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Two-phase approach for deblurring images corrupted by impulse plus gaussian noise
A nonstandard smoothing in reconstruction of apparent diffusion coefficient profiles from diffusion weighted images
1. | Department of Mathematics, University of Florida, Gainesville, FL 32611, United States, United States |
2. | Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487, United States |
3. | Department of Psychiatry & Neuroscience, University of Florida, Gainesville, FL 32653, United States |
References:
[1] |
D. LeBihan and P. J. Basser, Molecular diffusion and nuclear magnetic resonance, Diffusion and perfusion magnetic resonance imaging, 1995. |
[2] |
M. E. Moseley, Y. Cohen, J. Mintorovitch, J. L. Chileuitt, D. Norman and P. Weinstein, Evidence of anisotropic self-diffusion in cat brain, Proc. of the 8th ISMRM, (1989), 136-136. |
[3] |
M. E. Moseley, J. Kucharczyk, H. S. Asgari and D. Norman, Anisotropy in diffusion weighted MRI, Magn. Reson. Med., 19 (1991), 321-326.
doi: 10.1002/mrm.1910190222. |
[4] |
P. J. Basser and C. Pierpaoli, Microstructual and physiological features of tissues elucidated by quantitative diffusion tensor {MRI}, Magn. Reson. Med., 111(B) 1996, 209-219. |
[5] |
E. O. Stejskal and J. E. Tanner, Spin diffusion measurements: Spin echoes in the presence of a time-dependent field gradient, Chem. Phys., 42 (1965), 288-292. |
[6] |
P. J. Basser, J. Mattiello and D. LeBihan, MR diffusion tensor spectroscopy and imaging, Biophys, 66 1994, 259-267.
doi: 10.1016/S0006-3495(94)80775-1. |
[7] |
D. S. Tuch, R. M. Weisskoff, J. W. Belliveau and V. J. Wedeen, High angular resolution diffusion imaging of the human brain, Proc. of the 7th ISMRM, (1999), 321-321. |
[8] |
V. J. Wedeen, T. G. Reese, D. S. Tuch, M. R. Weigel, J.-G. Dou, R. M. Weisskoff and D. Chesler, Mapping fiber orientation spectra in cerebral white matter with fourier transform diffusion {MRI}, Proc. of the 8th ISMRM, (2000), 82-82. |
[9] |
P. J. Basser, J. Mattiello and D. Lebihan, Estimation of the effective self-diffusion tensor from the NMR, Spin Echo. J. Magn. Reson., series B, 103 (1994), 247-254. |
[10] |
T. L. Chenevert, J. A. Brunberg and J. G. Pipe, Anisotropic diffusion in human white matter: demonstration with MR techniques in vivo, Radiology, 177 (1990), 401-405. |
[11] |
E. W. Hsu and S. Mori, Analytical expression for the NMR apparent diffusion coefficients in an anisotropy system and a simplified method for determing fiber orientation, Magn. Reson. Med., 34 (1995), 194-200.
doi: 10.1002/mrm.1910340210. |
[12] |
L. Frank, Characterization of anisotropy in high angular resolution diffusion weighted mri, in "Proc. of 9th ISMRM," Glasgow, Scotland, (2001). |
[13] |
A. L. Alexander, K. M. Hasan, M. Lazar, J. S. Tsuruda and D. L. Parker, Analysis of partial volume effects in diffusion-tensor MRI, Magn. Reson. Med., 45 (2001), 770-780.
doi: 10.1002/mrm.1105. |
[14] |
L. Frank, Anisotropy in high angular resolution diffusion-weighted MRI, Magn. Reson. Med., 45 (2001), 935-939.
doi: 10.1002/mrm.1125. |
[15] |
D. C. Alexander, G. J. Barker and S. R. Arridge, Detection and modeling of non-Gaussian apparent diffusion coefficient profiles in human brain data, Magn. Reson. Med., 48 (2002), 331-340.
