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Volumn 2, Issue 2, 1995, Pages 101-126

Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; ITERATIVE METHODS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; WAVELET TRANSFORMS;

EID: 0029288068     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1006/acha.1995.1008     Document Type: Article
Times cited : (515)

References (61)
  • 1
    • 0037907127 scopus 로고
    • On the use of linear functionals for Abel-type integral equations in applications
    • R. S. Anderssen, F. De Hoog, andM. A. Lukas, Eds.), Sijthoff and Noordhof, the Netherlands
    • R. S. Anderssen, On the use of linear functionals for Abel-type integral equations in applications, in ‘The Application and Numerical Solution of Integral Equations” (R. S. Anderssen, F. De Hoog, andM. A. Lukas, Eds.), Sijthoff and Noordhof, the Netherlands, 1980.
    • (1980) The Application and Numerical Solution of Integral Equations
    • Anderssen, R.S.1
  • 4
    • 0002121183 scopus 로고
    • On the recovery and resolutionof exponential relaxation rates from experimental data: A singularvalue analysis of the Laplace transform inversion in the presence ofnoise
    • M. Bertero, P. Bocacci, and E. R. Pike, On the recovery and resolutionof exponential relaxation rates from experimental data: A singularvalue analysis of the Laplace transform inversion in the presence ofnoise, Proc. Roy. Soc. London Ser. A 383 (1982), 15-29.
    • (1982) Proc. Roy. Soc. London Ser. A , vol.383 , pp. 15-29
    • Bertero, M.1    Bocacci, P.2    Pike, E.R.3
  • 5
    • 0024945384 scopus 로고
    • Computation of the singular system for a class of integral operators related to data inversion in confocalmicroscopy
    • M. Bertero and P. Bocacci, Computation of the singular system for a class of integral operators related to data inversion in confocalmicroscopy, Inverse Problems 5 (1989), 935-957.
    • (1989) Inverse Problems , vol.5 , pp. 935-957
    • Bertero, M.1    Bocacci, P.2
  • 6
    • 0001176372 scopus 로고
    • Linear inverse problems with discrete data. I. General formulation and singular system analysis
    • M. Bertero, C. De Mol, and E. R. Pike, Linear inverse problems with discrete data. I. General formulation and singular system analysis, Inverse Problems 1 (1985), 301-330.
    • (1985) Inverse Problems , vol.1 , pp. 301-330
    • Bertero, M.1    De Mol, C.2    Pike, E.R.3
  • 7
    • 0000738186 scopus 로고
    • Particle size distributions from spectral turbidity: A singular system analysis
    • M. Bertero, C. De Mol, and E. R. Pike, Particle size distributions from spectral turbidity: A singular system analysis, Inverse Problems2 (1986), 301-330.
    • (1986) Inverse Problems , vol.2 , pp. 301-330
    • Bertero, M.1    De Mol, C.2    Pike, E.R.3
  • 8
    • 0542442326 scopus 로고
    • Intensity fluctuation distributions from photon counting distributions: A singular-system analysis of Poissontransform inversion
    • M. Bertero and E. R. Pike, Intensity fluctuation distributions from photon counting distributions: A singular-system analysis of Poissontransform inversion. Inverse Problems 2 (1986), 259-269.
    • (1986) Inverse Problems , vol.2 , pp. 259-269
    • Bertero, M.1    Pike, E.R.2
  • 9
    • 84983618206 scopus 로고    scopus 로고
    • Asymptotic equivalence of nonpara-metric regression and white noise
    • L. D. Brown and M. G. Low, Asymptotic equivalence of nonpara-metric regression and white noise, Ann. Statist., to appear.
    • Ann. Statist
    • Brown, L.D.1    Low, M.G.2
  • 10
    • 0027809451 scopus 로고
    • Bessel sequences and affine frames
    • C. K. Chui and X. Shi, Bessel sequences and affine frames, Appl.Comput. Harmonic Anal. 1 (1993), 29-50.
    • (1993) Appl.Comput. Harmonic Anal , vol.1 , pp. 29-50
    • Chui, C.K.1    Shi, X.2
  • 11
    • 0002118102 scopus 로고
    • Nonseparable bidimensional wavelet bases
    • A. Cohen and I. Daubechies, Nonseparable bidimensional wavelet bases. Rev. Mat. Iberoamericana, 9 (1993), 51-137.
    • (1993) Rev. Mat. Iberoamericana , vol.9 , pp. 51-137
    • Cohen, A.1    Daubechies, I.2
  • 12
  • 13
    • 84990575058 scopus 로고
    • Orthonormal bases of compactly supported wavelets
    • I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41 (1988), 909-996.
