메뉴 건너뛰기




Volumn 56, Issue 3, 2012, Pages 543-558

Locally adaptive image denoising by a statistical multiresolution criterion

Author keywords

Bandwidth selection; Image reconstruction; Statistical multiresolution criterion

Indexed keywords

ADAPTIVE IMAGES; BANDWIDTH SELECTIONS; EDGE DETECTORS; EFFICIENT METHOD; IMAGE DE-NOISING; MULTI-RESOLUTIONS; NUMERICAL EXAMPLE; REGULARIZATION SCHEMES; SMOOTHING PARAMETER; TOTAL VARIATION REGULARIZATION;

EID: 80455177091     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2011.08.018     Document Type: Article
Times cited : (18)

References (70)
  • 3
    • 85049184544 scopus 로고    scopus 로고
    • Mathematical problems in image processing: Partial differential equations and the calculus of variations
    • Springer New York
    • G. Aubert, and P. Kornprobst Mathematical problems in image processing: partial differential equations and the calculus of variations Applied Mathematical Sciences vol. 147 2002 Springer New York
    • (2002) Applied Mathematical Sciences , vol.147 VOL.
    • Aubert, G.1    Kornprobst, P.2
  • 5
    • 41549168778 scopus 로고    scopus 로고
    • Convergence rates of general regularization methods for statistical inverse problems and applications
    • N. Bissantz, T. Hohage, F. Ruymgaart, and A. Munk Convergence rates of general regularization methods for statistical inverse problems and applications SIAM Journal on Numerical Analysis 45 2007 2610 2636
    • (2007) SIAM Journal on Numerical Analysis , vol.45 , pp. 2610-2636
    • Bissantz, N.1    Hohage, T.2    Ruymgaart, F.3    Munk, A.4
  • 8
    • 65349195520 scopus 로고    scopus 로고
    • Consistencies and rates of convergence of jump penalized least squares estimators
    • L. Boysen, A. Kempe, A. Munk, V. Liebscher, and O. Wittich Consistencies and rates of convergence of jump penalized least squares estimators Annals of Statistics 37 2009 157 183
    • (2009) Annals of Statistics , vol.37 , pp. 157-183
    • Boysen, L.1    Kempe, A.2    Munk, A.3    Liebscher, V.4    Wittich, O.5
  • 9
    • 52249122440 scopus 로고    scopus 로고
    • Scale space consistency of piecewise constant least squares estimators another look at the regressogram
    • E.A. Cator, G. Jongbloed, C. Kraaikamp, H.P. Lopuha, J.A. Wellner, IMS Lecture Notes Institute of Mathematical Statistics Beachwood, Ohio
    • L. Boysen, V. Liebscher, A. Munk, and O. Wittich Scale space consistency of piecewise constant least squares estimators another look at the regressogram E.A. Cator, G. Jongbloed, C. Kraaikamp, H.P. Lopuha, J.A. Wellner, Asymptotics: Particles, Processes and Inverse Problems: Festschrift for Piet Groeneboom IMS Lecture Notes vol. 55 2007 Institute of Mathematical Statistics Beachwood, Ohio 65 84
    • (2007) Asymptotics: Particles, Processes and Inverse Problems: Festschrift for Piet Groeneboom , vol.55 VOL. , pp. 65-84
    • Boysen, L.1    Liebscher, V.2    Munk, A.3    Wittich, O.4
  • 10
    • 69249128415 scopus 로고    scopus 로고
    • The root-unroot algorithm for density estimation as implemented via wavelet block thresholding
    • L.D. Brown, T.T. Cai, R. Zhang, L.H. Zhao, and H.H. Zhou The root-unroot algorithm for density estimation as implemented via wavelet block thresholding Probability Theory and Related Fields 146 2010 401 433
    • (2010) Probability Theory and Related Fields , vol.146 , pp. 401-433
    • Brown, L.D.1    Cai, T.T.2    Zhang, R.3    Zhao, L.H.4    Zhou, H.H.5
  • 12
    • 33645653318 scopus 로고    scopus 로고
    • A review of image denoising algorithms, with a new one
    • DOI 10.1137/040616024
    • A. Buades, B. Coll, and J. Morel A review of image denoising algorithms, with a new one Multiscale Modeling and Simulation (SIAM Interdisciplinary Journal) 4 2005 490 530 (Pubitemid 43890582)
    • (2005) Multiscale Modeling and Simulation , vol.4 , Issue.2 , pp. 490-530
    • Buades, A.1    Coll, B.2    Morel, J.M.3
  • 13
    • 0038006811 scopus 로고    scopus 로고
    • Wavelet denoising of Poisson-distributed data and applications
