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A geometry guided image denoising scheme
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References:
[1] |
D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Comm. Pure Appl. Math., 42 (1989), 577-685.
doi: 10.1002/cpa.3160420503. |
[2] |
P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis and Machine Intelligence, 12 (1990), 629-639.
doi: 10.1109/34.56205. |
[3] |
L. I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithm, Physica D: Nonlinear Phenomena, 60 (1992), 259-268.
doi: 10.1016/0167-2789(92)90242-F. |
[4] |
M. Bertalmio, V. Caselles, B. Rougé and A. Solé, TV based image restoration with local constraints, Journal of Scientific Computing, 19 (2003), 95-122.
doi: 10.1023/A:1025391506181. |
[5] |
S. Geman and D. Geman, Stochastic relaxation, gibbs distributions, and the bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6 (1984), 721-741. |
[6] |
P. Saint-Marc, J. S. Chen and G. Medioni, Adaptive smoothing: A general tool for early vision, IEEE Transactions on Pattern Analysis and Machine Intelligence, 13 (1991), 514-529. |
[7] |
S. M. Smith and J. M. Brady, SUSAN - A new approach to low level image processing, International Journal of Computer Vision, 23 (1995), 45-78. |
[8] |
C. Tomasi and R. Manduchi, Bilateral filtering for gray and color images, in "Proceedings of Sixth International Conference on Computer Vision," (1998), 839-846.
doi: 10.1109/ICCV.1998.710815. |
[9] |
M. Elad, On the origin of the bilateral filter and ways to improve it, IEEE Transactions on Image Processing, 11 (2002), 1141-1151.
doi: 10.1109/TIP.2002.801126. |
[10] |
S. Durand and J. Froment, Reconstruction of wavelet coefficients using total variation minimization, SIAM J. Sci. Comput., 24 (2003), 1754-1767.
doi: 10.1137/S1064827501397792. |
[11] |
A. Buades, B. Coll and J. M. Morel, A non-local algorithm for image denoising, IEEE Computer Society, 2 (2005), 60-65.
doi: 10.1109/CVPR.2005.38. |
[12] |
S. Kindermann, S. Osher and P. W. Jones, Deblurring and Denoising of Images by Nonlocal Functionals, Multiscale Modelling and Simulation, 4 (2005), 1091-1115.
doi: 10.1137/050622249. |
[13] |
T. Brox and D. Cremers, Iterated nonlocal means for texture restoration, Scale Space and Variational Methods in Computer Vision, (2008), 13-24.
doi: 10.1007/978-3-540-72823-8_2. |
[14] |
C. Kervrann, J. Boulanger and P. Coupé, Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal, Scale Space and Variational Methods in Computer Vision, (2007), 520-532.
doi: 10.1007/978-3-540-72823-8_45. |
[15] |
B. Goossens, Q. Luong, A. Pizurica and W. Philips, An improved non-local denoising algorithm, in "Local and Non-Local Approximation in Image Processing, International Workshop, Proceedings," (2008). |
[16] |
G. Gilboa and S. Osher, Nonlocal operators with applications to image processing, Multiscale Modeling and Simulation, 7 (2008), 1005-1028.
doi: 10.1137/070698592. |
[17] |
C-A. Deledalle, L. Denis and F. Tupin, Iterative wieghted maximum likelihood denoising with probabilistic patch-based weights, Transactions on Image Processing, 18 (2009), 2661-2672.
doi: 10.1109/TIP.2009.2029593. |
[18] |
D. Peter, V. Govindan and A. Mathew, Nonlocal-means image denoising techonology using robust M-estimator, Journal of Computer Science and Technology, 25 (2010), 623-631. |
[19] |
N. Wiest-Daesslé, S. Prima, P. Coupé, S. P. Morrissey and C. Barillot, Rician noise removal by non-local means filtering for low signal-to-noise ratio MRI: Applications to DT-MRI, in "Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention," (2008), 171-179.
doi: 10.1007/978-3-540-85990-1_21. |
[20] |
P. Coupé, P. Yger, S. Prima, P. Hellier, C. Kervrann and C. Barillot, An optimized blockwise nonlocal means denoising filter for 3-D magnetic resonance images, Medical Imaging, IEEE Transactions on, 27 (2008), 425-441.
