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Model-based reconstruction for magnetic particle imaging in 2D and 3D
1. | Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quater, Woodstock Road, Oxford OX2 6GG, United Kingdom |
2. | Department of Mathematics and Natural Sciences, Hochschule Darmstadt, Schöfferstraße 3, 64295 Darmstadt, Germany |
References:
[1] |
L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, vol. 254, Clarendon Press, Oxford, 2000. |
[2] |
M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging, CRC press, Boca Raton, 1998.
doi: 10.1887/0750304359. |
[3] |
F. Bornemann and T. März, Fast image inpainting based on coherence transport, Joural of Mathematical Imaging and Vision, 28 (2007), 259-278.
doi: 10.1007/s10851-007-0017-6. |
[4] |
S. Chikazumi and S. Charap, Physics of Magnetism, Krieger Publishing, New York, 1978. |
[5] |
H. Engl, M. Hanke and A. Neubauer, Regularization of Inverse Problems, Kluwer Academic Publishers, Dordrecht, 1996.
doi: 10.1007/978-94-009-1740-8. |
[6] |
R. Ferguson, K. Minard and K. Krishnan, Optimization of nanoparticle core size for magnetic particle imaging, Journal of Magnetism and Magnetic Materials, 321 (2009), 1548-1551.
doi: 10.1016/j.jmmm.2009.02.083. |
[7] |
B. Gleich and J. Weizenecker, Tomographic imaging using the nonlinear response of magnetic particles, Nature, 435 (2005), 1214-1217.
doi: 10.1038/nature03808. |
[8] |
B. Gleich, J. Weizenecker and J. Borgert, Experimental results on fast 2D-encoded magnetic particle imaging, Physics in Medicine and Biology, 53 (2008), N81-N84.
doi: 10.1088/0031-9155/53/6/N01. |
[9] |
G. Golub and C. Van Loan, Matrix Computations, JHU Press, 2012. |
[10] |
P. Goodwill and S. Conolly, The X-space formulation of the magnetic particle imaging process: 1-D signal, resolution, bandwidth, {SNR}, {SAR}, and magnetostimulation, IEEE Transactions on Medical Imaging, 29 (2010), 1851-1859.
doi: 10.1109/TMI.2010.2052284. |
[11] |
P. Goodwill and S. Conolly, Multidimensional X-space magnetic particle imaging, IEEE Transactions on Medical Imaging, 30 (2011), 1581-1590.
doi: 10.1109/TMI.2011.2125982. |
[12] |
P. Goodwill, E. Saritas, L. Croft, T. Kim, K. Krishnan, D. Schaffer and S. Conolly, X-space mpi: Magnetic nanoparticles for safe medical imaging, Advanced Materials, 24 (2012), 3870-3877.
doi: 10.1002/adma.201200221. |
[13] |
M. Grüttner, T. Knopp, J. Franke, M. Heidenreich, J. Rahmer, A. Halkola, C. Kaethner, J. Borgert and T. Buzug, On the formulation of the image reconstruction problem in magnetic particle imaging, Biomedical Engineering, 58 (2013), 583-591. |
[14] | |
[15] |
D. Jiles, Introduction to Magnetism and Magnetic Materials, CRC press, 1998. |
[16] |
A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems, vol. 120, Springer, Heidelberg, 2011.
doi: 10.1007/978-1-4419-8474-6. |
[17] |
T. Knopp and T. Buzug, Magnetic Particle Imaging: An Introduction to Imaging Principles and Scanner Instrumentation, Springer, 2012.
doi: 10.1007/978-3-642-04199-0. |
[18] |
T. Knopp, Effiziente Rekonstruktion und alternative Spulentopologien für Magnetic Particle Imaging, Dissertation, University of Lübeck, 2011.
doi: 10.1007/978-3-8348-8129-8. |
[19] |
T. Knopp, S. Biederer, T. Sattel, M. Erbe and T. Buzug, Prediction of the spatial resolution of magnetic particle imaging using the modulation transfer function of the imaging process, IEEE Transactions on Medical Imaging, 30 (2011), 1284-1292.
