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Magnetic Particle Imaging (MPI) is a tracer based medical imaging modality with great potential due to its high sensitivity, high spatio-temporal resolution, and ability to quantify the tracer concentration. Image reconstruction in MPI is an ill-posed problem, which can be addressed by the use of regularization methods. The corresponding optimization problem is most commonly solved using the Kaczmarz algorithm. Reconstruction using the Kaczmarz method for single-contrast MPI is very efficient as it produces the desired images fast with a small number of iterations. For multi-contrast MPI, however, the regular Kaczmarz algorithm fails to obtain good quality images without channel leakage when using a small number of iterations. In this work, we propose to use an accelerated Kaczmarz method in order to reduce the reconstruction time needed to achieve a good separation of the channels and a good image quality in multi-contrast MPI.