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Due to the topology of a single-sided MPI device, the magnetic field suffers from inhomogeneities which are limiting the penetration depth. Additionally, the sensitivity profile of the receive coils compromises the measured signal. Therefore, the signal spectrum shows a relatively high noise level. To achieve a sufficient reconstruction and reduce the reconstruction time, only the frequency components are used, that have a sufficiently high signal to noise ratio (SNR). The algorithm presented in this paper allows for computing optimal SNR-thresholds which promise reconstructed images with high quality. For now, the algorithm is limited to 2D-reconstruction, but it already promises to enhance the existing reconstruction algorithm for the single-sided field free point MPI device significantly.