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Empirical average-case relation between undersampling and sparsity in X-ray CT
4D-CT reconstruction with unified spatial-temporal patch-based regularization
1. | The Manchester X-ray Imaging Facility, School of Materials, The University of Manchester, Manchester, M13 9PL, United Kingdom, United Kingdom, United Kingdom, United Kingdom |
2. | School of Mathematics, The University of Manchester, Alan Turing Building, Manchester, M13 9PL, United Kingdom, United Kingdom |
3. | iMinds-Vision Lab, The University of Antwerp, Wilrijk, B-2610, Belgium |
4. | Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut (PSI), Villigen, 5232, Switzerland |
References:
[1] |
S. Bougleux, G. Peyre and L. Cohen, Non-local regularization of inverse problems, Inverse Probl. Imaging, 5 (2011), 511-530.
doi: 10.3934/ipi.2011.5.511. |
[2] |
K. S. Brown, S. Schluter, A. Sheppard and D. Wildenschild, On the challenges of measuring interfacial characteristics of three-phase fluid flow with x-ray microtomography, Journal of Microscopy, 253 (2014), 171-182.
doi: 10.1111/jmi.12106. |
[3] |
A. Buades, B. Coll and J. M. Morel, A review of image denoising algorithms with a new one, Multiscale Model. Simul., 4 (2005), 490-530.
doi: 10.1137/040616024. |
[4] |
C. L. Byrne, Applied Iterative Methods, Natick, MA: Peters, 2008.
doi: 10.1201/b10651. |
[5] |
P. L. Combettes and J.-C. Pesquet, Proximal splitting methods in signal processing, in Fixed-Point Algorithms for Inverse Problems in Science and Engineering, Springer Optim. Appl., {49}, Springer, New York, 2011, 185-212.
doi: 10.1007/978-1-4419-9569-8_10. |
[6] |
H. Gao, J-F. Cai, Z. Shen and H. Zhao, Robust principal component analysis-based four-dimensional computed tomography, Phys Med. Biol., 56 (2011), 3181-3198.
doi: 10.1088/0031-9155/56/11/002. |
[7] |
X. Jia, Y. Lou, B. Dong, Z. Tian and S. Jiang, 4D computed tomography reconstruction from few-projection data via temporal non-local regularization, in Medical Image Computing and Computer-Assisted Intervention - MICCAI 2010, Lecture Notes in Computer Science, 6361, Springer, Berlin-Heidelberg, 2010, 143-150.
doi: 10.1007/978-3-642-15705-9_18. |
[8] |
A. P. Kaestner, S. Hartmann, G. Kuhne, G. Frei, C. Grunzweig, L. Josic, F. Schmid and E. H. Lehmann, The ICON beamline - a facility for cold neutron imaging at SINQ, Nuclear Instruments and Methods in Physics Research, 659 (2011), 387-393.
doi: 10.1016/j.nima.2011.08.022. |
[9] |
A. P. Kaestner, B. Muench, P. Trtik and L. G. Butler, Spatio-temporal computed tomography of dynamic processes, SPIE Optical Engineering, 50 (2011), 1-10. |
[10] |
J. Kaipio and E. Somersalo, Statistical inverse problems: discretization, model reduction and inverse crimes, Journal of Computational and Applied Mathematics, 198 (2007), 493-504.
doi: 10.1016/j.cam.2005.09.027. |
[11] |
A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging, IEEE Press, New York, 1998.
doi: 10.1137/1.9780898719277. |
[12] |
D. Kazantsev, W. R. B. Lionheart, P. J. Withers and P. D. Lee, GPU accelerated 4D-CT reconstruction using higher order PDE regularization in spatial and temporal domains, in Proc. CMSSE, 3, Almeria, Spain, 2013, 843-852. |
[13] |
D. Kazantsev, S. R. Arridge, S. Pedemonte, A. Bousse, K. Erlandsson, B. F. Hutton and S. Ourselin, An anatomically driven anisotropic diffusion filtering method for 3D SPECT reconstruction, Phys Med. Biol., 57 (2012), 3793-3810.
