메뉴 건너뛰기




Volumn 29, Issue 2, 2010, Pages 543-558

Regularized interpolation for noisy images

Author keywords

Interpolation; Regularization; Regularization parameter; Splines; Tikhonov functional; Total variation functional

Indexed keywords

DATA SAMPLE; DATA-DRIVEN; DISCRETE DATA; EDGE PRESERVING; NOISY DATA; NOISY IMAGE; NONQUADRATIC REGULARIZATION; NUMERICAL EXAMPLE; REGULARIZATION; REGULARIZATION PARAMETERS; REGULARIZED INTERPOLATION; SCALE-INVARIANT; SMOOTHNESS CONSTRAINTS; TIKHONOV FUNCTIONAL; TOTAL-VARIATION; VARIATIONAL PRINCIPLES;

EID: 76249083326     PISSN: 02780062     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMI.2009.2038576     Document Type: Article
Times cited : (15)

References (54)
  • 1
    • 0033233099 scopus 로고    scopus 로고
    • Survey: Interpolation methods in medical image processing
    • Nov.
    • T. M. Lehmann, C. Gönner, and K. Spitzer, "Survey: Interpolation methods in medical image processing, " IEEE Trans. Med. Imag., vol.18, no.11, pp. 1049-1075, Nov. 1999.
    • (1999) IEEE Trans. Med. Imag. , vol.18 , Issue.11 , pp. 1049-1075
    • Lehmann, T.M.1    Gönner, C.2    Spitzer, K.3
  • 2
    • 0035384874 scopus 로고    scopus 로고
    • Addendum: B-spline interpolation in medical image processing
    • Jul.
    • T. M. Lehmann, C. Gönner, and K. Spitzer, "Addendum: B-spline interpolation in medical image processing, " IEEE Trans. Med. Imag., vol.20, no.7, pp. 660-665, Jul. 2001.
    • (2001) IEEE Trans. Med. Imag. , vol.20 , Issue.7 , pp. 660-665
    • Lehmann, T.M.1    Gönner, C.2    Spitzer, K.3
  • 3
    • 0027180279 scopus 로고
    • Towards statistically optimal interpolation for 3-D medical imaging
    • Sep.
    • R. W. Parrot, M. R. Stytz, P. Amburn, and D. Robinson, "Towards statistically optimal interpolation for 3-D medical imaging, " IEEE Eng. Med. Biol., vol.12, no.5, pp. 49-59, Sep. 1993.
    • (1993) IEEE Eng. Med. Biol. , vol.12 , Issue.5 , pp. 49-59
    • Parrot, R.W.1    Stytz, M.R.2    Amburn, P.3    Robinson, D.4
  • 4
    • 0035384145 scopus 로고    scopus 로고
    • Quantitative evaluation of convolution-based methods for medical image interpolation
    • Jun.
    • E. Meijering, W. J. Niessen, and M. A. Viergever, "Quantitative evaluation of convolution-based methods for medical image interpolation, " Med. Img. Anal., vol.5, no.2, pp. 111-126, Jun. 2001.
    • (2001) Med. Img. Anal. , vol.5 , Issue.2 , pp. 111-126
    • Meijering, E.1    Niessen, W.J.2    Viergever, M.A.3
  • 6
    • 33645766239 scopus 로고    scopus 로고
    • A chronology of interpolation: From ancient astronomy to modern signal and image processing
    • DOI 10.1109/5.993400, PII S0018921902028992
    • E. Meijering, "A chronology of interpolation: From ancient astronomy to modern signal and image processing, " Proc. IEEE, vol.90, no.3, pp. 319-342, Mar. 2002. (Pubitemid 43779293)
    • (2002) Proceedings of the IEEE , vol.90 , Issue.3 , pp. 319-342
    • Meijering, E.1
  • 7
    • 0032637933 scopus 로고    scopus 로고
    • Image registration for digital subtraction angiography
    • E. Meijering, K. J. Zuiderveld, and M. A. Viergever, "Image registration for digital subtraction angiography, " Int. J. Comput. Vis., vol.32, no.2-3, pp. 227-246, 1999.
