International Journal on Magnetic Particle Imaging

Vol 6 No 1 (2020): Int J Mag Part Imag

https://doi.org/10.18416/IJMPI.2020.2003003

###
Magnetic Particle Imaging Using Discrete Sampling and Image Reconstruction with Few Orthogonal Bases Obtained by Singular Value Decomposition of Selected Delta Responses

### Main Article Content

This work is licensed under a Creative Commons Attribution 4.0 International License.

### Abstract

The conventional magnetic particle imaging reconstruction methods use observed signals and system functions, which result in an enormous amount of data and long processing time being required to reconstruct large image matrices. We propose a new image reconstruction method that uses less data and a limited number of orthogonal bases obtained via the singular value decomposition (SVD) of selected point spread functions (PSFs). By using the features of the diagonal and nondiagonal elements of a singular value matrix, image blurring and artifacts can be reduced in the reconstructed image. This is because the diagonal components commonly indicate the similarities between each orthogonal basis for the system function and an observed signal, whereas the nondiagonal components indicate the differences of both them. In this paper, we use numerical analyses to demonstrate that image reconstruction is possible by using effective orthogonal bases obtained through the SVD of a limited number of PSFs selected from a general system function. The reconstruction time is reduced to 1/12th to 1/50th of that of the conventional method.

Int. J. Mag. Part. Imag. 6(1), 2020, Article ID: 2003003, DOI: 10.18416/IJMPI.2020.2003003

Int. J. Mag. Part. Imag. 6(1), 2020, Article ID: 2003003, DOI: 10.18416/IJMPI.2020.2003003

### Article Details

### References

[1] B. Gleich and J. Weizenecker. Tomographic imaging using the nonlinear response of magnetic particles.Nature, 435(7046):1214–1217, 2005, doi:10.1038/nature03808.

[2] 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(21):6363–6374, 2007, doi:10.1088/0031-9155/52/21/001.

[3] T. Takagi, S. Shimizu, H. Tsuchiya, T. Hatsuda, T. Noguchi, and Y. Ishihara, Image reconstruction method based on orthonormal basis of observation signal by singular value decomposition for magnetic particle imaging, in 2015 5th International Workshop on Magnetic Particle Imaging (IWMPI), IEEE, 2015. doi:10.1109/IWMPI.2015.7107052.

[4] T. Takagi, H. Tsuchiya, T. Hatsuda, and Y. Ishihara. Image Reconstruction Method Using Orthonormal Basis by Singular Value Decomposition for Magnetic Particle Imaging. Transactions of Japanese Society for Medical and Biological Engineering, 53(5):276–282, 2015, doi:10.11239/jsmbe.53.276.

[5] Y. Ishihara and K.Mori,Magnetic resonance imaging, Japanese Patent, JPA 1994-86763, 1992.

[6] T. Idé and K. Tsuda, Change-Point Detection using Krylov Subspace Learning, in Proceedings of the 2007 SIAM International Conference on Data Mining, 515–520, Philadelphia, PA: Society for Industrial and Applied Mathematics, 2007. doi:10.1137/1.9781611972771.54.

[7] J. Lampe, C. Bassoy, J. Rahmer, J. Weizenecker, H. Voss, B. Gleich, and J. Borgert. Fast reconstruction in magnetic particle imaging. Physics inMedicine and Biology, 57(4):1113–1134, 2012, doi:10.1088/0031-9155/57/4/1113.

[8] T. Knopp and A. Weber. Sparse reconstruction of the magnetic particle imaging system matrix. IEEE Transactions on Medical Imaging, 32(8):1473–1480, 2013, doi:10.1109/TMI.2013.2258029.

[9] A. Weber and T. Knopp. Reconstruction of the Magnetic Particle Imaging System Matrix Using Symmetries and Compressed Sensing. Advances inMathematical Physics, 2015, 2015, doi:10.1155/2015/460496.

[10] M. Maass, M. Ahlborg, A. Bakenecker, F. Katzberg, H. Phan, T. M. Buzug, and A. Mertins. A Trajectory Study for Obtaining MPI System Matrices in a Compressed-Sensing Framework. International Journal on Magnetic Particle Imaging, 3(2), 2017, doi:10.18416/IJMPI.2017.1706005.

[11] Y. Ono and Y. Ishihara, Image reconstruction method of magnetic particle imaging using orthogonality of singular value decomposition, in International Workshop on Magnetic Particle Imaging, 2019.

