Diffractive imaging using the intense and coherent beam of X-ray free-electron 
lasers opens new perspectives for structural studies of single nanoparticles and 
biomolecules. Simulations were carried out to generate 3D oversampled 
diffraction patterns of non-crystalline biological samples, ranging from 
peptides and proteins to megadalton complex assemblies, and to recover their 
molecular structure from nanometer to near-atomic resolutions. Using these 
simulated data, we show here that iterative reconstruction methods based on 
standard and variant forms of the charge flipping algorithm, can efficiently 
solve the phase retrieval problem and extract a unique and reliable molecular 
structure. Contrary to the case of conventional algorithms, where the estimation 
and the use of a compact support is imposed, our approach does not require any 
prior information about the molecular assembly, and is amenable to a wide range 
of biological assemblies. Importantly, the robustness of this ab initio approach 
is illustrated by the fact that it tolerates experimental noise and 
incompleteness of the intensity data at the center of the speckle pattern.