doi: 10.1002/mrm.10209. |
[16] |
Y. Chen, W. Guo, Q. Zeng, X. Yan, F. Huang, H. Zhang, G. He, B. Vemuri and Y. Liu, Estimation, smoothing, and charaterization of apparent diffusion coefficient profiles from high angular resolution DWI, Proc. of CVPR, (2004), 588-593. |
[17] |
L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithm, Physica D, 60 (1992), 259-268.
doi: 10.1016/0167-2789(92)90242-F. |
[18] |
P. Blomgren, T. Chan, P. Mulet and C. K. Wong, Total variation image restoration: Numerical methods and extensions, Proceeding of IEEE Int'l Conference on Image Processing, 3 (1997), 384-387. |
[19] |
A. Chambolle and P-L.Lions, Image recovery via total variation minimization and related problems, Numerische Mathematik, 76 (1997), 167-188.
doi: 10.1007/s002110050258. |
[20] |
Y. Chen, S. Levine and M. Rao, Variable exponent, linear growth functionals in image restoration, SIAM Journal of AMath., 66 (2006), 1383-1406.
doi: 10.1137/050624522. |
[21] |
P. Blomgren and T. Chan, Color TV: total variation methods for restoration of vector-valued images, IEEE Trans. on Image Processing, 7 (1998), 304-309.
doi: 10.1109/83.661180. |
[22] |
Z. Wang, B. C. Vemuri, Y. Chen and T. Mareci, A constrained variational principle for direct estimation and smoothing of the tensor field from complex DWI, IEEE TMI, 23 (2004), 930-939. |
[23] |
J. Weickert, B. Romeny and M. Viergever, Efficient and reliable schemes for nonlinear diffusion filtering, IEEE Trans. on Img. Proc., 7 (1998), 398-410. |
[24] |
T. Lu, P. Neittaanm and X. Tai, A parallel splitting up method and its application to Navier-Stokes equations, Applied Mathematics Letters, 4 (1991), 25-29.
doi: 10.1016/0893-9659(91)90161-N. |
[25] |
T. F. Chan and L. A. Vese, Active contours without edges, IEEE Trans. Image Processing, 10 (2001), 266-277.
doi: 10.1109/83.902291. |
[26] |
S. D. Conte and C. DeBoor, "Elementary Numerical Analysis," McGraw-Hill, New York, 1972. |
show all references
References:
[1] |
D. LeBihan and P. J. Basser, Molecular diffusion and nuclear magnetic resonance, Diffusion and perfusion magnetic resonance imaging, 1995. |
[2] |
M. E. Moseley, Y. Cohen, J. Mintorovitch, J. L. Chileuitt, D. Norman and P. Weinstein, Evidence of anisotropic self-diffusion in cat brain, Proc. of the 8th ISMRM, (1989), 136-136. |
[3] |
M. E. Moseley, J. Kucharczyk, H. S. Asgari and D. Norman, Anisotropy in diffusion weighted MRI, Magn. Reson. Med., 19 (1991), 321-326.
doi: 10.1002/mrm.1910190222. |
[4] |
P. J. Basser and C. Pierpaoli, Microstructual and physiological features of tissues elucidated by quantitative diffusion tensor {MRI}, Magn. Reson. Med., 111(B) 1996, 209-219. |
[5] |
E. O. Stejskal and J. E. Tanner, Spin diffusion measurements: Spin echoes in the presence of a time-dependent field gradient, Chem. Phys., 42 (1965), 288-292. |
