In coherent x-ray diffractive imaging, the oversampled far-field diffraction pattern for phase retrieval iterative algorithm is used in order to reconstruct the information about the real space. The support constraint is one of the most important steps of the 3D phase retrieval process. Here we use a small nonperiodic 2D digital image as an object for studying the algorithm of pursuing support constraint automatically and noise correction for different types of noises in the diffraction pattern. We find an efficient method of noise correction while the traditional methods do not work well in the high noise condition. The result shows that this method can be used to reduce the effect effectively for the reconstruction. We also study the 3D reconstruction for the electron density distribution of Au nano-particles. We achieve a good reconstruction separately with and without noise effect in the diffraction pattern and we find that the signal-to-noise ratio should be bigger than 27 for successful 3D reconstruction.