Compressed Sensing of the System Matrix and Sparse Reconstruction of the Particle Concentration in Magnetic Particle Imaging

The reconstruction of a particle concentration in magnetic particle imaging is commonly based on using a system matrix, whose acquisition is time consuming and whose storing is challenging. It has been shown recently that the acquisition time can be reduced with methods of compressed sensing and storage requirements can be reduced by storing in sparse representation. To improve the reconstruction, signals of low signal-to-noise ratio (SNR) are discarded. The determination of the SNR is difficult for undersampled signals. In this paper, the mixing order of the acquired harmonics is calculated to estimate the SNR. The spatial resolution of a system matrix can be increased by compressed sensing. A system matrix of small spatial resolution can be fully acquired in the same amount of time as a high resoluted system matrix that is undersampled correspondingly.