    • (1988) Comm. Pure Appl. Math , vol.41 , pp. 909-996
    • Daubechies, I.1
  • 14
    • 84983611262 scopus 로고
    • Two recent developments: Wavelets on the interval and biorthogonal decompositions of the differentiation operator
    • L. Schumaker and G. Webb, Eds.), Academic Press, New York
    • I. Daubechies, Two recent developments: Wavelets on the interval and biorthogonal decompositions of the differentiation operator, in"Recent Advances in Wavelet Analysis" (L. Schumaker and G. Webb, Eds.), Academic Press, New York, 1993.
    • (1993) Recent Advances in Wavelet Analysis
    • Daubechies, I.1
  • 15
    • 0019714329 scopus 로고
    • A singular value decomposition for the Radon transform in «-dimensional space
    • M. E. Davisson, A singular value decomposition for the Radon transform in «-dimensional space, Numer. Fund. Anal. Optim. 3 (1981), 321.
    • (1981) Numer. Fund. Anal. Optim , vol.3 , pp. 321
    • Davisson, M.E.1
  • 19
    • 0027873602 scopus 로고
    • Unconditional bases are optimal bases for data compression and statistical estimation
    • D. L. Donoho, Unconditional bases are optimal bases for data compression and statistical estimation, Appl. Comput. Harmonic Anal. 1 (1993), 100-115.
    • (1993) Appl. Comput. Harmonic Anal , vol.1 , pp. 100-115
    • Donoho, D.L.1
  • 20
    • 0002463284 scopus 로고    scopus 로고
    • Wavelet shrinkage and W.V.D-A ten minute tour
    • Y. Meyer and S. Roques, EdsÉditions Frontières, Gif-sur-Yvette
    • D. L. Donoho, Wavelet shrinkage and W.V.D-A ten minute tour, in “Progress in Wavelet Analysis and Applications” (Y. Meyer and S. Roques, Eds.), Éditions Frontières, Gif-sur-Yvette, 1993.
    • Progress in Wavelet Analysis and Applications , pp. 1993
    • Donoho, D.L.1
  • 21
    • 0000370306 scopus 로고
    • Nonlinear wavelet methods for recovery of signals, images, and densities from incomplete and noisy data
    • I. Daub, Ed.), Providence, RI
    • D. L. Donoho, Nonlinear wavelet methods for recovery of signals, images, and densities from incomplete and noisy data, in “DifferentPerspectives on Wavelets” (I. Daubechies, Ed.), Amer. Math. Soc., Providence, RI, 1993.
    • (1993) DifferentPerspectives on Wavelets
    • Donoho, D.L.1
  • 23
  • 24
    • 0001014229 scopus 로고
    • Minimax risk over hyperrectangles, and implications
    • D. L. Donoho, R. C. Liu, and K. B. MacGibbon, Minimax risk over hyperrectangles, and implications, Ann. Statist. 18(1990), 1416-1437.
    • (1990) Ann. Statist , vol.18 , pp. 1416-1437
    • Donoho, D.L.1    Liu, R.C.2    Macgibbon, K.B.3
  • 25
    • 38249016845 scopus 로고
    • Minimax quadratic estimation of aquadratic functional
    • D. L. Donoho and M. Nussbaum, Minimax quadratic estimation of aquadratic functional, J. Complexity 6 (1990), 290-323.
    • (1990) J. Complexity , vol.6 , pp. 290-323
    • Donoho, D.L.1    Nussbaum, M.2
  • 26
    • 0001573354 scopus 로고
    • Renormalization exponents and optimal pointwise rates of convergence
    • D. L. Donoho and M. G. Low, Renormalization exponents and optimal pointwise rates of convergence, Ann. Statist. 20 (1992), 944-970.
    • (1992) Ann. Statist , vol.20 , pp. 944-970
    • Donoho, D.L.1    Low, M.G.2
  • 28
    • 0039626258 scopus 로고
    • Estimation of square-integrable [spectral] density based on a sequence of observations
    • Russian]; Problems Inform. Transmission 17 (1982), 182-196 [in English]
    • S. Y. Efroimovich and M. S. Pinsker, Estimation of square-integrable [spectral] density based on a sequence of observations, ProblemyPeredatsii Informats 2 17 (1981), 50-68; Problems Inform. Transmission 17 (1982), 182-196 [in English].