    • (1999) Int. J. Comput. Vis. , vol.32 , Issue.2-3 , pp. 227-246
    • Meijering, E.1    Zuiderveld, K.J.2    Viergever, M.A.3
  • 8
    • 33751331184 scopus 로고    scopus 로고
    • Automatic elastic image registration by interpolation of 3-D rotations and translations from discrete rigid-body transformations
    • V. Walimbe and R. Shekhar, "Automatic elastic image registration by interpolation of 3-D rotations and translations from discrete rigid-body transformations, " Med. Img. Anal., vol.10, no.6, pp. 899-914, 2006.
    • (2006) Med. Img. Anal. , vol.10 , Issue.6 , pp. 899-914
    • Walimbe, V.1    Shekhar, R.2
  • 9
    • 37549005928 scopus 로고    scopus 로고
    • A review of geometric transformations for nonrigid body registration
    • Jan.
    • M. Holden, "A review of geometric transformations for nonrigid body registration, " IEEE Trans. Med. Imag., vol.27, no.1, pp. 111-128, Jan. 2008.
    • (2008) IEEE Trans. Med. Imag. , vol.27 , Issue.1 , pp. 111-128
    • Holden, M.1
  • 10
    • 0023894189 scopus 로고
    • Efficient algorithms for generating interpolated (zoomed) MR images
    • Jun.
    • M. R. Smith and S. T. Nichols, "Efficient algorithms for generating interpolated (zoomed) MR images, " Magn. Reson. Med., vol.7, no.2, pp. 156-171, Jun. 1988.
    • (1988) Magn. Reson. Med. , vol.7 , Issue.2 , pp. 156-171
    • Smith, M.R.1    Nichols, S.T.2
  • 11
    • 34247247680 scopus 로고    scopus 로고
    • New spline quasi-interpolant for fitting 3-D data on the sphere: Applications to medical imaging
    • May
    • E. B. Ameur, D. Sbibih, A. Almhdie, and C. Léger, "New spline quasi-interpolant for fitting 3-D data on the sphere: Applications to medical imaging, " IEEE Sig. Proc. Lett., vol.14, no.5, pp. 333-336, May 2007.
    • (2007) IEEE Sig. Proc. Lett. , vol.14 , Issue.5 , pp. 333-336
    • Ameur, E.B.1    Sbibih, D.2    Almhdie, A.3    Léger, C.4
  • 12
    • 0242579148 scopus 로고    scopus 로고
    • Tricubic interpolation of discrete surfaces for binary volumes
    • Oct.-Dec.
    • A. Kadosh, D. Cohen-Or, and R. Yagel, "Tricubic interpolation of discrete surfaces for binary volumes, " IEEE Trans. Vis. Comput. Graph., vol.9, no.4, pp. 580-586, Oct.-Dec. 2003.
    • (2003) IEEE Trans. Vis. Comput. Graph. , vol.9 , Issue.4 , pp. 580-586
    • Kadosh, A.1    Cohen-Or, D.2    Yagel, R.3
  • 13
    • 0032682784 scopus 로고    scopus 로고
    • An interactive visualization and navigation tool for medical volume data
    • O. Sommer, A. Dietz, R. Westermann, and T. Ertl, "An interactive visualization and navigation tool for medical volume data, " Computers Graphics, vol.23, no.2, pp. 233-244, 1999.
    • (1999) Computers Graphics , vol.23 , Issue.2 , pp. 233-244
    • Sommer, O.1    Dietz, A.2    Westermann, R.3    Ertl, T.4
  • 14
    • 38649087631 scopus 로고    scopus 로고
    • An evaluation of prefiltered reconstruction schemes for volume rendering
    • Mar.-Apr.
    • B. Csébfalvi, "An evaluation of prefiltered reconstruction schemes for volume rendering, " IEEE Trans. Vis. Comput. Graph., vol.14, no.2, pp. 289-301, Mar.-Apr. 2008.
    • (2008) IEEE Trans. Vis. Comput. Graph. , vol.14 , Issue.2 , pp. 289-301
    • Csébfalvi, B.1
  • 15
    • 0027541354 scopus 로고
    • B-spline signal processing: Part I-Theory
    • Feb.
