System matrix compression using Chebyshev polynomials of first and second kind

Abstract

A common procedure for the reconstruction in Lissajous-type magnetic particle imaging is solving a linear system of equations which is based on the measurement of the so-called system matrix and the induced voltage signal of the unknown magnetic particle distribution. To speed up the reconstruction process and to reduce memory consumption, different compression techniques for the system matrix have been investigated. In this work, we propose a system matrix compression using the tensor product of Chebyshev polynomials of first and second kind. This method is motivated by recently published theoretical findings on the system function. For evaluation, simulated and real-world system matrices have been compressed with the proposed method and other state-of-the-art techniques. When using only one compression coefficient per row, the proposed compression outperforms the compared methods for all tested system matrices in terms of the normalized error metric and better reconstruction results.

Int. J. Mag. Part. Imag. 8(2), 2022, Article ID: 2212003, DOI: 10.18416/IJMPI.2022.2212003