doi: 10.1109/TMI.2011.2113188. |
[20] |
T. Knopp, S. Biederer, T. Sattel, J. Rahmer, J. Weizenecker, B. Gleich, J. Borgert and T. Buzug, 2D model-based reconstruction for magnetic particle imaging, Medical Physics, 37 (2010), 485-491.
doi: 10.1118/1.3271258. |
[21] |
T. Knopp, M. Erbe, T. Sattel, S. Biederer and T. Buzug, A Fourier slice theorem for magnetic particle imaging using a field-free line, Inverse Problems, 27 (2011), 095004, 14pp.
doi: 10.1088/0266-5611/27/9/095004. |
[22] |
T. Knopp, J. Rahmer, T. Sattel, S. Biederer, J. Weizenecker, B. Gleich, J. Borgert and T. Buzug, Weighted iterative reconstruction for magnetic particle imaging, Physics in Medicine and Biology, 55 (2010), 1577-1589. |
[23] |
T. Knopp, T. Sattel, S. Biederer, J. Rahmer, J. Weizenecker, B. Gleich, J. Borgert and T. Buzug, Model-Based Reconstruction for magnetic particle imaging, IEEE Transactions on Medical Imaging, 29 (2010), 12-18. |
[24] |
J. Konkle, P. Goodwill and S. Conolly, Development of a field free line magnet for projection MPI, in SPIE Medical Imaging, 7965 (2011), 79650X.
doi: 10.1117/12.878435. |
[25] |
D. Kuhl and R. Edwards, Image separation radioisotope scanning, Radiology, 80 (1963), 653-662.
doi: 10.1148/80.4.653. |
[26] |
J. Lampe, C. Bassoy, J. Rahmer, J. Weizenecker, H. Voss, B. Gleich and J. Borgert, Fast reconstruction in magnetic particle imaging, Physics in Medicine and Biology, 57 (2012), 1113-1134.
doi: 10.1088/0031-9155/57/4/1113. |
[27] |
J. Lawrence, A Catalog of Special Plane Curves, Courier Corporation, 2013. |
[28] |
A. Louis, Inverse Und Schlecht Gestellte Probleme, Teubner, Stuttgart, 1989.
doi: 10.1007/978-3-322-84808-6. |
[29] |
T. März, Image inpainting based on coherence transport with adapted distance functions, SIAM Journal on Imaging Sciences, 4 (2011), 981-1000.
doi: 10.1137/100807296. |
[30] |
T. März, A well-posedness framework for inpainting based on coherence transport, Foundations of Computational Mathematics, 15 (2015), 973-1033.
doi: 10.1007/s10208-014-9199-7. |
[31] |
J. Rahmer, J. Weizenecker, B. Gleich and J. Borgert, Signal encoding in magnetic particle imaging: Properties of the system function, BMC Medical Imaging, 9 (2009), p4.
doi: 10.1186/1471-2342-9-4. |
[32] |
J. Rahmer, J. Weizenecker, B. Gleich and J. Borgert, Analysis of a 3-D system function measured for magnetic particle imaging, IEEE Transactions on Medical Imaging, 31 (2012), 1289-1299.
doi: 10.1109/TMI.2012.2188639. |
[33] |
L. 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. |
[34] |
E. Saritas, P. Goodwill, L. Croft, J. Konkle, K. Lu, B. Zheng and S. Conolly, Magnetic particle imaging (MPI) for NMR and MRI researchers, Journal of Magnetic Resonance, 229 (2013), 116-126.
doi: 10.1016/j.jmr.2012.11.029. |
[35] |
T. Sattel, T. Knopp, S. Biederer, B. Gleich, J. Weizenecker, J. Borgert and T. Buzug, Single-sided device for magnetic particle imaging, Journal of Physics D: Applied Physics, 42 (2009), 022001.
doi: 10.1088/0022-3727/42/2/022001. |
[36] |
O. Scherzer, M. Grasmair, H. Grossauer, M. Haltmeier and F. Lenzen, Variational Methods in Imaging, Springer, 2009. |
[37] |
H. Schomberg, Magnetic particle imaging: Model and reconstruction, in 2010 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2010, 992-995.
doi: 10.1109/ISBI.2010.5490155. |
[38] |
M. Storath and A. Weinmann, Fast partitioning of vector-valued images, SIAM Journal on Imaging Sciences, 7 (2014), 1826-1852.