doi: 10.1109/TMI.2007.906087. |
[21] |
C-A. Deledalle, F. Tupin and L. Denis, Poisson NL means: Unsupervised non local means for Poisson noise, in "Proc. of ICIP", Hongkong, (2010).
doi: 10.1109/ICIP.2010.5653394. |
[22] |
S. Osher and J. A. Sethian, Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, 79 (1988), 12-49.
doi: 10.1016/0021-9991(88)90002-2. |
[23] |
T. F. Chan and L. A. Vese, Active contours without edges, Image Processing, IEEE Transactions on, 10 (2001), 266-277.
doi: 10.1109/83.902291. |
[24] |
L. A. Vese and T. F. Chan, A multiphase level set framework for image segmentation using the mumford and shah model, International Journal of Computer Vision, 50 (2002), 271-293. |
[25] |
K. Krishnamoorthy, "Handbook of Statistical Distributions with Applications," Chapman and Hall/CRC Press, London/Boca Raton, 2006.
doi: 10.1201/9781420011371. |
[26] |
T. Gasser, L. Sroka and C. Jennen-Steinmetz, Residual variance and residual pattern in nonlinear regression, Biometrika, 73 (1986), 625-633.
doi: 10.1093/biomet/73.3.625. |
[27] |
M. N. Do and M. Vetterli, The contourlet transform: an efficient directional multiresolution image representation, IEEE Transactions on Image Processing, 14 (2005), 2091-2106.
doi: 10.1109/TIP.2005.859376. |
[28] |
Z. Wang, A. C. Bovik, H. R. Sheikh and E. P. Simoncelli, Image quality assessment: From error visibility to structural similarity, Image Processing, IEEE Transactions on, 13 (2004), 600-612.
doi: 10.1109/TIP.2003.819861. |
[29] |
E. Candés and D. Donoho, "Curvelets: A Surprisingly Effective Nonadaptive Representation of Objects with Edges," in "Curves and Surfaces" (eds. L. L. Schumaker et al. ), Vanderbilt University Press, Nashville, TN. |
[30] |
K. Guo, G. Kutyniok and D. Labate, "Sparse Multidimensional Representations using Anisotropic Dilation and Shear Operators," Wavelets and Splines (Athens, GA, 2005), Nashboro Press, Nashville, TN. |
[31] |
E. A. Nadaraya, On estimating regression, Theory Probab. Appl., 9 (1964), 141-142.
doi: 10.1137/1109020. |
[32] |
F. J. Anscombe, The transformation of Poisson, binomial and negative-binomial data, Biometrika, 35 (1948), 246-254. |
[33] |
M. D. DeVore, A. D. Lanterman and J. A. O'Sullivan, ATR performance of a rician model for SAR images, in "Automatic Target Recognition X, Proc. SPIE 4050," (2000), 34-45.
doi: 10.1117/12.395589. |
[34] |
J. Sijbers, A. J. Den Dekker, P. Scheunders and D. Van Dyck, Maximum-likelihood estimation of Rician distribution parameters, Medical Imaging, IEEE Transactions on, 17 (1998), 357-361.
doi: 10.1109/42.712125. |
[35] |
T. Loupas, W. N. McDicken and P. L. Allan, An adaptive weighted median filter for speckle suppression in medical ultrasonic images, Circuits and Systems, IEEE Transactions on, 36 (1989), 129-135.
doi: 10.1109/31.16577. |
[36] |
K. Krissian, Speckle-constrained anisotropic diffusion for ultrasound images, in "Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition," (2005), 547-552. |
[37] |
K. Dabov, A. Foi, V. Katkovnik and K. Egiazarian, Image denoising with block-matching and 3D filtering, in "Electronic Imaging" 06, Proc. SPIE 6064", (2006).
doi: 10.1117/12.643267. |
[38] |
M. Elad and M. Aharon, Image denoising via sparse and redundant representations over learned dictionaries, Image Processing, IEEE Transactions on, 15 (2006), 3736-3745.
doi: 10.1109/TIP.2006.881969. |
[39] |
P. Coupé, P. Hellier, C. Kervrann and C. Barillot, Bayesian non local means-based speckle filtering, in "Proceedings of ISBI," (2008), 1291-1294.