[6] |
P. J. Basser, J. Mattiello and D. LeBihan, MR diffusion tensor spectroscopy and imaging, Biophys, 66 1994, 259-267.
doi: 10.1016/S0006-3495(94)80775-1. |
[7] |
D. S. Tuch, R. M. Weisskoff, J. W. Belliveau and V. J. Wedeen, High angular resolution diffusion imaging of the human brain, Proc. of the 7th ISMRM, (1999), 321-321. |
[8] |
V. J. Wedeen, T. G. Reese, D. S. Tuch, M. R. Weigel, J.-G. Dou, R. M. Weisskoff and D. Chesler, Mapping fiber orientation spectra in cerebral white matter with fourier transform diffusion {MRI}, Proc. of the 8th ISMRM, (2000), 82-82. |
[9] |
P. J. Basser, J. Mattiello and D. Lebihan, Estimation of the effective self-diffusion tensor from the NMR, Spin Echo. J. Magn. Reson., series B, 103 (1994), 247-254. |
[10] |
T. L. Chenevert, J. A. Brunberg and J. G. Pipe, Anisotropic diffusion in human white matter: demonstration with MR techniques in vivo, Radiology, 177 (1990), 401-405. |
[11] |
E. W. Hsu and S. Mori, Analytical expression for the NMR apparent diffusion coefficients in an anisotropy system and a simplified method for determing fiber orientation, Magn. Reson. Med., 34 (1995), 194-200.
doi: 10.1002/mrm.1910340210. |
[12] |
L. Frank, Characterization of anisotropy in high angular resolution diffusion weighted mri, in "Proc. of 9th ISMRM," Glasgow, Scotland, (2001). |
[13] |
A. L. Alexander, K. M. Hasan, M. Lazar, J. S. Tsuruda and D. L. Parker, Analysis of partial volume effects in diffusion-tensor MRI, Magn. Reson. Med., 45 (2001), 770-780.
doi: 10.1002/mrm.1105. |
[14] |
L. Frank, Anisotropy in high angular resolution diffusion-weighted MRI, Magn. Reson. Med., 45 (2001), 935-939.
doi: 10.1002/mrm.1125. |
[15] |
D. C. Alexander, G. J. Barker and S. R. Arridge, Detection and modeling of non-Gaussian apparent diffusion coefficient profiles in human brain data, Magn. Reson. Med., 48 (2002), 331-340.
doi: 10.1002/mrm.10209. |
[16] |
Y. Chen, W. Guo, Q. Zeng, X. Yan, F. Huang, H. Zhang, G. He, B. Vemuri and Y. Liu, Estimation, smoothing, and charaterization of apparent diffusion coefficient profiles from high angular resolution DWI, Proc. of CVPR, (2004), 588-593. |
[17] |
L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithm, Physica D, 60 (1992), 259-268.
doi: 10.1016/0167-2789(92)90242-F. |
[18] |
P. Blomgren, T. Chan, P. Mulet and C. K. Wong, Total variation image restoration: Numerical methods and extensions, Proceeding of IEEE Int'l Conference on Image Processing, 3 (1997), 384-387. |
[19] |
A. Chambolle and P-L.Lions, Image recovery via total variation minimization and related problems, Numerische Mathematik, 76 (1997), 167-188.
doi: 10.1007/s002110050258. |
[20] |
Y. Chen, S. Levine and M. Rao, Variable exponent, linear growth functionals in image restoration, SIAM Journal of AMath., 66 (2006), 1383-1406.
doi: 10.1137/050624522. |
[21] |
P. Blomgren and T. Chan, Color TV: total variation methods for restoration of vector-valued images, IEEE Trans. on Image Processing, 7 (1998), 304-309.
doi: 10.1109/83.661180. |
[22] |
Z. Wang, B. C. Vemuri, Y. Chen and T. Mareci, A constrained variational principle for direct estimation and smoothing of the tensor field from complex DWI, IEEE TMI, 23 (2004), 930-939. |
[23] |
J. Weickert, B. Romeny and M. Viergever, Efficient and reliable schemes for nonlinear diffusion filtering, IEEE Trans. on Img. Proc., 7 (1998), 398-410. |
[24] |
T. Lu, P. Neittaanm and X. Tai, A parallel splitting up method and its application to Navier-Stokes equations, Applied Mathematics Letters, 4 (1991), 25-29.
doi: 10.1016/0893-9659(91)90161-N. |
[25] |
T. F. Chan and L. A. Vese, Active contours without edges, IEEE Trans. Image Processing, 10 (2001), 266-277.
doi: 10.1109/83.902291. |
[26] |
S. D. Conte and C. DeBoor, "Elementary Numerical Analysis," McGraw-Hill, New York, 1972. |
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