doi: 10.1137/130950367. |
[39] |
M. Storath, A. Weinmann, J. Frikel and M. Unser, Joint image reconstruction and segmentation using the Potts model, Inverse Problems, 31 (2015), 025003, 29pp.
doi: 10.1088/0266-5611/31/2/025003. |
[40] |
M. Ter-Pogossian, M. Phelps, E. Hoffman and N. Mullani, A positron-emission transaxial tomograph for nuclear imaging (PETT), Radiology, 114 (1975), 89-98.
doi: 10.1148/114.1.89. |
[41] |
A. Weinmann, M. Storath and L. Demaret, The $L^1$-Potts functional for robust jump-sparse reconstruction, SIAM Journal on Numerical Analysis, 53 (2015), 644-673.
doi: 10.1137/120896256. |
[42] |
A. Weinmann and M. Storath, Iterative Potts and Blake-Zisserman minimization for the recovery of functions with discontinuities from indirect measurements, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471 (2015), 20140638, 25pp.
doi: 10.1098/rspa.2014.0638. |
[43] |
J. Weizenecker, B. Gleich and J. Borgert, Magnetic particle imaging using a field free line, Journal of Physics D: Applied Physics, 41 (2008), 105-114.
doi: 10.1088/0022-3727/41/10/105009. |
[44] |
J. Weizenecker, J. Borgert and B. Gleich, A simulation study on the resolution and sensitivity of magnetic particle imaging, Physics in Medicine and Biology, 52 (2007), 6363-6374.
doi: 10.1088/0031-9155/52/21/001. |
[45] |
J. Weizenecker, B. Gleich, J. Rahmer, H. Dahnke and J. Borgert, Three-dimensional real-time in vivo magnetic particle imaging, Physics in Medicine and Biology, 54 (2009), L1-L10. |
[46] |
B. Zheng, T. Vazin, W. Yang, P. Goodwill, E. Saritas, L. Croft, D. Schaffer and S. Conolly, Quantitative stem cell imaging with magnetic particle imaging, in IEEE International Workshop on Magnetic Particle Imaging, 2013, p1.
doi: 10.1109/IWMPI.2013.6528323. |
show all references
References:
[1] |
L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, vol. 254, Clarendon Press, Oxford, 2000. |
[2] |
M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging, CRC press, Boca Raton, 1998.
doi: 10.1887/0750304359. |
[3] |
F. Bornemann and T. März, Fast image inpainting based on coherence transport, Joural of Mathematical Imaging and Vision, 28 (2007), 259-278.
doi: 10.1007/s10851-007-0017-6. |
[4] |
S. Chikazumi and S. Charap, Physics of Magnetism, Krieger Publishing, New York, 1978. |
[5] |
H. Engl, M. Hanke and A. Neubauer, Regularization of Inverse Problems, Kluwer Academic Publishers, Dordrecht, 1996.
doi: 10.1007/978-94-009-1740-8. |
[6] |
R. Ferguson, K. Minard and K. Krishnan, Optimization of nanoparticle core size for magnetic particle imaging, Journal of Magnetism and Magnetic Materials, 321 (2009), 1548-1551.
doi: 10.1016/j.jmmm.2009.02.083. |
[7] |
B. Gleich and J. Weizenecker, Tomographic imaging using the nonlinear response of magnetic particles, Nature, 435 (2005), 1214-1217.
doi: 10.1038/nature03808. |
[8] |
B. Gleich, J. Weizenecker and J. Borgert, Experimental results on fast 2D-encoded magnetic particle imaging, Physics in Medicine and Biology, 53 (2008), N81-N84.
doi: 10.1088/0031-9155/53/6/N01. |
[9] |
G. Golub and C. Van Loan, Matrix Computations, JHU Press, 2012. |
[10] |
P. Goodwill and S. Conolly, The X-space formulation of the magnetic particle imaging process: 1-D signal, resolution, bandwidth, {SNR}, {SAR}, and magnetostimulation, IEEE Transactions on Medical Imaging, 29 (2010), 1851-1859.