doi: 10.1109/ISBI.2008.4541240. |
show all references
References:
[1] |
D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Comm. Pure Appl. Math., 42 (1989), 577-685.
doi: 10.1002/cpa.3160420503. |
[2] |
P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis and Machine Intelligence, 12 (1990), 629-639.
doi: 10.1109/34.56205. |
[3] |
L. I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithm, Physica D: Nonlinear Phenomena, 60 (1992), 259-268.
doi: 10.1016/0167-2789(92)90242-F. |
[4] |
M. Bertalmio, V. Caselles, B. Rougé and A. Solé, TV based image restoration with local constraints, Journal of Scientific Computing, 19 (2003), 95-122.
doi: 10.1023/A:1025391506181. |
[5] |
S. Geman and D. Geman, Stochastic relaxation, gibbs distributions, and the bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6 (1984), 721-741. |
[6] |
P. Saint-Marc, J. S. Chen and G. Medioni, Adaptive smoothing: A general tool for early vision, IEEE Transactions on Pattern Analysis and Machine Intelligence, 13 (1991), 514-529. |
[7] |
S. M. Smith and J. M. Brady, SUSAN - A new approach to low level image processing, International Journal of Computer Vision, 23 (1995), 45-78. |
[8] |
C. Tomasi and R. Manduchi, Bilateral filtering for gray and color images, in "Proceedings of Sixth International Conference on Computer Vision," (1998), 839-846.
doi: 10.1109/ICCV.1998.710815. |
[9] |
M. Elad, On the origin of the bilateral filter and ways to improve it, IEEE Transactions on Image Processing, 11 (2002), 1141-1151.
doi: 10.1109/TIP.2002.801126. |
[10] |
S. Durand and J. Froment, Reconstruction of wavelet coefficients using total variation minimization, SIAM J. Sci. Comput., 24 (2003), 1754-1767.
doi: 10.1137/S1064827501397792. |
[11] |
A. Buades, B. Coll and J. M. Morel, A non-local algorithm for image denoising, IEEE Computer Society, 2 (2005), 60-65.
doi: 10.1109/CVPR.2005.38. |
[12] |
S. Kindermann, S. Osher and P. W. Jones, Deblurring and Denoising of Images by Nonlocal Functionals, Multiscale Modelling and Simulation, 4 (2005), 1091-1115.
doi: 10.1137/050622249. |
[13] |
T. Brox and D. Cremers, Iterated nonlocal means for texture restoration, Scale Space and Variational Methods in Computer Vision, (2008), 13-24.
doi: 10.1007/978-3-540-72823-8_2. |
[14] |
C. Kervrann, J. Boulanger and P. Coupé, Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal, Scale Space and Variational Methods in Computer Vision, (2007), 520-532.
doi: 10.1007/978-3-540-72823-8_45. |
[15] |
B. Goossens, Q. Luong, A. Pizurica and W. Philips, An improved non-local denoising algorithm, in "Local and Non-Local Approximation in Image Processing, International Workshop, Proceedings," (2008). |
[16] |
G. Gilboa and S. Osher, Nonlocal operators with applications to image processing, Multiscale Modeling and Simulation, 7 (2008), 1005-1028.
doi: 10.1137/070698592. |
[17] |
C-A. Deledalle, L. Denis and F. Tupin, Iterative wieghted maximum likelihood denoising with probabilistic patch-based weights, Transactions on Image Processing, 18 (2009), 2661-2672.
doi: 10.1109/TIP.2009.2029593. |
[18] |
D. Peter, V. Govindan and A. Mathew, Nonlocal-means image denoising techonology using robust M-estimator, Journal of Computer Science and Technology, 25 (2010), 623-631. |
[19] |
N. Wiest-Daesslé, S. Prima, P. Coupé, S. P. Morrissey and C. Barillot, Rician noise removal by non-local means filtering for low signal-to-noise ratio MRI: Applications to DT-MRI, in "Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention," (2008), 171-179.
doi: 10.1007/978-3-540-85990-1_21. |
[20] |
P. Coupé, P. Yger, S. Prima, P. Hellier, C. Kervrann and C. Barillot, An optimized blockwise nonlocal means denoising filter for 3-D magnetic resonance images, Medical Imaging, IEEE Transactions on, 27 (2008), 425-441.