doi: 10.1088/0031-9155/57/12/3793. |
[14] |
T. Kohler, A projection access scheme for iterative reconstruction based on the golden section, in IEEE Symposium Conference Record Nuclear Science 2004, Vol. 6, IEEE, 2004, 3961-3965.
doi: 10.1109/NSSMIC.2004.1466745. |
[15] |
D. S. Lalush and M. N. Wernick, Iterative image reconstruction, in Emission Tomography (ed. Mark T. Madsen), Academic Press, 2004, 443-472.
doi: 10.1016/B978-012744482-6/50024-7. |
[16] |
D. S. Lalush and B. M. W. Tsui, Block-iterative techniques for fast 4D reconstruction using a priori motion models in gated cardiac SPECT, Phys Med. Biol., 43 (1998), 875-886.
doi: 10.1088/0031-9155/43/4/015. |
[17] |
S. Z. Li, Markov Random Field Modeling in Image Analysis, Springer, 2009.
doi: 10.1007/978-1-84800-279-1. |
[18] |
J. Nocedal and S. Wright, Numerical Optimization, Springer, 2006.
doi: 10.1007/978-0-387-40065-5. |
[19] |
W. J. Palenstijn, K. J. Batenburg and J. Sijbers, Performance improvements for iterative electron tomography reconstruction using graphics processing units (GPUs), J. of Struct. Biol., 176 (2011), 250-253.
doi: 10.1016/j.jsb.2011.07.017. |
[20] |
, PB regularization package (open-source code),, , ().
|
[21] |
K. Perlin, Improving noise, ACM T. Graphic., 21 (2002), 681-682.
doi: 10.1145/566654.566636. |
[22] |
J. Qi and R. M. Leahy, Iterative reconstruction techniques in emission computed tomography, Phys Med. Biol., 51 (2006), R541-R578.
doi: 10.1088/0031-9155/51/15/R01. |
[23] |
A. Rahmim, J. Tang and H. Zaidi, Four-dimensional (4D) image reconstruction strategies in dynamic PET: Beyond conventional independent frame reconstruction, Med. Phys., 36 (2009), 3654-3670.
doi: 10.1118/1.3160108. |
[24] |
L. Ritschl, S. Sawall, M. Knaup, A. Hess and M. Kachelrieß, Iterative 4D cardiac micro-CT image reconstruction using an adaptive spatio-temporal sparsity prior, Phys Med. Biol., 57 (2012), 1517-1526.
doi: 10.1088/0031-9155/57/6/1517. |
[25] |
L. I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D., 60 (1992), 259-268.
doi: 10.1016/0167-2789(92)90242-F. |
[26] |
M. Strobl, I. Manke, N. Kardjilov, A. Hilger, M. Dawson and J. Banhart, Advances in neutron radiography and tomography, J. Phys. D: Appl. Phys., 42 (2009), 1-21.
doi: 10.1088/0022-3727/42/24/243001. |
[27] |
W. M. Thompson, W. R. Lionheart and E. J. Morton, Real-Time Imaging with a high speed X-Ray CT system, in Proc. 6th International Symposium on Process Tomography, 2012. |
[28] |
G. Van Eyndhoven, K. J. Batenburg and J. Sijbers, Region-based iterative reconstruction of structurally changing objects in CT, IEEE Trans. on Image Process, 23 (2014), 909-919.
doi: 10.1109/TIP.2013.2297024. |
[29] |
H. Wu, A. Maier, R. Fahrig and J. Hornegger, Spatial-temporal total variation regularization (STTVR) for 4D-CT reconstruction, Proc. SPIE, 8313 (2012), 237-240.
doi: 10.1117/12.911162. |
[30] |
G. Wang and J. Qi, Penalized likelihood PET image reconstruction using patch-based edge-preserving regularization, IEEE Transactions on Medical Imaging, 31 (2012), 2194-2204.
doi: 10.1109/tmi.2012.2211378. |
[31] |
Z. Yang and M. Jacob, Nonlocal regularization of inverse problems: A unified variational framework, IEEE Trans. on Image Process, 22 (2013), 3192-3203.