[12] Y. Ishihara, T. Kuwabara, T. Honma, and Y. Nakagawa. Correlation-Based Image Reconstruction Methods for Magnetic Particle Imaging. IEICE Transactions on Information and Systems, E95-D(3):872–879, 2012, doi:10.1587/transinf.E95.D.872.

[13] Y. Ishihara, T.Honma, S.Nohara, and Y. Ito. Evaluation of magnetic nanoparticle samples made from biocompatible ferucarbotran by time-correlation magnetic particle imaging reconstruction method. BMCMedical Imaging, 13(1):15, 2013, doi:10.1186/1471-2342-13-15.

[14] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, Second edi. Cambridge University Press, 1992, ISBN: 0-521-43108-5.

[15] J. Rahmer, J.Weizenecker, B. Gleich, and J. Borgert. Signal encoding in magnetic particle imaging: properties of the system function. BMC Medical Imaging, 9:4, 2009, doi:10.1186/1471-2342-9-4.

[2] 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(21):6363–6374, 2007, doi:10.1088/0031-9155/52/21/001.

[3] T. Takagi, S. Shimizu, H. Tsuchiya, T. Hatsuda, T. Noguchi, and Y. Ishihara, Image reconstruction method based on orthonormal basis of observation signal by singular value decomposition for magnetic particle imaging, in 2015 5th International Workshop on Magnetic Particle Imaging (IWMPI), IEEE, 2015. doi:10.1109/IWMPI.2015.7107052.

[4] T. Takagi, H. Tsuchiya, T. Hatsuda, and Y. Ishihara. Image Reconstruction Method Using Orthonormal Basis by Singular Value Decomposition for Magnetic Particle Imaging. Transactions of Japanese Society for Medical and Biological Engineering, 53(5):276–282, 2015, doi:10.11239/jsmbe.53.276.

[5] Y. Ishihara and K.Mori,Magnetic resonance imaging, Japanese Patent, JPA 1994-86763, 1992.

[6] T. Idé and K. Tsuda, Change-Point Detection using Krylov Subspace Learning, in Proceedings of the 2007 SIAM International Conference on Data Mining, 515–520, Philadelphia, PA: Society for Industrial and Applied Mathematics, 2007. doi:10.1137/1.9781611972771.54.

[7] J. Lampe, C. Bassoy, J. Rahmer, J. Weizenecker, H. Voss, B. Gleich, and J. Borgert. Fast reconstruction in magnetic particle imaging. Physics inMedicine and Biology, 57(4):1113–1134, 2012, doi:10.1088/0031-9155/57/4/1113.

[8] T. Knopp and A. Weber. Sparse reconstruction of the magnetic particle imaging system matrix. IEEE Transactions on Medical Imaging, 32(8):1473–1480, 2013, doi:10.1109/TMI.2013.2258029.

[9] A. Weber and T. Knopp. Reconstruction of the Magnetic Particle Imaging System Matrix Using Symmetries and Compressed Sensing. Advances inMathematical Physics, 2015, 2015, doi:10.1155/2015/460496.

[10] M. Maass, M. Ahlborg, A. Bakenecker, F. Katzberg, H. Phan, T. M. Buzug, and A. Mertins. A Trajectory Study for Obtaining MPI System Matrices in a Compressed-Sensing Framework. International Journal on Magnetic Particle Imaging, 3(2), 2017, doi:10.18416/IJMPI.2017.1706005.

[11] Y. Ono and Y. Ishihara, Image reconstruction method of magnetic particle imaging using orthogonality of singular value decomposition, in International Workshop on Magnetic Particle Imaging, 2019.

[12] Y. Ishihara, T. Kuwabara, T. Honma, and Y. Nakagawa. Correlation-Based Image Reconstruction Methods for Magnetic Particle Imaging. IEICE Transactions on Information and Systems, E95-D(3):872–879, 2012, doi:10.1587/transinf.E95.D.872.

[13] Y. Ishihara, T.Honma, S.Nohara, and Y. Ito. Evaluation of magnetic nanoparticle samples made from biocompatible ferucarbotran by time-correlation magnetic particle imaging reconstruction method. BMCMedical Imaging, 13(1):15, 2013, doi:10.1186/1471-2342-13-15.

[14] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, Second edi. Cambridge University Press, 1992, ISBN: 0-521-43108-5.

[15] J. Rahmer, J.Weizenecker, B. Gleich, and J. Borgert. Signal encoding in magnetic particle imaging: properties of the system function. BMC Medical Imaging, 9:4, 2009, doi:10.1186/1471-2342-9-4.