    • PII S0167947302002086
    • C. Charles, and J.P. Rasson Wavelet denoising of Poisson-distributed data and applications Computational Statistics & Data Analysis 43 2003 139 148 (Pubitemid 36708986)
    • (2003) Computational Statistics and Data Analysis , vol.43 , Issue.2 , pp. 139-148
    • Charles, C.1    Rasson, J.P.2
  • 17
    • 80455141093 scopus 로고    scopus 로고
    • Quantifying the cost of simultaneous non-parametric approximation of several samples
    • P.L. Davies, and A. Kovac Quantifying the cost of simultaneous non-parametric approximation of several samples Electronic Journal of Statistics 3 2009 747 780
    • (2009) Electronic Journal of Statistics , vol.3 , pp. 747-780
    • Davies, P.L.1    Kovac, A.2
  • 18
    • 0035608644 scopus 로고    scopus 로고
    • Local extremes, runs, strings and multiresolution
    • P.L. Davies, and A. Kovac Local extremes, runs, strings and multiresolution The Annals of Statistics 29 2001 1 65
    • (2001) The Annals of Statistics , vol.29 , pp. 1-65
    • Davies, P.L.1    Kovac, A.2
  • 19
    • 69049098949 scopus 로고    scopus 로고
    • Nonparametric regression, confidence regions and regularization
    • P.L. Davies, A. Kovac, and M. Meise Nonparametric regression, confidence regions and regularization The Annals of Statistics 37 2009 2597 2625
    • (2009) The Annals of Statistics , vol.37 , pp. 2597-2625
    • Davies, P.L.1    Kovac, A.2    Meise, M.3
  • 22
    • 0035592604 scopus 로고    scopus 로고
    • Multiscale testing of qualitative hypotheses
    • L. Dmbgen, and V. Spokoiny Multiscale testing of qualitative hypotheses The Annals of Statistics 29 2001 124 152
    • (2001) The Annals of Statistics , vol.29 , pp. 124-152
    • Dmbgen, L.1    Spokoiny, V.2
  • 23
    • 51049118624 scopus 로고    scopus 로고
    • Multiscale inference about a density
    • L. Dmbgen, and G. Walther Multiscale inference about a density The Annals of Statistics 36 2008 1758 1785
    • (2008) The Annals of Statistics , vol.36 , pp. 1758-1785
    • Dmbgen, L.1    Walther, G.2
  • 24
    • 0033248623 scopus 로고    scopus 로고
    • Wedgelets: Nearly-minimax estimation of edges
    • D.L. Donoho Wedgelets: nearly-minimax estimation of edges The Annals of Statistics 27 1999 859 897
    • (1999) The Annals of Statistics , vol.27 , pp. 859-897
    • Donoho, D.L.1
  • 25
    • 0031508912 scopus 로고    scopus 로고
    • CART and best-ortho-basis: A connection
    • D.L. Donoho CART and best-ortho-basis: a connection The Annals of Statistics 25 1997 1870 1911
    • (1997) The Annals of Statistics , vol.25 , pp. 1870-1911
    • Donoho, D.L.1
  • 26
    • 34249915076 scopus 로고    scopus 로고
    • Quantum register based on individual electronic and nuclear spin qubits in diamond
    • DOI 10.1126/science.1139831
    • M.V.G. Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A.S. Zibrov, P.R. Hemmer, and M.D. Lukin Quantum register based on individual electronic and nuclear spin qubits in diamond Science 316 2007 1312 1316 http://www.sciencemag.org/cgi/reprint/316/5829/1312.pdf (Pubitemid 46871647)
    • (2007) Science , vol.316 , Issue.5829 , pp. 1312-1316
    • Gurudev Dutt, M.V.1    Childress, L.2    Jiang, L.3    Togan, E.4    Maze, J.5    Jelezko, F.6    Zibrov, A.S.7    Hemmer, P.R.8    Lukin, M.D.9
  • 27
    • 11244324581 scopus 로고    scopus 로고
    • Theory and practice of finite elements
    • Springer New York
    • A. Ern, and J.L. Guermond Theory and practice of finite elements Applied Mathematical Sciences vol. 159 2004 Springer New York
    • (2004) Applied Mathematical Sciences , vol.159 VOL.
    • Ern, A.1    Guermond, J.L.2
  • 29
    • 41449119247 scopus 로고    scopus 로고
    • Efficient moment computation over polygonal domains with an application to rapid wedgelet approximation
    • DOI 10.1137/050646597
    • F. Friedrich, L. Demaret, H. Fhr, and K. Wicker Efficient moment computation over polygonal domains with an application to rapid wedgelet approximation SIAM Journal on Scientific Computing 29 2007 842 863 (Pubitemid 351456417)
