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In this paper, we study the efficiency of five different field free point trajectories in two-dimensional magnetic particle imaging for the compressed-sensing based reconstruction of partially measured system matrices. To show the suitability of the trajectories, different trajectories with identical repetition times were simulated using on the same scanner setup. We show that for all trajectories, the compressed-sensing based reconstruction approach for the system matrix is possible and promising for real-world scenarios. Also we validate the already known fact that the Lissajous trajectory is appropriate for the compressed sensing approach. However, there are still other trajectory choices which show similar and even better performance in the compressed-sensing based reconstruction.