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Dynamic linear inverse problems with moderate movements of the object: Ill-posedness and regularization
1. | Tufts University, Department of Mathematics, Medford, MA 02155, United States |
References:
[1] |
D. Atkinson, D. L. Hill, P. N. Stoyle, P. E. Summers, S. Clare, R. Bowtell and S. F. Keevil, Automatic compensation of motion artefacts in MRI, Magn. Reson. Med., 41 (1999), 163-170.
doi: 10.1002/(SICI)1522-2594(199901)41:1<163::AID-MRM23>3.3.CO;2-0. |
[2] |
L. Desbat, S. Roux and P. Grangeat, Compensation of some time dependent deformations in tomography, IEEE Trans. Med. Imag., 26 (2007), 261-269.
doi: 10.1109/TMI.2006.889743. |
[3] |
H. W. Engl and C. W. Groetsch, Inverse and Ill-Posed Problems, Academic Press, New York, 1986. |
[4] |
J. Fitzgerald and P.G. Danias, Effect of motion on cardiac SPECT imaging: Recognition and motion correction, J. Nucl. Cardiol., 8 (2001), 701-706.
doi: 10.1067/mnc.2001.118694. |
[5] |
F. Gigengack, L. Ruthotto, M. Burger, C. H. Wolters, X. Jiang and K. P. Schäfers, Motion correction in dual gated cardiac PET using mass-preserving image registration, IEEE Trans. Med. Imag., 31 (2012), 698-712.
doi: 10.1109/TMI.2011.2175402. |
[6] |
G. H. Glover and J. M. Pauly, Projection Reconstruction Techniques for reduction of motion effects in MRI, Mag. Reson. Med., 28 (1992), 275-289.
doi: 10.1002/mrm.1910280209. |
[7] |
B. Hahn, Reconstruction of dynamic objects with affine deformations in dynamic computerized tomography, J. Inverse Ill-Posed Probl., 22 (2014), 323-339.
doi: 10.1515/jip-2012-0094. |
[8] |
B. N. Hahn, Efficient algorithms for linear dynamic inverse problems with known motion, Inverse Problems, 30 (2014), 035008, 20pp.
doi: 10.1088/0266-5611/30/3/035008. |
[9] |
B. Hofmann, Regularization for Applied Inverse and Ill-posed Problems, Teubner, Leipzig, 1986.
doi: 10.1007/978-3-322-93034-7. |
[10] |
A. Katsevich, An accurate approximate algorithm for motion compensation in two-dimensional tomography, Inverse Problems, 26 (2010), 065007, 16pp.
doi: 10.1088/0266-5611/26/6/065007. |
[11] |
A. Katsevich, M. Silver and A. Zamayatin, Local tomography and the motion estimation problem, SIAM J. Imaging Sci., 4 (2011), 200-219.
doi: 10.1137/100796728. |
[12] |
S. Kindermann and A. Leitão, On regularization methods for inverse problems of dynamic type, Numer. Func. Anal. Opt., 27 (2006), 139-160.
doi: 10.1080/01630560600569973. |
[13] |
D. Le Bihan, C. Poupon, A. Amadon and F. Lethimonnier, Artifacts and pitfalls in diffusion MRI, JMRI - J. Magn. Reson. Im., 24 (2006), 478-488. |
[14] |
A. K. Louis, Inverse und Schlecht Gestellte Probleme, Teubner, Stuttgart, 1989.
doi: 10.1007/978-3-322-84808-6. |
[15] |
A. K. Louis, Diffusion reconstruction from very noisy tomographic data, Inverse Probl. Imagine, 4 (2010), 675-683.
doi: 10.3934/ipi.2010.4.675. |
[16] |
W. Lu and T. R. Mackie, Tomographic motion detection and correction directly in sinogram space, Phys. Med. Biol., 47 (2002), 1267-1284.
doi: 10.1088/0031-9155/47/8/304. |
[17] |
S. J. McQuaid and B. F. Hutton, Sources of attenuation-correction artefacts in cardiac PET/CT and SPECT/CT, Eur. J. Nucl. Med. Mol. Imaging, 35 (2008), 1117-1123.
doi: 10.1007/s00259-008-0718-0. |
[18] |
J. L. Müller and S. Siltanen, Linear and Nonlinear Inverse Problems with Practical Applications, SIAM, Philadelphia, 2012. |
[19] |
F. Natterer, The Mathematics of Computerized Tomography, John Wiley & Sons, Chichester, 1986. |
[20] |
F. Qiao, T. Pan, J. W. Clark, O. R. Mawlawi, A motion-incorporated reconstruction method for gated PET studies, Phys. Med. Biol., 51 (2006), 3769-3783.
doi: 10.1088/0031-9155/51/15/012. |
[21] |
U. Schmitt and A. K. Louis, Efficient algorithms for the regularization of dynamic inverse problems: I. Theory, Inverse Problems, 18 (2002), 645-658.
doi: 10.1088/0266-5611/18/3/308. |
[22] |
U. Schmitt, A. K. Louis, C. Wolters and M. Vauhkonen, Efficient algorithms for the regularization of dynamic inverse problems: II. Applications, Inverse Problems, 18 (2002), 659-676.
doi: 10.1088/0266-5611/18/3/309. |
[23] |
A. Shankaranarayanan, M. Wendt, J. S. Lewin and J. L. Duerk, Two-step navigatorless correction algorithm for radial k-space MRI acquisitions, Magn. Reson. Med., 45 (2001), 277-288. |
[24] |
L. Shepp, S. Hilal and R. Schulz, The tuning fork artifact in computerized tomography, Comput. Graph. Image Process., 10 (1979), 246-255.
