Symmetries of the 2D magnetic particle imaging system matrix
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Symmetries of the 2D magnetic particle imaging system matrix. / Weber, A; Knopp, T.
In: PHYS MED BIOL, Vol. 60, No. 10, 21.05.2015, p. 4033-44.Research output: SCORING: Contribution to journal › SCORING: Journal article › Research › peer-review
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TY - JOUR
T1 - Symmetries of the 2D magnetic particle imaging system matrix
AU - Weber, A
AU - Knopp, T
PY - 2015/5/21
Y1 - 2015/5/21
N2 - In magnetic particle imaging (MPI), the relation between the particle distribution and the measurement signal can be described by a linear system of equations. For 1D imaging, it can be shown that the system matrix can be expressed as a product of a convolution matrix and a Chebyshev transformation matrix. For multidimensional imaging, the structure of the MPI system matrix is not yet fully explored as the sampling trajectory complicates the physical model. It has been experimentally found that the MPI system matrix rows have symmetries and look similar to the tensor products of Chebyshev polynomials. In this work we will mathematically prove that the 2D MPI system matrix has symmetries that can be used for matrix compression.
AB - In magnetic particle imaging (MPI), the relation between the particle distribution and the measurement signal can be described by a linear system of equations. For 1D imaging, it can be shown that the system matrix can be expressed as a product of a convolution matrix and a Chebyshev transformation matrix. For multidimensional imaging, the structure of the MPI system matrix is not yet fully explored as the sampling trajectory complicates the physical model. It has been experimentally found that the MPI system matrix rows have symmetries and look similar to the tensor products of Chebyshev polynomials. In this work we will mathematically prove that the 2D MPI system matrix has symmetries that can be used for matrix compression.
KW - Algorithms
KW - Data Compression
KW - Diagnostic Imaging
KW - Magnetite Nanoparticles
KW - Models, Theoretical
U2 - 10.1088/0031-9155/60/10/4033
DO - 10.1088/0031-9155/60/10/4033
M3 - SCORING: Journal article
C2 - 25919400
VL - 60
SP - 4033
EP - 4044
JO - PHYS MED BIOL
JF - PHYS MED BIOL
SN - 0031-9155
IS - 10
ER -