From medical imaging perspective the robustness of a phase retrieval method is of critical importance. In this presentation we compare the robustness of two general phase retrieval methods, namely the transport of intensity equation inversion (TIE-inversion) method and the attenuation partition based (AP-based) method. We showed that the TIE-inversion method, regardless if being assisted with the Tikhonov regularization, failed to retrieve the phase maps in two experimental studies. The failure exposes this method's weakness as being unstable against the noise. In contrast, the sample phase maps are retrieved successfully by using the AP-based method. The stark performance differences of the two methods are rooted in their different techniques dealing with the singularity problem. This comparison shows that the robust AP-based phase retrieval method will be superior to the TIE-inversion method for medical imaging applications where radiation doses are stringently limited.© 2013 IOP Publishing Ltd and Sissa Medialab srl.