    • (1981) ProblemyPeredatsii Informats , vol.2 , Issue.17 , pp. 50-68
    • Efroimovich, S.Y.1    Pinsker, M.S.2
  • 29
    • 0009407925 scopus 로고
    • Estimation of square-integrable probability density of a random variable
    • Problems Inform. Transmission18 (1983), 175-189 [in English]
    • S. Y. Efroimovich and M. S. Pinsker, Estimation of square-integrable probability density of a random variable, Problemy Peredatsii Informats 2 18 (1983), 19-38; Problems Inform. Transmission18 (1983), 175-189 [in English]
    • (1983) Problemy Peredatsii Informats , vol.2 , Issue.18 , pp. 19-38
    • Efroimovich, S.Y.1    Pinsker, M.S.2
  • 30
  • 31
    • 0002319407 scopus 로고
    • A discrete transform and decomposition of distribution spaces
    • M. Frazier and B. Jawerth, A discrete transform and decomposition of distribution spaces, J. Fund. Anal. 93 (1990), 34-170.
    • (1990) J. Fund. Anal , vol.93 , pp. 34-170
    • Frazier, M.1    Jawerth, B.2
  • 32
    • 0003292476 scopus 로고
    • Littlewood-Paley Theory and the Study of Function Spaces
    • American Math. Soc., Providence, RI
    • M. Frazier, B. Jawerth, and G. Weiss, "Littlewood-Paley Theory and the Study of Function Spaces,” NSF-CBMS Regional ConferenceSeries in Mathematics, Vol. 79, American Math. Soc., Providence, RI, 1991.
    • (1991) NSF-CBMS Regional ConferenceSeries in Mathematics , vol.79
    • Frazier, M.1    Jawerth, B.2    Weiss, G.3
  • 33
    • 0001068070 scopus 로고
    • A method of adjoints for solving some ill-posed equations of the first kind
    • M. Golberg, A method of adjoints for solving some ill-posed equations of the first kind, Appl. Math. Comput. 5 (1979), 123-130.
    • (1979) Appl. Math. Comput , vol.5 , pp. 123-130
    • Golberg, M.1
  • 34
    • 16244404147 scopus 로고
    • Signal restoration for linear systems withweighted impulse; Singular value analysis for two cases of low-passfiltering
    • F. Gori and G. Guattari, Signal restoration for linear systems withweighted impulse; Singular value analysis for two cases of low-passfiltering, Inverse Problems 1 (1985), 67.
    • (1985) Inverse Problems , vol.1 , pp. 67
    • Gori, F.1    Guattari, G.2
  • 35
    • 0002282584 scopus 로고
    • Nonparametric estimation ofthe value of a linear functional in a Gaussian white noise
    • I. A. Ibragimov and R. Z. Has’minskii, Nonparametric estimation ofthe value of a linear functional in a Gaussian white noise, TheoryProbab. Appl. 29 (1984), 1-17.
    • (1984) TheoryProbab. Appl , vol.29 , pp. 1-17
    • Ibragimov, I.A.1    Has’Minskii, R.Z.2
  • 36
    • 0000263131 scopus 로고
    • Density estimationusing wavelets: Comparison between linear and nonlinear methods
    • I. M. Johnstone, G. Kerkyacharian, and D. Picard, Density estimationusing wavelets: Comparison between linear and nonlinear methods, C. R. Acad. Sci. Paris Ser. A 315 (1992), 211-216.
    • (1992) C. R. Acad. Sci. Paris Ser. A , vol.315 , pp. 211-216
    • Johnstone, I.M.1    Kerkyacharian, G.2    Picard, D.3
  • 37
    • 0000319983 scopus 로고
    • Speeds of estimation in positronemission tomography
    • I. M. Johnstone and B. W. Silverman, Speeds of estimation in positronemission tomography, Ann. Statist. 18 (1990), 251-280.
    • (1990) Ann. Statist , vol.18 , pp. 251-280
    • Johnstone, I.M.1    Silverman, B.W.2
  • 38
    • 0001855706 scopus 로고
    • Discretization effects in statistical inverse problems
    • I. M. Johnstone and B. W. Silverman, Discretization effects in statistical inverse problems, J. Complexity 7 (1991), 1-34.
    • (1991) J. Complexity , vol.7 , pp. 1-34
    • Johnstone, I.M.1    Silverman, B.W.2
  • 39
    • 84857887285 scopus 로고
    • Prolate spheroidal wave functions, Fourier analysis, and uncertainty II
    • H. J. Landau and H. O. Poliak, Prolate spheroidal wave functions, Fourier analysis, and uncertainty II, Bell System Tech. J. 40 (1961), 65.
    • (1961) Bell System Tech. J , vol.40 , pp. 65
    • Landau, H.J.1    Poliak, H.O.2
  • 41
    • 0000423051 scopus 로고
    • Analyses multi-resolutions non orthogonales, commutation entre projecteurs et derivation et ondelettes vecteurs ádivergence nulle
    • P. G. Lemarié-Rieusset, Analyses multi-resolutions non orthogonales, commutation entre projecteurs et derivation et ondelettes vecteurs ádivergence nulle. Rev Mat. Iberoamericana 8 (1992), 221-238.