    • (2007) SIAM Journal of Scientific Computing , vol.29 , Issue.2 , pp. 842-863
    • Friedrich, F.1    Demaret, L.2    Fuhr, H.3    Wicker, K.4
  • 30
  • 32
    • 0040579167 scopus 로고    scopus 로고
    • Local Adaptivity of Kernel Estimates with Plug-in Local Bandwidth Selectors
    • I. Gijbels, and E. Mammen Local adaptivity of kernel estimates with plug-in local bandwidth selectors Scandinavian Journal of Statistics 25 1998 503 520 (Pubitemid 128129446)
    • (1998) Scandinavian Journal of Statistics , vol.25 , Issue.3 , pp. 503-520
    • Gijbels, I.1    Mammen, E.2
  • 38
    • 84996143974 scopus 로고    scopus 로고
    • Shao's theorem on the maximum of standardized random walk increments for multidimensional arrays
    • Z. Kabluchko, and A. Munk Shao's theorem on the maximum of standardized random walk increments for multidimensional arrays ESAIM Probability and Statistics 13 2009 409 416
    • (2009) ESAIM Probability and Statistics , vol.13 , pp. 409-416
    • Kabluchko, Z.1    Munk, A.2
  • 39
    • 0021136434 scopus 로고
    • The structure of images
    • J.J. Koenderink The structure of images Biological Cybernetics 50 1984 363 370 (Pubitemid 14070727)
    • (1984) Biological Cybernetics , vol.50 , Issue.5 , pp. 363-370
    • Koenderink, J.J.1
  • 40
    • 29144499428 scopus 로고    scopus 로고
    • Multiscale, multigranular statistical image segmentation
    • DOI 10.1198/016214505000000385
    • E.D. Kolaczyk, J. Ju, and S. Gopal Multiscale, multigranular statistical image segmentation Journal of the American Statistical Association 100 2005 1358 1369 (Pubitemid 41801281)
    • (2005) Journal of the American Statistical Association , vol.100 , Issue.472 , pp. 1358-1369
    • Kolaczyk, E.D.1    Ju, J.2    Gopal, S.3
  • 42
    • 0003910552 scopus 로고
    • Extremes and related properties of random sequences and processes
    • Springer-Verlag New York
    • M. Leadbetter, G. Lindgren, and H. Rootzén Extremes and related properties of random sequences and processes Springer Series in Statistics 1983 Springer-Verlag New York
    • (1983) Springer Series in Statistics
    • Leadbetter, M.1    Lindgren, G.2    Rootzén, H.3
  • 43
    • 0000012624 scopus 로고
    • On a problem of adaptive estimation in Gaussian white noise
    • O.V. Lepskii On a problem of adaptive estimation in Gaussian white noise Theory of Probability and its Applications 35 1990 454 466
    • (1990) Theory of Probability and Its Applications , vol.35 , pp. 454-466
    • Lepskii, O.V.1
  • 44
    • 0031504935 scopus 로고    scopus 로고
    • Optimal spatial adaptation to inhomogeneous smoothness: An approach based on kernel estimates with variable bandwidth selectors
    • O.V. Lepskii, E. Mammen, and V.G. Spokoiny Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors The Annals of Statistics 25 1997 929 947
    • (1997) The Annals of Statistics , vol.25 , pp. 929-947
    • Lepskii, O.V.1    Mammen, E.2    Spokoiny, V.G.3
  • 45
    • 0040276000 scopus 로고
    • Honest confidence regions for nonparametric regression
    • K.C. Li Honest confidence regions for nonparametric regression The Annals of Satistics 17 1989 1001 1008
    • (1989) The Annals of Satistics , vol.17 , pp. 1001-1008
    • Li, K.C.1
  • 48
    • 33750256531 scopus 로고    scopus 로고
    • On robust estimation and smoothing with spatial and tonal kernels
    • R. Klette, R. Kozera, L. Noakes, J. Weickert, Computational Imaging and Vision Springer Netherlands
    • P. Mrázek, J. Weickert, and A. Bruhn On robust estimation and smoothing with spatial and tonal kernels R. Klette, R. Kozera, L. Noakes, J. Weickert, Geometric Properties for Incomplete Data Computational Imaging and Vision vol. 31 2006 Springer Netherlands 335 352
    • (2006) Geometric Properties for Incomplete Data , vol.31 VOL. , pp. 335-352
    • Mrázek, P.1    Weickert, J.2    Bruhn, A.3
  • 50
    • 51049112668 scopus 로고    scopus 로고
    • The distribution of maxima of approximately Gaussian random fields
