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Computing the fibre orientation from Radon data using local Radon transform
1. | Ceramic Materials Engineering, University of Bayreuth, 95440 Bayreuth, Germany, Germany, Germany |
References:
[1] |
E. J. Candès, "Ridgelets: Theory and Applications," Ph.D. Thesis, Department of Statistics, Stanford University, 1998. |
[2] |
E. J. Candès and D. L. Donoho, Curvelets-a surprisingly effective nonadaptive representation for objects with edges, in "Curves and Surfaces," Vanderbilt University Press, Nashville, TN, 1999. |
[3] |
E. J. Candès and D. L. Donoho, New tight frames of curvelets and optimal representations of objects with piecewise $C^2$ singularities, Comm. on Pure and Appl. Math., 57 (2004), 219-266. |
[4] |
E. J. Candès and J. Romberg, Practical signal recovery from random projections, Wavelet Applications in Signal and Image Processing XI, Proc. SPIE Conf. 5914, 2004. |
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A. Faridani, E. Ritman, K. Smith and T. Kennan, Local tomography, SIAM, J. Appl. Math., 52 (1992), 459-484.
doi: 10.1137/0152026. |
[6] |
A. Faridani, D. Finch, E. Ritman, K. Smith and T. Kennan, Local tomography II, SIAM, J. Appl. Math., 57 (1997), 1095-1127.
doi: 10.1137/S0036139995286357. |
[7] |
L. Gang, O. Chutape and M. Krishnan, Detection and measurement of retinal vessels in fundus images using amplitude modified second-order gaussian filter, IEEE Transactions on Biomedical Engineering, 49 (2002), 168-172.
doi: 10.1109/10.979356. |
[8] |
A. Hoover, V. Kouznetsova and M. Goldbaum, Locating blood vessels in retinal images by piecewise threshold probing of a matched filter response, IEEE Transactions on Medical Imaging, 19 (2000), 203-210. |
[9] |
M. Krause, R. M. Alles, B. Burgeth and J. Weickert, Retinal vessel detection via second derivative of local Radon transform, Technical Report No. 212, Universität des Saarlandes, 2009. |
[10] |
M. Krause, J. M. Hausherr, B. Burgeth, C. Herrmann and W. Krenkel, Determination of the fibre orientation in composites using the structure tensor and local X-ray transform, Journal of Materials Science, 45 (2010), 888-896.
doi: 10.1007/s10853-009-4016-4. |
[11] |
A. K. Louis, Approximate inverse for linear and some nonlinear problems, Inverse Problems, 12 (1996), 175-190. |
[12] |
A. K. Louis, Combining image reconstruction and image analysis with an application to two-dimensional tomography, SIAM J. Imaging Sciences, 1 (2008), 188-208.
doi: 10.1137/070700863. |
[13] |
A. K. Louis, Diffusion reconstruction from very noisy tomographic data, Inverse Problems and Imaging, 4 (2010), 675-683.
doi: 10.3934/ipi.2010.4.675. |
[14] |
F. Natterer, "The Mathematics of Computerized Tomography," B. G. Teubner, Stuttgart, John Wiley & Sons, Ltd., Chichester, 1986. |
[15] |
A. Rieder, R. Dietz and T. Schuster, Approximate inverse meets local tomography, Math. Meth. Appl. Sci., 23 (2000), 1373-1387.
doi: 10.1002/1099-1476(200010)23:15<1373::AID-MMA170>3.0.CO;2-A. |
[16] |
M. Sofka and C. Stewart, Retinal vessel centerline extraction using multiscale matched filters, confidence and edge measures, IEEE Transactions on Medical Imaging, 25 (2006), 1531-1546. |
[17] |
M. Van Ginkel, "Image Analysis Using Orientation Space Based on Steerable Filters," Ph.D thesis, Delft University of Technology, 2002. |
[18] |
K. Vermeer, F. Vos, H. Lemij and A. Vossepoel, A model based method for retinal blood vessel detection, Computers in Biology and Medecine, 34 (2004), 209-219.