    • M. Unser, A. Aldroubi, and M. Eden, "B-spline signal processing: Part I-Theory, " IEEE Trans. Signal Process., vol.41, no.2, pp. 821-832, Feb. 1993.
    • (1993) IEEE Trans. Signal Process. , vol.41 , Issue.2 , pp. 821-832
    • Unser, M.1    Aldroubi, A.2    Eden, M.3
  • 16
    • 0031118495 scopus 로고    scopus 로고
    • Evaluation and design of filters using a Taylor series expansion
    • Apr.-Jun.
    • T. Möller, R. Machiraju, K. Mueller, and R. Yagel, "Evaluation and design of filters using a Taylor series expansion, " IEEE Trans. Vis. Comput. Graph., vol.3, no.2, pp. 184-199, Apr.-Jun. 1997.
    • (1997) IEEE Trans. Vis. Comput. Graph. , vol.3 , Issue.2 , pp. 184-199
    • Möller, T.1    MacHiraju, R.2    Mueller, K.3    Yagel, R.4
  • 17
    • 0031366077 scopus 로고    scopus 로고
    • Texture mapping 3D models of real-world scenes
    • Dec.
    • F. M. Weinhaus and V. Devarajan, "Texture mapping 3D models of real-world scenes, " ACM Comput. Surv., vol.29, no.4, pp. 325-365, Dec. 1997.
    • (1997) ACM Comput. Surv. , vol.29 , Issue.4 , pp. 325-365
    • Weinhaus, F.M.1    Devarajan, V.2
  • 18
    • 0037681607 scopus 로고    scopus 로고
    • RBF-based constrained texture mapping
    • Y. Tang, J. Wang, H. Bao, and Q. Peng, "RBF-based constrained texture mapping, " Comput. Graph., vol.27, no.3, pp. 415-422, 2003.
    • (2003) Comput. Graph. , vol.27 , Issue.3 , pp. 415-422
    • Tang, Y.1    Wang, J.2    Bao, H.3    Peng, Q.4
  • 19
    • 34547144842 scopus 로고    scopus 로고
    • 3D space-varying coefficient models with application to diffusion tensor imaging
    • S. Heim, L. Fahrmeir, P. H. C. Eilers, and B. D. Marx, "3D space-varying coefficient models with application to diffusion tensor imaging, " Comput. Stat. Data Anal., vol.51, no.12, pp. 6212-6228, 2007.
    • (2007) Comput. Stat. Data Anal. , vol.51 , Issue.12 , pp. 6212-6228
    • Heim, S.1    Fahrmeir, L.2    Eilers, P.H.C.3    Marx, B.D.4
  • 20
    • 0034214895 scopus 로고    scopus 로고
    • Interpolation revisited
    • Jul.
    • P. Thévenaz, T. Blu, and M. Unser, "Interpolation revisited, " IEEE Trans. Med. Imag., vol.19, no.7, pp. 739-758, Jul. 2000.
    • (2000) IEEE Trans. Med. Imag. , vol.19 , Issue.7 , pp. 739-758
    • Thévenaz, P.1    Blu, T.2    Unser, M.3
  • 21
    • 0028427322 scopus 로고
    • A Bayesian approach to image expansion for improved definition
    • May
    • R. R. Schultz and R. L. Stevenson, "A Bayesian approach to image expansion for improved definition, " IEEE Trans. Image Process., vol.3, no.3, pp. 233-242, May 1994.
    • (1994) IEEE Trans. Image Process. , vol.3 , Issue.3 , pp. 233-242
    • Schultz, R.R.1    Stevenson, R.L.2
  • 22
    • 34047200699 scopus 로고    scopus 로고
    • Fast and stable Bayesian image expansion using sparse edge priors
    • Apr.
    • A. Raj andK. Thakur, "Fast and stable Bayesian image expansion using sparse edge priors, " IEEE Trans. Image Process., vol.16, no.4, pp. 1073-1084, Apr. 2007.
    • (2007) IEEE Trans. Image Process. , vol.16 , Issue.4 , pp. 1073-1084
    • Raj, A.1    Thakur, K.2
  • 23
    • 0032140918 scopus 로고    scopus 로고
    • Regularized iterative image interpolation and its application to spatially scalable coding
    • Aug.