    • Y. Nardi, D.O. Siegmund, and B. Yakir The distribution of maxima of approximately Gaussian random fields The Annals of Statistics 36 2008 1375 1403
    • (2008) The Annals of Statistics , vol.36 , pp. 1375-1403
    • Nardi, Y.1    Siegmund, D.O.2    Yakir, B.3
  • 51
    • 0030160662 scopus 로고    scopus 로고
    • Data dependent wavelet thresholding in nonparametric regression with change-point applications
    • T. Ogden, and E. Parzen Data dependent wavelet thresholding in nonparametric regression with change-point applications Computational Statistics & Data Analysis 22 1996 53 70
    • (1996) Computational Statistics & Data Analysis , vol.22 , pp. 53-70
    • Ogden, T.1    Parzen, E.2
  • 54
    • 21144455623 scopus 로고    scopus 로고
    • Image denoising: Pointwise adaptive approach
    • J. Polzehl, and V. Spokoiny Image denoising: pointwise adaptive approach The Annals of Statistics 31 2003 30 57
    • (2003) The Annals of Statistics , vol.31 , pp. 30-57
    • Polzehl, J.1    Spokoiny, V.2
  • 55
    • 84949554702 scopus 로고    scopus 로고
    • Image processing and jump regression analysis
    • Wiley-Interscience Hoboken, NJ
    • P. Qiu Image processing and jump regression analysis Wiley Series in Probability and Statistics 2005 Wiley-Interscience Hoboken, NJ
    • (2005) Wiley Series in Probability and Statistics
    • Qiu, P.1
  • 56
    • 34250703103 scopus 로고    scopus 로고
    • Jump surface estimation, edge detection and image restoration
    • P. Qiu Jump surface estimation, edge detection and image restoration Journal of the American Statistical Association 102 2007 745 756
    • (2007) Journal of the American Statistical Association , vol.102 , pp. 745-756
    • Qiu, P.1
  • 57
  • 60
    • 21844489952 scopus 로고
    • Using the generalized likelihood ratio statistic for sequential detection of a change-point
    • D.O. Siegmund, and E.S. Venkatraman Using the generalized likelihood ratio statistic for sequential detection of a change-point The Annals of Statistics 23 1995 255 271
    • (1995) The Annals of Statistics , vol.23 , pp. 255-271
    • Siegmund, D.O.1    Venkatraman, E.S.2
  • 61
    • 0004454158 scopus 로고
    • Testing for a signal with unknown location and scale in a stationary Gaussian random field
    • D.O. Siegmund, and K.J. Worsley Testing for a signal with unknown location and scale in a stationary Gaussian random field The Annals of Statistics 23 1995 608 639
    • (1995) The Annals of Statistics , vol.23 , pp. 608-639
    • Siegmund, D.O.1    Worsley, K.J.2
  • 62
    • 0003265138 scopus 로고    scopus 로고
    • Tail probabilities for the null distribution of scanning statistics
    • D.O. Siegmund, and B. Yakir Tail probabilities for the null distribution of scanning statistics Bernoulli 6 2000 191 213
    • (2000) Bernoulli , vol.6 , pp. 191-213
    • Siegmund, D.O.1    Yakir, B.2
  • 65
    • 0032243618 scopus 로고    scopus 로고
    • Pointwise and sup-norm sharp adaptive estimation of functions on the Sobolev classes
    • A.B. Tsybakov Pointwise and sup-norm sharp adaptive estimation of functions on the Sobolev classes The Annals of Statistics 26 1998 2420 2469 (Pubitemid 128376943)
    • (1998) Annals of Statistics , vol.26 , Issue.6 , pp. 2420-2469
    • Tsybakov, A.B.1
  • 66
    • 4043182719 scopus 로고    scopus 로고
    • Computational methods for inverse problems
    • SIAM Philadelphia
    • C.R. Vogel Computational methods for inverse problems Frontiers in Applied Mathematics vol. 23 2002 SIAM Philadelphia
    • (2002) Frontiers in Applied Mathematics , vol.23 VOL.
    • Vogel, C.R.1
  • 69
    • 0003455701 scopus 로고    scopus 로고
    • Image analysis, random fields and Markov chain Monte Carlo methods
    • 2nd edition Springer
    • G. Winkler Image analysis, random fields and Markov chain Monte Carlo methods 2nd edition Applications of Mathematics vol. 27 2003 Springer
    • (2003) Applications of Mathematics , vol.27 VOL.
    • Winkler, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.