doi: 10.1016/S0010-4825(03)00055-6. |
show all references
References:
[1] |
E. J. Candès, "Ridgelets: Theory and Applications," Ph.D. Thesis, Department of Statistics, Stanford University, 1998. |
[2] |
E. J. Candès and D. L. Donoho, Curvelets-a surprisingly effective nonadaptive representation for objects with edges, in "Curves and Surfaces," Vanderbilt University Press, Nashville, TN, 1999. |
[3] |
E. J. Candès and D. L. Donoho, New tight frames of curvelets and optimal representations of objects with piecewise $C^2$ singularities, Comm. on Pure and Appl. Math., 57 (2004), 219-266. |
[4] |
E. J. Candès and J. Romberg, Practical signal recovery from random projections, Wavelet Applications in Signal and Image Processing XI, Proc. SPIE Conf. 5914, 2004. |
[5] |
A. Faridani, E. Ritman, K. Smith and T. Kennan, Local tomography, SIAM, J. Appl. Math., 52 (1992), 459-484.
doi: 10.1137/0152026. |
[6] |
A. Faridani, D. Finch, E. Ritman, K. Smith and T. Kennan, Local tomography II, SIAM, J. Appl. Math., 57 (1997), 1095-1127.
doi: 10.1137/S0036139995286357. |
[7] |
L. Gang, O. Chutape and M. Krishnan, Detection and measurement of retinal vessels in fundus images using amplitude modified second-order gaussian filter, IEEE Transactions on Biomedical Engineering, 49 (2002), 168-172.
doi: 10.1109/10.979356. |
[8] |
A. Hoover, V. Kouznetsova and M. Goldbaum, Locating blood vessels in retinal images by piecewise threshold probing of a matched filter response, IEEE Transactions on Medical Imaging, 19 (2000), 203-210. |
[9] |
M. Krause, R. M. Alles, B. Burgeth and J. Weickert, Retinal vessel detection via second derivative of local Radon transform, Technical Report No. 212, Universität des Saarlandes, 2009. |
[10] |
M. Krause, J. M. Hausherr, B. Burgeth, C. Herrmann and W. Krenkel, Determination of the fibre orientation in composites using the structure tensor and local X-ray transform, Journal of Materials Science, 45 (2010), 888-896.
doi: 10.1007/s10853-009-4016-4. |
[11] |
A. K. Louis, Approximate inverse for linear and some nonlinear problems, Inverse Problems, 12 (1996), 175-190. |
[12] |
A. K. Louis, Combining image reconstruction and image analysis with an application to two-dimensional tomography, SIAM J. Imaging Sciences, 1 (2008), 188-208.
doi: 10.1137/070700863. |
[13] |
A. K. Louis, Diffusion reconstruction from very noisy tomographic data, Inverse Problems and Imaging, 4 (2010), 675-683.
doi: 10.3934/ipi.2010.4.675. |
[14] |
F. Natterer, "The Mathematics of Computerized Tomography," B. G. Teubner, Stuttgart, John Wiley & Sons, Ltd., Chichester, 1986. |
[15] |
A. Rieder, R. Dietz and T. Schuster, Approximate inverse meets local tomography, Math. Meth. Appl. Sci., 23 (2000), 1373-1387.
doi: 10.1002/1099-1476(200010)23:15<1373::AID-MMA170>3.0.CO;2-A. |
[16] |
M. Sofka and C. Stewart, Retinal vessel centerline extraction using multiscale matched filters, confidence and edge measures, IEEE Transactions on Medical Imaging, 25 (2006), 1531-1546. |
[17] |
M. Van Ginkel, "Image Analysis Using Orientation Space Based on Steerable Filters," Ph.D thesis, Delft University of Technology, 2002. |
[18] |
K. Vermeer, F. Vos, H. Lemij and A. Vossepoel, A model based method for retinal blood vessel detection, Computers in Biology and Medecine, 34 (2004), 209-219.
doi: 10.1016/S0010-4825(03)00055-6. |
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