    • J. H. Shin, J. H. Jung, and J. K. Paik, "Regularized iterative image interpolation and its application to spatially scalable coding, " IEEE Trans. Consum. Electron., vol.44, no.3, pp. 1042-1047, Aug. 1998.
    • (1998) IEEE Trans. Consum. Electron. , vol.44 , Issue.3 , pp. 1042-1047
    • Shin, J.H.1    Jung, J.H.2    Paik, J.K.3
  • 24
    • 34250516079 scopus 로고
    • Smoothing by spline functions
    • C. M. Reinsch, "Smoothing by spline functions, " Numer. Math., vol.10, no.3, pp. 177-183, 1967.
    • (1967) Numer. Math. , vol.10 , Issue.3 , pp. 177-183
    • Reinsch, C.M.1
  • 25
    • 0001426609 scopus 로고
    • Spline functions and the problem of graduation
    • I. J. Schoenberg, "Spline functions and the problem of graduation, " Proc. Nat. Acad. Sci. U. S. A., vol.52, no.4, pp. 947-950, 1964.
    • (1964) Proc. Nat. Acad. Sci. U. S. A. , vol.52 , Issue.4 , pp. 947-950
    • Schoenberg, I.J.1
  • 26
    • 34250263445 scopus 로고
    • Smoothing noisy data with spline functions-Estimating the correct degree of smoothing by the method of generalized cross-validation
    • P. Craven and G. Wahba, "Smoothing noisy data with spline functions-Estimating the correct degree of smoothing by the method of generalized cross-validation, " Numer. Math., vol.31, no.4, pp. 377-403, 1979.
    • (1979) Numer. Math. , vol.31 , Issue.4 , pp. 377-403
    • Craven, P.1    Wahba, G.2
  • 27
    • 20544471671 scopus 로고    scopus 로고
    • Generalized smoothing splines and the optimal discretization of the Wiener filter
    • Jun.
    • M. Unser and T. Blu, "Generalized smoothing splines and the optimal discretization of the Wiener filter, " IEEE Trans. Signal Process., vol.53, no.6, pp. 2146-2159, Jun. 2005.
    • (2005) IEEE Trans. Signal Process. , vol.53 , Issue.6 , pp. 2146-2159
    • Unser, M.1    Blu, T.2
  • 28
    • 33745713091 scopus 로고    scopus 로고
    • Nonideal sampling and interpolation from noisy observations in shift-invariant spaces
    • Y. C. Eldar and M. Unser, "Nonideal sampling and interpolation from noisy observations in shift-invariant spaces, " IEEE Trans. Signal Process., vol.54, no.7, pp. 2636-2651, Jul. 2006.
    • (2006) IEEE Trans. Signal Process. , vol.54 , Issue.7 , pp. 2636-2651
    • Eldar, Y.C.1    Unser, M.2
  • 29
  • 30
    • 1342332031 scopus 로고    scopus 로고
    • A tutorial on MM algorithms
    • Feb.
    • D. R. Hunter and K. Lange, "A tutorial on MM algorithms, " Amer. Statist., vol.59, no.1, pp. 30-37, Feb. 2004.
    • (2004) Amer. Statist. , vol.59 , Issue.1 , pp. 30-37
    • Hunter, D.R.1    Lange, K.2
  • 31
    • 0002999362 scopus 로고    scopus 로고
    • Splines: A perfect fit for signal and image processing
    • Nov.
    • M. Unser, "Splines: A perfect fit for signal and image processing, " IEEE Signal Process. Mag., vol.16, no.6, pp. 22-38, Nov. 1999.