doi: 10.1109/tip.2012.2216278. |
[32] |
Z. Yang and M. Jacob, Robust non-local regularization framework for motion compensated dynamic imaging without explicit motion estimation, in 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI), 2012, 1056-1059.
doi: 10.1109/ISBI.2012.6235740. |
show all references
References:
[1] |
S. Bougleux, G. Peyre and L. Cohen, Non-local regularization of inverse problems, Inverse Probl. Imaging, 5 (2011), 511-530.
doi: 10.3934/ipi.2011.5.511. |
[2] |
K. S. Brown, S. Schluter, A. Sheppard and D. Wildenschild, On the challenges of measuring interfacial characteristics of three-phase fluid flow with x-ray microtomography, Journal of Microscopy, 253 (2014), 171-182.
doi: 10.1111/jmi.12106. |
[3] |
A. Buades, B. Coll and J. M. Morel, A review of image denoising algorithms with a new one, Multiscale Model. Simul., 4 (2005), 490-530.
doi: 10.1137/040616024. |
[4] |
C. L. Byrne, Applied Iterative Methods, Natick, MA: Peters, 2008.
doi: 10.1201/b10651. |
[5] |
P. L. Combettes and J.-C. Pesquet, Proximal splitting methods in signal processing, in Fixed-Point Algorithms for Inverse Problems in Science and Engineering, Springer Optim. Appl., {49}, Springer, New York, 2011, 185-212.
doi: 10.1007/978-1-4419-9569-8_10. |
[6] |
H. Gao, J-F. Cai, Z. Shen and H. Zhao, Robust principal component analysis-based four-dimensional computed tomography, Phys Med. Biol., 56 (2011), 3181-3198.
doi: 10.1088/0031-9155/56/11/002. |
[7] |
X. Jia, Y. Lou, B. Dong, Z. Tian and S. Jiang, 4D computed tomography reconstruction from few-projection data via temporal non-local regularization, in Medical Image Computing and Computer-Assisted Intervention - MICCAI 2010, Lecture Notes in Computer Science, 6361, Springer, Berlin-Heidelberg, 2010, 143-150.
doi: 10.1007/978-3-642-15705-9_18. |
[8] |
A. P. Kaestner, S. Hartmann, G. Kuhne, G. Frei, C. Grunzweig, L. Josic, F. Schmid and E. H. Lehmann, The ICON beamline - a facility for cold neutron imaging at SINQ, Nuclear Instruments and Methods in Physics Research, 659 (2011), 387-393.
doi: 10.1016/j.nima.2011.08.022. |
[9] |
A. P. Kaestner, B. Muench, P. Trtik and L. G. Butler, Spatio-temporal computed tomography of dynamic processes, SPIE Optical Engineering, 50 (2011), 1-10. |
[10] |
J. Kaipio and E. Somersalo, Statistical inverse problems: discretization, model reduction and inverse crimes, Journal of Computational and Applied Mathematics, 198 (2007), 493-504.
doi: 10.1016/j.cam.2005.09.027. |
[11] |
A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging, IEEE Press, New York, 1998.
doi: 10.1137/1.9780898719277. |
[12] |
D. Kazantsev, W. R. B. Lionheart, P. J. Withers and P. D. Lee, GPU accelerated 4D-CT reconstruction using higher order PDE regularization in spatial and temporal domains, in Proc. CMSSE, 3, Almeria, Spain, 2013, 843-852. |
[13] |
D. Kazantsev, S. R. Arridge, S. Pedemonte, A. Bousse, K. Erlandsson, B. F. Hutton and S. Ourselin, An anatomically driven anisotropic diffusion filtering method for 3D SPECT reconstruction, Phys Med. Biol., 57 (2012), 3793-3810.
doi: 10.1088/0031-9155/57/12/3793. |
[14] |
T. Kohler, A projection access scheme for iterative reconstruction based on the golden section, in IEEE Symposium Conference Record Nuclear Science 2004, Vol. 6, IEEE, 2004, 3961-3965.
