.C.2    Willsky, A.S.3
  • 30
    • 0029324960 scopus 로고    scopus 로고
    • Multiresolution tomographic reconstruction using wavelets
    • vol. 4, pp. 799-813, 1995
    • A. H. Delaney and Y. Bresler, "Multiresolution tomographic reconstruction using wavelets," IEEE Trans. Image Processing, vol. 4, pp. 799-813, 1995.
    • IEEE Trans. Image Processing
    • Delaney, A.H.1    Bresler, Y.2
  • 32
    • 0033410025 scopus 로고    scopus 로고
    • Wavelet shrinkage estimation of certain Poisson intensity signals using corrected thresholds
    • vol. 9, pp. 119-135, 1999
    • E. D. Kolaczyk, "Wavelet shrinkage estimation of certain Poisson intensity signals using corrected thresholds," Statist. Sinica, vol. 9, pp. 119-135, 1999.
    • Statist. Sinica
    • Kolaczyk, E.D.1
  • 33
    • 0032634507 scopus 로고    scopus 로고
    • Wavelet-based filtering for photon imaging systems
    • vol. 8, pp. 666-678, May 1999
    • R. D. Nowak and R. G. Baraniuk, "Wavelet-based filtering for photon imaging systems," IEEE Trans. Image Processing, vol. 8, pp. 666-678, May 1999.
    • IEEE Trans. Image Processing
    • Nowak, R.D.1    Baraniuk, R.G.2
  • 34
    • 0032269963 scopus 로고    scopus 로고
    • A multiscale MAP estimation method for Poisson inverse problems
    • 32nd Asilomar Conf. Signals, Systems, and Comp. Pacific Grove, CA: IEEE Computer Soc. Press, 1998, pp. 1682-1686
    • R. Nowak and E. Kolaczyk, "A multiscale MAP estimation method for Poisson inverse problems," in P roc. 32nd Asilomar Conf. Signals, Systems, and Comp. Pacific Grove, CA: IEEE Computer Soc. Press, 1998, pp. 1682-1686.
    • P Roc.
    • Nowak, R.1    Kolaczyk, E.2
  • 39
    • 21144483382 scopus 로고    scopus 로고
    • Polya trees and random distributions, A
    • vol. 20, pp. 1203-1221, 1992
    • R. D. Mauldin, W. D. Sudderth, and S. C. Williams, "Polya trees and random distributions," A. Statist., vol. 20, pp. 1203-1221, 1992.
    • Statist.
    • Mauldin, R.D.1    Sudderth, W.D.2    Williams, S.C.3
  • 40
    • 21144477858 scopus 로고    scopus 로고
    • Some aspects of Polya tree distributions for statistical modeling, A
    • vol. 20, pp. 1222-1235, 1992
    • M. Lavine, "Some aspects of Polya tree distributions for statistical modeling," A. Statist., vol. 20, pp. 1222-1235, 1992.
    • Statist.
    • Lavine, M.1
  • 41
    • 0029267626 scopus 로고    scopus 로고
    • A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography
    • 132-137, 1995
    • A. R. Depierro, "A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography," IEEE Trans. Med. Imag., pp. 132-137, 1995.
    • IEEE Trans. Med. Imag., Pp.
    • Depierro, A.R.1
  • 42
    • 0021327145 scopus 로고    scopus 로고
    • EM reconstruction algorithms for emission and transmission tomography
    • vol. 8, pp. 302-316, 1984
    • K. Lange and R. Carson, "EM reconstruction algorithms for emission and transmission tomography," J. Comp. Assist. Tomogr., vol. 8, pp. 302-316, 1984.
    • J. Comp. Assist. Tomogr.
    • Lange, K.1    Carson, R.2
  • 43
    • 0021393382 scopus 로고    scopus 로고
    • An algorithm for maximizing expected log investment return
    • 30, pp. 369-373, Mar. 1984
    • T. M. Cover, "An algorithm for maximizing expected log investment return," IEEE Trans. Inform. Theory, vol. IT-30, pp. 369-373, Mar. 1984.
    • IEEE Trans. Inform. Theory, Vol. IT
    • Cover, T.M.1
  • 44
    • 0025587714 scopus 로고    scopus 로고
    • Convergence of em image reconstruction algorithm with Gibbs smoothing
    • vol. 9, pp. 439446, 1990
    • K. Lange, "Convergence of em image reconstruction algorithm with Gibbs smoothing," IEEE Trans. Med. Imag., vol. 9, pp. 439446, 1990.
    • IEEE Trans. Med. Imag.
    • Lange, K.1
  • 46
    • 0002210265 scopus 로고    scopus 로고
    • On the convergence properties of the em algorithm
    • vol. 11, pp. 95-103, 1984
    • C. F. J. Wu, "On the convergence properties of the EM algorithm," Ann. Statist., vol. 11, pp. 95-103, 1984.
    • Ann. Statist.
    • Wu, C.F.J.1
  • 48
    • 0030247744 scopus 로고    scopus 로고
    • Modeling the power spectra of natural images
    • vol. 36, no. 17, pp. 2759-2770, 1996
    • A. van der Schaaf and J. van Hateren, "Modeling the power spectra of natural images," Vision Res., vol. 36, no. 17, pp. 2759-2770, 1996.
    • Vision Res.
    • Van Der Schaaf, A.1    Van Hateren, J.2
  • 49
    • 0001693735 scopus 로고    scopus 로고
    • -Solar abundances from gamma-ray spectroscopyComparisons with energetic particle, photospheric, and coronal abundances,Astrophys
    • vol. 371, pp. 793-803, 1991
    • R. J. Murphy, R. Ramaty, D. V. Reames, and B. Kozlovsky, "-Solar abundances from gamma-ray spectroscopyComparisons with energetic particle, photospheric, and coronal abundances,"Astrophys. J., vol. 371, pp. 793-803, 1991.
    • J.
    • Murphy, R.J.1    Ramaty, R.2    Reames, D.V.3    Kozlovsky, B.4
  • 50
    • 12044250116 scopus 로고    scopus 로고
    • Instrument description and performance of the imaging gamma-ray telescope COMPTEE aboard the compton gamma-ray observatory, Astrophys. J., Suppl. ser
    • vol. 86, pp. 657-692, 1993
    • V. Schoenfelder et al, "Instrument description and performance of the imaging gamma-ray telescope COMPTEE aboard the compton gamma-ray observatory," Astrophys. J., Suppl. Ser, vol. 86, pp. 657-692, 1993.
    • Et Al
    • Schoenfelder, V.1
  • 54
    • 0028517016 scopus 로고    scopus 로고
    • Space alternating generalized expectationmaximization algorithm
    • vol. 42, pp. 2664-2677, Oct. 1994
    • J. A. Fessier and A. O. Hero, "Space alternating generalized expectationmaximization algorithm," IEEE Trans. Signal Processing, vol. 42, pp. 2664-2677, Oct. 1994.
    • IEEE Trans. Signal Processing
    • Fessier, J.A.1    Hero, A.O.2
  • 55
    • 0028700063 scopus 로고    scopus 로고
    • Accelerated image reconstruction using ordered subsets of projection data
    • vol. 13, pp. 601-609, 1994
    • H. M. Hudson and R. S. Earkin, "Accelerated image reconstruction using ordered subsets of projection data," IEEE Trans. Med. Imag., vol. 13, pp. 601-609, 1994.
    • IEEE Trans. Med. Imag.
    • Hudson, H.M.1    Earkin, R.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.