Direct Image Reconstruction of Lissajous-Type Magnetic Particle Imaging Data Using Chebyshev-Based Matrix Compression

Image reconstruction in magnetic particle imaging (MPI) is done using an algebraic approach for Lissajous-type measurement sequences. By solving a large linear system of equations, the spatial distribution of magnetic nanoparticles can be determined. Despite the use of iterative solvers that converge rapidly, the size of the MPI system matrix leads to reconstruction times that are typically much longer than the actual data acquisition time. For this reason, matrix compression techniques have been introduced that transform the MPI system matrix into a sparse domain and then utilize this sparsity for accelerated reconstruction. Within this work, we investigate the Chebyshev transformation for matrix compression and show that it can provide better reconstruction results for high compression rates than the commonly applied Cosine transformation. By reducing the number of coefficients per matrix row to one, it is even possible to derive a direct reconstruction method that obviates the usage of iterative solvers.