doi: 10.1109/NSSMIC.2004.1466745. |
[15] |
D. S. Lalush and M. N. Wernick, Iterative image reconstruction, in Emission Tomography (ed. Mark T. Madsen), Academic Press, 2004, 443-472.
doi: 10.1016/B978-012744482-6/50024-7. |
[16] |
D. S. Lalush and B. M. W. Tsui, Block-iterative techniques for fast 4D reconstruction using a priori motion models in gated cardiac SPECT, Phys Med. Biol., 43 (1998), 875-886.
doi: 10.1088/0031-9155/43/4/015. |
[17] |
S. Z. Li, Markov Random Field Modeling in Image Analysis, Springer, 2009.
doi: 10.1007/978-1-84800-279-1. |
[18] |
J. Nocedal and S. Wright, Numerical Optimization, Springer, 2006.
doi: 10.1007/978-0-387-40065-5. |
[19] |
W. J. Palenstijn, K. J. Batenburg and J. Sijbers, Performance improvements for iterative electron tomography reconstruction using graphics processing units (GPUs), J. of Struct. Biol., 176 (2011), 250-253.
doi: 10.1016/j.jsb.2011.07.017. |
[20] |
, PB regularization package (open-source code),, , ().
|
[21] |
K. Perlin, Improving noise, ACM T. Graphic., 21 (2002), 681-682.
doi: 10.1145/566654.566636. |
[22] |
J. Qi and R. M. Leahy, Iterative reconstruction techniques in emission computed tomography, Phys Med. Biol., 51 (2006), R541-R578.
doi: 10.1088/0031-9155/51/15/R01. |
[23] |
A. Rahmim, J. Tang and H. Zaidi, Four-dimensional (4D) image reconstruction strategies in dynamic PET: Beyond conventional independent frame reconstruction, Med. Phys., 36 (2009), 3654-3670.
doi: 10.1118/1.3160108. |
[24] |
L. Ritschl, S. Sawall, M. Knaup, A. Hess and M. Kachelrieß, Iterative 4D cardiac micro-CT image reconstruction using an adaptive spatio-temporal sparsity prior, Phys Med. Biol., 57 (2012), 1517-1526.
doi: 10.1088/0031-9155/57/6/1517. |
[25] |
L. I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D., 60 (1992), 259-268.
doi: 10.1016/0167-2789(92)90242-F. |
[26] |
M. Strobl, I. Manke, N. Kardjilov, A. Hilger, M. Dawson and J. Banhart, Advances in neutron radiography and tomography, J. Phys. D: Appl. Phys., 42 (2009), 1-21.
doi: 10.1088/0022-3727/42/24/243001. |
[27] |
W. M. Thompson, W. R. Lionheart and E. J. Morton, Real-Time Imaging with a high speed X-Ray CT system, in Proc. 6th International Symposium on Process Tomography, 2012. |
[28] |
G. Van Eyndhoven, K. J. Batenburg and J. Sijbers, Region-based iterative reconstruction of structurally changing objects in CT, IEEE Trans. on Image Process, 23 (2014), 909-919.
doi: 10.1109/TIP.2013.2297024. |
[29] |
H. Wu, A. Maier, R. Fahrig and J. Hornegger, Spatial-temporal total variation regularization (STTVR) for 4D-CT reconstruction, Proc. SPIE, 8313 (2012), 237-240.
doi: 10.1117/12.911162. |
[30] |
G. Wang and J. Qi, Penalized likelihood PET image reconstruction using patch-based edge-preserving regularization, IEEE Transactions on Medical Imaging, 31 (2012), 2194-2204.
doi: 10.1109/tmi.2012.2211378. |
[31] |
Z. Yang and M. Jacob, Nonlocal regularization of inverse problems: A unified variational framework, IEEE Trans. on Image Process, 22 (2013), 3192-3203.
doi: 10.1109/tip.2012.2216278. |
[32] |
Z. Yang and M. Jacob, Robust non-local regularization framework for motion compensated dynamic imaging without explicit motion estimation, in 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI), 2012, 1056-1059.
doi: 10.1109/ISBI.2012.6235740. |
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