doi: 10.1109/TMI.2010.2052284. |
[11] |
P. Goodwill and S. Conolly, Multidimensional X-space magnetic particle imaging, IEEE Transactions on Medical Imaging, 30 (2011), 1581-1590.
doi: 10.1109/TMI.2011.2125982. |
[12] |
P. Goodwill, E. Saritas, L. Croft, T. Kim, K. Krishnan, D. Schaffer and S. Conolly, X-space mpi: Magnetic nanoparticles for safe medical imaging, Advanced Materials, 24 (2012), 3870-3877.
doi: 10.1002/adma.201200221. |
[13] |
M. Grüttner, T. Knopp, J. Franke, M. Heidenreich, J. Rahmer, A. Halkola, C. Kaethner, J. Borgert and T. Buzug, On the formulation of the image reconstruction problem in magnetic particle imaging, Biomedical Engineering, 58 (2013), 583-591. |
[14] | |
[15] |
D. Jiles, Introduction to Magnetism and Magnetic Materials, CRC press, 1998. |
[16] |
A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems, vol. 120, Springer, Heidelberg, 2011.
doi: 10.1007/978-1-4419-8474-6. |
[17] |
T. Knopp and T. Buzug, Magnetic Particle Imaging: An Introduction to Imaging Principles and Scanner Instrumentation, Springer, 2012.
doi: 10.1007/978-3-642-04199-0. |
[18] |
T. Knopp, Effiziente Rekonstruktion und alternative Spulentopologien für Magnetic Particle Imaging, Dissertation, University of Lübeck, 2011.
doi: 10.1007/978-3-8348-8129-8. |
[19] |
T. Knopp, S. Biederer, T. Sattel, M. Erbe and T. Buzug, Prediction of the spatial resolution of magnetic particle imaging using the modulation transfer function of the imaging process, IEEE Transactions on Medical Imaging, 30 (2011), 1284-1292.
doi: 10.1109/TMI.2011.2113188. |
[20] |
T. Knopp, S. Biederer, T. Sattel, J. Rahmer, J. Weizenecker, B. Gleich, J. Borgert and T. Buzug, 2D model-based reconstruction for magnetic particle imaging, Medical Physics, 37 (2010), 485-491.
doi: 10.1118/1.3271258. |
[21] |
T. Knopp, M. Erbe, T. Sattel, S. Biederer and T. Buzug, A Fourier slice theorem for magnetic particle imaging using a field-free line, Inverse Problems, 27 (2011), 095004, 14pp.
doi: 10.1088/0266-5611/27/9/095004. |
[22] |
T. Knopp, J. Rahmer, T. Sattel, S. Biederer, J. Weizenecker, B. Gleich, J. Borgert and T. Buzug, Weighted iterative reconstruction for magnetic particle imaging, Physics in Medicine and Biology, 55 (2010), 1577-1589. |
[23] |
T. Knopp, T. Sattel, S. Biederer, J. Rahmer, J. Weizenecker, B. Gleich, J. Borgert and T. Buzug, Model-Based Reconstruction for magnetic particle imaging, IEEE Transactions on Medical Imaging, 29 (2010), 12-18. |
[24] |
J. Konkle, P. Goodwill and S. Conolly, Development of a field free line magnet for projection MPI, in SPIE Medical Imaging, 7965 (2011), 79650X.
doi: 10.1117/12.878435. |
[25] |
D. Kuhl and R. Edwards, Image separation radioisotope scanning, Radiology, 80 (1963), 653-662.
doi: 10.1148/80.4.653. |
[26] |
J. Lampe, C. Bassoy, J. Rahmer, J. Weizenecker, H. Voss, B. Gleich and J. Borgert, Fast reconstruction in magnetic particle imaging, Physics in Medicine and Biology, 57 (2012), 1113-1134.
doi: 10.1088/0031-9155/57/4/1113. |
[27] |
J. Lawrence, A Catalog of Special Plane Curves, Courier Corporation, 2013. |
[28] |
A. Louis, Inverse Und Schlecht Gestellte Probleme, Teubner, Stuttgart, 1989.
doi: 10.1007/978-3-322-84808-6. |
[29] |
T. März, Image inpainting based on coherence transport with adapted distance functions, SIAM Journal on Imaging Sciences, 4 (2011), 981-1000.
