Using Low-Rank Tensors for the Recovery of MPI System Matrices

In Magnetic Particle Imaging (MPI), the system matrix plays an important role, as it encodes the relationship between particle concentration and the measured signal. Its acquisition requires a time-consuming calibration scan, whereas its size leads to a high memory-demand. Both of these aspects can be limiting factors in practice. In order to reduce measurement time, compressed sensing exploits the knowledge that the MPI system matrix has a sparse representation in a suitably chosen domain. In this work we demonstrate that the rows of the system matrix allow a representation as low-rank tensors. We show that such an approximation leads to a denoising of the system matrix while introducing only a negligible bias. As an application, we develop a new matrix recovery method exploiting aforementioned low rank property in addition to sparsity in the DCT domain. Experiments show that the proposed matrix recovery method yields system matrices with reduced error when compared to a standard compressed sensing recovery.