    • (1992) Rev Mat. Iberoamericana , vol.8 , pp. 221-238
    • Lemarié-Rieusset, P.G.1
  • 42
    • 0037580140 scopus 로고
    • Incomplete data problems in x-ray computerized tomography. I. Singular value decomposition of the limited-angle transform
    • A. K. Louis, Incomplete data problems in x-ray computerized tomography. I. Singular value decomposition of the limited-angle transform, Numer. Math. 48 (1986), 251.
    • (1986) Numer. Math , vol.48 , pp. 251
    • Louis, A.K.1
  • 43
    • 84966210236 scopus 로고
    • Multiresolution approximations and wavelet orthonormal bases of L?(R)
    • S. G. Mallat, Multiresolution approximations and wavelet orthonormal bases of L?(R), Trans. Amer. Math. Soc. 315 (1989), 69-87.
    • (1989) Trans. Amer. Math. Soc , vol.315 , pp. 69-87
    • Mallat, S.G.1
  • 45
    • 0004198869 scopus 로고
    • Cambridge Univ. Press, Cambridge
    • Y. Meyer, “Wavelets and Operators,” Cambridge Univ. Press, Cambridge, 1993 [Engl, trans.]
    • (1993) Wavelets and Operators
    • Meyer, Y.1
  • 48
    • 84972545853 scopus 로고
    • A statistical perspective on ill-posed inverse problems
    • F. O’Sullivan, A statistical perspective on ill-posed inverse problems, Statist. Sci. 1 (1986), 502-527.
    • (1986) Statist. Sci , vol.1 , pp. 502-527
    • O’Sullivan, F.1
  • 49
    • 38249043477 scopus 로고
    • Minimax linear regression estimation with symmetric parametric restrictions
    • J. Pilz, Minimax linear regression estimation with symmetric parametric restrictions, J. Statist. Plann. Inference 13 (1986), 297-318.
    • (1986) J. Statist. Plann. Inference , vol.13 , pp. 297-318
    • Pilz, J.1
  • 50
    • 0000056063 scopus 로고
    • Optimal filtering of square integrable signals in Gaussian white noise
    • [in Russian]; Problems Inform. Transmission 16 (1980), 120-133 [in English]
    • M. S. Pinsker, Optimal filtering of square integrable signals in Gaussian white noise, Problemy Peredatsii Informatsii 16, No. 2 (1980), 52-68; Problems Inform. Transmission 16 (1980), 120-133 [in English]
    • (1980) Problemy Peredatsii Informatsii , vol.16 , Issue.2 , pp. 52-68
    • Pinsker, M.S.1
  • 52
    • 0008332271 scopus 로고
    • Theory and methods related to the singular functionexpansion and Landweber’s iteration for integral equations of the firstkind
    • O. N. Strand, Theory and methods related to the singular functionexpansion and Landweber’s iteration for integral equations of the firstkind, SIAM J. Numer. Anal. 5 (1973), 287.
    • (1973) SIAM J. Numer. Anal , vol.5 , pp. 287
    • Strand, O.N.1
  • 53
    • 0000007952 scopus 로고
    • Biorthogonalité et théorie des opérateurs
    • Ph. Tchamitchian, Biorthogonalité et théorie des opérateurs, Rev. Mat. Iberoamericana 3 (1987), 163-190.
    • (1987) Rev. Mat. Iberoamericana , vol.3 , pp. 163-190
    • Tchamitchian, P.H.1
  • 54
    • 0001300994 scopus 로고
    • Solution of incorrectly formulated problems and theregularization method
    • A. N. Tikhonov, Solution of incorrectly formulated problems and theregularization method, Soviet Math. Dok. 4 (1963), 1035.
    • (1963) Soviet Math. Dok , vol.4 , pp. 1035
    • Tikhonov, A.N.1
  • 59
    • 84945709185 scopus 로고
    • On the numerical solution of Fredholm integral equationsof the first kind by the inversion of the linear system produced byquadrature
    • S. Twomey, On the numerical solution of Fredholm integral equationsof the first kind by the inversion of the linear system produced byquadrature. J. Ass. Comput. Mach. 10 (1963), 97.
    • (1963) J. Ass. Comput. Mach , vol.10 , pp. 97
    • Twomey, S.1
  • 60
    • 0000251164 scopus 로고
    • Geometrizing rates of convergence, III
    • D. L. Donoho and R. C. Liu, Geometrizing rates of convergence, III. Annals of Statistics, 18 (1991), 1416-1437.
    • (1991) Annals of Statistics , vol.18 , pp. 1416-1437
    • Donoho, D.L.1    Liu, R.C.2


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