    • (1999) IEEE Signal Process. Mag. , vol.16 , Issue.6 , pp. 22-38
    • Unser, M.1
  • 32
    • 0033321447 scopus 로고    scopus 로고
    • Quantitative Fourier analysis of approximation techniques: Part I - interpolators and projectors
    • DOI 10.1109/78.790659
    • T. Blu and M. Unser, "Quantitative Fourier analysis of approximation techniques: Part I-Interpolators and projectors, " IEEE Trans. Signal Process., vol.47, no.10, pp. 2783-2795, Oct. 1999. (Pubitemid 30514921)
    • (1999) IEEE Transactions on Signal Processing , vol.47 , Issue.10 , pp. 2783-2795
    • Blu Thierry1    Unser Michael2
  • 33
    • 0000357775 scopus 로고
    • On use of the em for penalized likelihood estimation
    • P. J. Green, "On use of the EM for penalized likelihood estimation, " J. R. Stat. Soc. B, vol.52, no.3, pp. 443-452, 1990.
    • (1990) J. R. Stat. Soc. B , vol.52 , Issue.3 , pp. 443-452
    • Green, P.J.1
  • 34
    • 0029267626 scopus 로고
    • A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography
    • Mar.
    • A. R. De Pierro, "A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography, " IEEE Trans. Med. Imag., vol.14, no.1, pp. 132-137, Mar. 1995.
    • (1995) IEEE Trans. Med. Imag. , vol.14 , Issue.1 , pp. 132-137
    • De Pierro, A.R.1
  • 35
    • 0033169213 scopus 로고    scopus 로고
    • Penalized-likelihood estimators and noise analysis for randoms-precorrected PET transmission scans
    • Aug.
    • M. Yavuz and J. A. Fessler, "Penalized-likelihood estimators and noise analysis for randoms-precorrected PET transmission scans, " IEEE Trans. Med. Imag., vol.18, no.8, pp. 665-674, Aug. 1999.
    • (1999) IEEE Trans. Med. Imag. , vol.18 , Issue.8 , pp. 665-674
    • Yavuz, M.1    Fessler, J.A.2
  • 37
    • 0020194763 scopus 로고
    • Maximum likelihood reconstruction for emission tomography
    • Oct.
    • L. A. Shepp and Y. Vardi, "Maximum likelihood reconstruction for emission tomography, " IEEE Trans. Med. Imag., vol.1, no.2, pp. 113-122, Oct. 1982.
    • (1982) IEEE Trans. Med. Imag. , vol.1 , Issue.2 , pp. 113-122
    • Shepp, L.A.1    Vardi, Y.2
  • 39
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • Nov.
    • L. I. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms, "Phys. D, vol.60, no.1-4, pp. 259-268, Nov. 1992.
    • (1992) Phys. D , vol.60 , Issue.1-4 , pp. 259-268
    • Rudin, L.I.1    Osher, S.2    Fatemi, E.3
  • 41
    • 34247500347 scopus 로고    scopus 로고
    • A variational approach to reconstructing images corrupted by poisson noise
    • T. Le, R. Chartrand, and T. J. Asaki, "A variational approach to reconstructing images corrupted by poisson noise, " J. Math. Img. Vis., vol.27, no.3, pp. 257-263, 2007.
    • (2007) J. Math. Img. Vis. , vol.27 , Issue.3 , pp. 257-263
    • Le, T.1    Chartrand, R.2    Asaki, T.J.3
  • 42
    • 0036685493 scopus 로고    scopus 로고
    • Generalized sampling: A variational approach - Part I: Theory
    • DOI 10.1109/TSP.2002.800391, PII 1011092002800391
    • J. Kybic, T. Blu, and M. Unser, "Generalized sampling: A variational approach-Part I: Theory, " IEEE Trans. Signal Process., vol.50, no.8, pp. 1965-1976, Aug. 2002. (Pubitemid 34891229)
    • (2002) IEEE Transactions on Signal Processing , vol.50 , Issue.8 , pp. 1965-1976
    • Kybic, J.1    Blu, T.2    Unser, M.3
  • 43
    • 0001935440 scopus 로고
    • Splines minimizing rotation-invariant semi-norms in Sobolev spaces
    • W. Schempp and K. Zeller, Eds. Berlin, Germany: Springer-Verlag
    • J. Duchon, "Splines minimizing rotation-invariant semi-norms in Sobolev spaces, " in Constructive Theory of Functions of Several Variables, W. Schempp and K. Zeller, Eds. Berlin, Germany: Springer-Verlag, 1977, pp. 85-100.