doi: 10.1137/100807296. |
[30] |
T. März, A well-posedness framework for inpainting based on coherence transport, Foundations of Computational Mathematics, 15 (2015), 973-1033.
doi: 10.1007/s10208-014-9199-7. |
[31] |
J. Rahmer, J. Weizenecker, B. Gleich and J. Borgert, Signal encoding in magnetic particle imaging: Properties of the system function, BMC Medical Imaging, 9 (2009), p4.
doi: 10.1186/1471-2342-9-4. |
[32] |
J. Rahmer, J. Weizenecker, B. Gleich and J. Borgert, Analysis of a 3-D system function measured for magnetic particle imaging, IEEE Transactions on Medical Imaging, 31 (2012), 1289-1299.
doi: 10.1109/TMI.2012.2188639. |
[33] |
L. 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. |
[34] |
E. Saritas, P. Goodwill, L. Croft, J. Konkle, K. Lu, B. Zheng and S. Conolly, Magnetic particle imaging (MPI) for NMR and MRI researchers, Journal of Magnetic Resonance, 229 (2013), 116-126.
doi: 10.1016/j.jmr.2012.11.029. |
[35] |
T. Sattel, T. Knopp, S. Biederer, B. Gleich, J. Weizenecker, J. Borgert and T. Buzug, Single-sided device for magnetic particle imaging, Journal of Physics D: Applied Physics, 42 (2009), 022001.
doi: 10.1088/0022-3727/42/2/022001. |
[36] |
O. Scherzer, M. Grasmair, H. Grossauer, M. Haltmeier and F. Lenzen, Variational Methods in Imaging, Springer, 2009. |
[37] |
H. Schomberg, Magnetic particle imaging: Model and reconstruction, in 2010 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2010, 992-995.
doi: 10.1109/ISBI.2010.5490155. |
[38] |
M. Storath and A. Weinmann, Fast partitioning of vector-valued images, SIAM Journal on Imaging Sciences, 7 (2014), 1826-1852.
doi: 10.1137/130950367. |
[39] |
M. Storath, A. Weinmann, J. Frikel and M. Unser, Joint image reconstruction and segmentation using the Potts model, Inverse Problems, 31 (2015), 025003, 29pp.
doi: 10.1088/0266-5611/31/2/025003. |
[40] |
M. Ter-Pogossian, M. Phelps, E. Hoffman and N. Mullani, A positron-emission transaxial tomograph for nuclear imaging (PETT), Radiology, 114 (1975), 89-98.
doi: 10.1148/114.1.89. |
[41] |
A. Weinmann, M. Storath and L. Demaret, The $L^1$-Potts functional for robust jump-sparse reconstruction, SIAM Journal on Numerical Analysis, 53 (2015), 644-673.
doi: 10.1137/120896256. |
[42] |
A. Weinmann and M. Storath, Iterative Potts and Blake-Zisserman minimization for the recovery of functions with discontinuities from indirect measurements, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471 (2015), 20140638, 25pp.
doi: 10.1098/rspa.2014.0638. |
[43] |
J. Weizenecker, B. Gleich and J. Borgert, Magnetic particle imaging using a field free line, Journal of Physics D: Applied Physics, 41 (2008), 105-114.
doi: 10.1088/0022-3727/41/10/105009. |
[44] |
J. Weizenecker, J. Borgert and B. Gleich, A simulation study on the resolution and sensitivity of magnetic particle imaging, Physics in Medicine and Biology, 52 (2007), 6363-6374.
doi: 10.1088/0031-9155/52/21/001. |
[45] |
J. Weizenecker, B. Gleich, J. Rahmer, H. Dahnke and J. Borgert, Three-dimensional real-time in vivo magnetic particle imaging, Physics in Medicine and Biology, 54 (2009), L1-L10. |
[46] |
B. Zheng, T. Vazin, W. Yang, P. Goodwill, E. Saritas, L. Croft, D. Schaffer and S. Conolly, Quantitative stem cell imaging with magnetic particle imaging, in IEEE International Workshop on Magnetic Particle Imaging, 2013, p1.
doi: 10.1109/IWMPI.2013.6528323. |
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