doi: 10.1016/0146-664X(79)90004-2. |
show all references
References:
[1] |
D. Atkinson, D. L. Hill, P. N. Stoyle, P. E. Summers, S. Clare, R. Bowtell and S. F. Keevil, Automatic compensation of motion artefacts in MRI, Magn. Reson. Med., 41 (1999), 163-170.
doi: 10.1002/(SICI)1522-2594(199901)41:1<163::AID-MRM23>3.3.CO;2-0. |
[2] |
L. Desbat, S. Roux and P. Grangeat, Compensation of some time dependent deformations in tomography, IEEE Trans. Med. Imag., 26 (2007), 261-269.
doi: 10.1109/TMI.2006.889743. |
[3] |
H. W. Engl and C. W. Groetsch, Inverse and Ill-Posed Problems, Academic Press, New York, 1986. |
[4] |
J. Fitzgerald and P.G. Danias, Effect of motion on cardiac SPECT imaging: Recognition and motion correction, J. Nucl. Cardiol., 8 (2001), 701-706.
doi: 10.1067/mnc.2001.118694. |
[5] |
F. Gigengack, L. Ruthotto, M. Burger, C. H. Wolters, X. Jiang and K. P. Schäfers, Motion correction in dual gated cardiac PET using mass-preserving image registration, IEEE Trans. Med. Imag., 31 (2012), 698-712.
doi: 10.1109/TMI.2011.2175402. |
[6] |
G. H. Glover and J. M. Pauly, Projection Reconstruction Techniques for reduction of motion effects in MRI, Mag. Reson. Med., 28 (1992), 275-289.
doi: 10.1002/mrm.1910280209. |
[7] |
B. Hahn, Reconstruction of dynamic objects with affine deformations in dynamic computerized tomography, J. Inverse Ill-Posed Probl., 22 (2014), 323-339.
doi: 10.1515/jip-2012-0094. |
[8] |
B. N. Hahn, Efficient algorithms for linear dynamic inverse problems with known motion, Inverse Problems, 30 (2014), 035008, 20pp.
doi: 10.1088/0266-5611/30/3/035008. |
[9] |
B. Hofmann, Regularization for Applied Inverse and Ill-posed Problems, Teubner, Leipzig, 1986.
doi: 10.1007/978-3-322-93034-7. |
[10] |
A. Katsevich, An accurate approximate algorithm for motion compensation in two-dimensional tomography, Inverse Problems, 26 (2010), 065007, 16pp.
doi: 10.1088/0266-5611/26/6/065007. |
[11] |
A. Katsevich, M. Silver and A. Zamayatin, Local tomography and the motion estimation problem, SIAM J. Imaging Sci., 4 (2011), 200-219.
doi: 10.1137/100796728. |
[12] |
S. Kindermann and A. Leitão, On regularization methods for inverse problems of dynamic type, Numer. Func. Anal. Opt., 27 (2006), 139-160.
doi: 10.1080/01630560600569973. |
[13] |
D. Le Bihan, C. Poupon, A. Amadon and F. Lethimonnier, Artifacts and pitfalls in diffusion MRI, JMRI - J. Magn. Reson. Im., 24 (2006), 478-488. |
[14] |
A. K. Louis, Inverse und Schlecht Gestellte Probleme, Teubner, Stuttgart, 1989.
doi: 10.1007/978-3-322-84808-6. |
[15] |
A. K. Louis, Diffusion reconstruction from very noisy tomographic data, Inverse Probl. Imagine, 4 (2010), 675-683.
doi: 10.3934/ipi.2010.4.675. |
[16] |
W. Lu and T. R. Mackie, Tomographic motion detection and correction directly in sinogram space, Phys. Med. Biol., 47 (2002), 1267-1284.
doi: 10.1088/0031-9155/47/8/304. |
[17] |
S. J. McQuaid and B. F. Hutton, Sources of attenuation-correction artefacts in cardiac PET/CT and SPECT/CT, Eur. J. Nucl. Med. Mol. Imaging, 35 (2008), 1117-1123.
doi: 10.1007/s00259-008-0718-0. |
[18] |
J. L. Müller and S. Siltanen, Linear and Nonlinear Inverse Problems with Practical Applications, SIAM, Philadelphia, 2012. |
[19] |
F. Natterer, The Mathematics of Computerized Tomography, John Wiley & Sons, Chichester, 1986. |
[20] |
F. Qiao, T. Pan, J. W. Clark, O. R. Mawlawi, A motion-incorporated reconstruction method for gated PET studies, Phys. Med. Biol., 51 (2006), 3769-3783.
doi: 10.1088/0031-9155/51/15/012. |
[21] |
U. Schmitt and A. K. Louis, Efficient algorithms for the regularization of dynamic inverse problems: I. Theory, Inverse Problems, 18 (2002), 645-658.
doi: 10.1088/0266-5611/18/3/308. |
[22] |
U. Schmitt, A. K. Louis, C. Wolters and M. Vauhkonen, Efficient algorithms for the regularization of dynamic inverse problems: II. Applications, Inverse Problems, 18 (2002), 659-676.
doi: 10.1088/0266-5611/18/3/309. |
[23] |
A. Shankaranarayanan, M. Wendt, J. S. Lewin and J. L. Duerk, Two-step navigatorless correction algorithm for radial k-space MRI acquisitions, Magn. Reson. Med., 45 (2001), 277-288. |
[24] |
L. Shepp, S. Hilal and R. Schulz, The tuning fork artifact in computerized tomography, Comput. Graph. Image Process., 10 (1979), 246-255.
doi: 10.1016/0146-664X(79)90004-2. |
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