    • (1977) Constructive Theory of Functions of Several Variables , pp. 85-100
    • Duchon, J.1
  • 45
    • 0026835074 scopus 로고
    • Constrained restoration and recovery of discontinuities
    • Mar.
    • D. Geman and G. Reynolds, "Constrained restoration and recovery of discontinuities, " IEEE Trans. Patttern Anal. Mach. Intell, vol.14, no.3, pp. 367-383, Mar. 1992.
    • (1992) IEEE Trans. Patttern Anal. Mach. Intell , vol.14 , Issue.3 , pp. 367-383
    • Geman, D.1    Reynolds, G.2
  • 46
    • 0031077064 scopus 로고    scopus 로고
    • Deterministic edge-preserving regularization in computed imaging
    • Feb.
    • P. Charbonnier, L. Blanc-Féraud, G. Aubert, and M. Barlaud, "Deterministic edge-preserving regularization in computed imaging, " IEEE Trans. Image Process., vol.2, no.6, pp. 298-311, Feb. 1997.
    • (1997) IEEE Trans. Image Process. , vol.2 , Issue.6 , pp. 298-311
    • Charbonnier, P.1    Blanc-Féraud, L.2    Aubert, G.3    Barlaud, M.4
  • 47
    • 33646596282 scopus 로고    scopus 로고
    • Analysis of half-quadratic minimization methods for signal and image recovery
    • M. Nikolova and M. K. Ng, "Analysis of half-quadratic minimization methods for signal and image recovery, " SIAM J. Sci. Comput., vol.27, no.3, pp. 937-966, 2005.
    • (2005) SIAM J. Sci. Comput. , vol.27 , Issue.3 , pp. 937-966
    • Nikolova, M.1    Ng, M.K.2
  • 48
    • 76249131733 scopus 로고    scopus 로고
    • Brainweb: Simulated MRI Volumes for Normal Brain McConnell Brain Imaging Center
    • Brainweb: Simulated MRI Volumes for Normal Brain McConnell Brain Imaging Center
  • 49
    • 76249125818 scopus 로고    scopus 로고
    • [Online]
    • [Online]. Available: http://www. bic. mni. mcgill. ca/brainweb/selection- normal. html
  • 50
    • 0019654284 scopus 로고
    • Cubic convolution interpolation for digital image processing
    • Dec.
    • R. G. Keys, "Cubic convolution interpolation for digital image processing, " IEEE Trans. Acoust. Speech, Signal Process., vol.ASSP-29, no.6, pp. 1153-1160, Dec. 1981.
    • (1981) IEEE Trans. Acoust. Speech, Signal Process. , vol.ASSP-29 , Issue.6 , pp. 1153-1160
    • Keys, R.G.1
  • 51
    • 0001182369 scopus 로고
    • L and generalized cross-validation in ridge regression with application to spline smoothing
    • L and generalized cross-validation in ridge regression with application to spline smoothing, " Ann. Stat., vol.14, no.3, pp. 1101-1112, 1986.
    • (1986) Ann. Stat. , vol.14 , Issue.3 , pp. 1101-1112
    • Li, K.C.1
  • 52
    • 0000169918 scopus 로고
    • Estimation of the mean of a multivariate normal distribution
    • C. Stein, "Estimation of the mean of a multivariate normal distribution, " Ann. Stat., vol.9, no.6, pp. 1135-1151, 1981.
    • (1981) Ann. Stat. , vol.9 , Issue.6 , pp. 1135-1151
    • Stein, C.1
  • 53
  • 54
    • 50549090016 scopus 로고    scopus 로고
    • Monte-Carlo SURE: A black-box optimization of regularization parameters for general denoising algorithms
    • Sep.
    • S. Ramani, T. Blu, and M. Unser, "Monte-Carlo SURE: A black-box optimization of regularization parameters for general denoising algorithms, " IEEE Trans. Image Process., vol.17, no.9, pp. 1540-1554, Sep. 2008.
    • (2008) IEEE Trans. Image Process. , vol.17 , Issue.9 , pp. 1540-1554
    • Ramani, S.1    Blu, T.2    Unser, M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.