The phase retrieval is an important task in x-ray phase contrast imaging. The robustness of phase retrieval is especially important for potential medical imaging applications such as phase contrast mammography. Recently the authors developed an iterative phase retrieval algorithm, the attenuation-partition based algorithm, for the phase retrieval in inline phase-contrast imaging . Applied to experimental images, the algorithm was proven to be fast and robust. However, a quantitative analysis of the performance of this new algorithm is desirable. In this work, we systematically compared the performance of this algorithm with other two widely used phase retrieval algorithms, namely the Gerchberg-Saxton (GS) algorithm and the Transport of Intensity Equation (TIE) algorithm. The systematical comparison is conducted by analyzing phase retrieval performances with a digital breast specimen model. We show that the proposed algorithm converges faster than the GS algorithm in the Fresnel diffraction regime, and is more robust against image noise than the TIE algorithm. These results suggest the significance of the proposed algorithm for future medical applications with the x-ray phase contrast imaging technique. © 2010 Optical Society of America.