Due to improved quantification capabilities and enhanced signal-to-noise ratio (SNR), phase-corrected real reconstruction in magnetic resonance imaging is superior to the common magnitude reconstruction, especially at low SNR. This requires the development of an automated phase-correction algorithm. Existing methods are not well suited for multiple unconnected regions of very low SNR. For this situation, a method based on the real-signal maximization is implemented, in which the experimental image phase is approximated by a three-dimensional polynomial of up to third order. The presented implementation was successfully applied to data originating from different samples and pulse sequences.