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In this work system-matrix based reconstruction in the context of magnetic particle imaging (MPI) is performed using 2D simulated system matrices and phantoms to study the effects of different approaches in the reconstruction chain. As an example, multi color reconstruction at different temperatures is chosen to show how the approach itself changes the reconstruction. It will be shown that a simple and trivial detail has important consequences for the reconstruction algorithms not only halving the number of unknowns but also giving commonly used solvers for the minimization problem a chance to converge to similar solutions.