doi: 10.1109/TMI.2007.906087. |
[21] |
C-A. Deledalle, F. Tupin and L. Denis, Poisson NL means: Unsupervised non local means for Poisson noise, in "Proc. of ICIP", Hongkong, (2010).
doi: 10.1109/ICIP.2010.5653394. |
[22] |
S. Osher and J. A. Sethian, Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, 79 (1988), 12-49.
doi: 10.1016/0021-9991(88)90002-2. |
[23] |
T. F. Chan and L. A. Vese, Active contours without edges, Image Processing, IEEE Transactions on, 10 (2001), 266-277.
doi: 10.1109/83.902291. |
[24] |
L. A. Vese and T. F. Chan, A multiphase level set framework for image segmentation using the mumford and shah model, International Journal of Computer Vision, 50 (2002), 271-293. |
[25] |
K. Krishnamoorthy, "Handbook of Statistical Distributions with Applications," Chapman and Hall/CRC Press, London/Boca Raton, 2006.
doi: 10.1201/9781420011371. |
[26] |
T. Gasser, L. Sroka and C. Jennen-Steinmetz, Residual variance and residual pattern in nonlinear regression, Biometrika, 73 (1986), 625-633.
doi: 10.1093/biomet/73.3.625. |
[27] |
M. N. Do and M. Vetterli, The contourlet transform: an efficient directional multiresolution image representation, IEEE Transactions on Image Processing, 14 (2005), 2091-2106.
doi: 10.1109/TIP.2005.859376. |
[28] |
Z. Wang, A. C. Bovik, H. R. Sheikh and E. P. Simoncelli, Image quality assessment: From error visibility to structural similarity, Image Processing, IEEE Transactions on, 13 (2004), 600-612.
doi: 10.1109/TIP.2003.819861. |
[29] |
E. Candés and D. Donoho, "Curvelets: A Surprisingly Effective Nonadaptive Representation of Objects with Edges," in "Curves and Surfaces" (eds. L. L. Schumaker et al. ), Vanderbilt University Press, Nashville, TN. |
[30] |
K. Guo, G. Kutyniok and D. Labate, "Sparse Multidimensional Representations using Anisotropic Dilation and Shear Operators," Wavelets and Splines (Athens, GA, 2005), Nashboro Press, Nashville, TN. |
[31] |
E. A. Nadaraya, On estimating regression, Theory Probab. Appl., 9 (1964), 141-142.
doi: 10.1137/1109020. |
[32] |
F. J. Anscombe, The transformation of Poisson, binomial and negative-binomial data, Biometrika, 35 (1948), 246-254. |
[33] |
M. D. DeVore, A. D. Lanterman and J. A. O'Sullivan, ATR performance of a rician model for SAR images, in "Automatic Target Recognition X, Proc. SPIE 4050," (2000), 34-45.
doi: 10.1117/12.395589. |
[34] |
J. Sijbers, A. J. Den Dekker, P. Scheunders and D. Van Dyck, Maximum-likelihood estimation of Rician distribution parameters, Medical Imaging, IEEE Transactions on, 17 (1998), 357-361.
doi: 10.1109/42.712125. |
[35] |
T. Loupas, W. N. McDicken and P. L. Allan, An adaptive weighted median filter for speckle suppression in medical ultrasonic images, Circuits and Systems, IEEE Transactions on, 36 (1989), 129-135.
doi: 10.1109/31.16577. |
[36] |
K. Krissian, Speckle-constrained anisotropic diffusion for ultrasound images, in "Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition," (2005), 547-552. |
[37] |
K. Dabov, A. Foi, V. Katkovnik and K. Egiazarian, Image denoising with block-matching and 3D filtering, in "Electronic Imaging" 06, Proc. SPIE 6064", (2006).
doi: 10.1117/12.643267. |
[38] |
M. Elad and M. Aharon, Image denoising via sparse and redundant representations over learned dictionaries, Image Processing, IEEE Transactions on, 15 (2006), 3736-3745.
doi: 10.1109/TIP.2006.881969. |
[39] |
P. Coupé, P. Hellier, C. Kervrann and C. Barillot, Bayesian non local means-based speckle filtering, in "Proceedings of ISBI," (2008), 1291-1294.
doi: 10.1109/ISBI.2008.4541240. |
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