2 research outputs found
Bivariate Lagrange interpolation at the node points of non-degenerate Lissajous curves
Motivated by an application in Magnetic Particle Imaging, we study bivariate
Lagrange interpolation at the node points of Lissajous curves. The resulting
theory is a generalization of the polynomial interpolation theory developed for
a node set known as Padua points. With appropriately defined polynomial spaces,
we will show that the node points of non-degenerate Lissajous curves allow
unique interpolation and can be used for quadrature rules in the bivariate
setting. An explicit formula for the Lagrange polynomials allows to compute the
interpolating polynomial with a simple algorithmic scheme. Compared to the
already established schemes of the Padua and Xu points, the numerical results
for the proposed scheme show similar approximation errors and a similar growth
of the Lebesgue constant.Comment: 19 pages, 5 figure
Moving Table Magnetic Particle Imaging: A stepwise approach preserving high spatio-temporal resolution
Magnetic Particle Imaging (MPI) is a highly sensitive imaging method that
enables the visualization of magnetic tracer materials with a temporal
resolution of more than 46 volumes per second. In MPI the size of the field of
view scales with the strengths of the applied magnetic fields. In clinical
applications those strengths are limited by peripheral nerve stimulation,
specific absorption rates, and the requirement to acquire images of high
spatial resolution. Therefore, the size of the field of view is usually a few
cubic centimeters. To bypass this limitation, additional focus fields and/or
external object movements can be applied. In this work, the latter approach is
investigated. An object is moved through the scanner bore one step at a time,
while the MPI scanner continuously acquires data from its static field of view.
Using a 3D phantom and dynamic 3D in vivo data it is shown that the data from
such a moving table experiment can be jointly reconstructed after reordering
the data with respect to the stepwise object shifts and heart beat phases