The short and intense pulses of the new X-ray free electron lasers, now 
operational or under construction, may make possible diffraction experiments on 
single molecule-sized objects with high resolution, before radiation damage 
destroys the sample. In a single molecule imaging (SMI) experiment thousands of 
diffraction patterns of single molecules with random orientations are recorded. 
One of the most challenging problems of SMI is how to assemble these noisy 
patterns of unknown orientations into a consistent single set of diffraction 
data. Here we present a new method which can solve the orientation problem of 
SMI efficiently even for large biological molecules and in the presence of 
noise. We show on simulated diffraction patterns of a large protein molecule, 
how the orientations of the patterns can be found and the structure to atomic 
resolution can be solved. The concept of our algorithm could be also applied to 
experiments where images of an object are recorded in unknown orientations 
and/or positions like in cryoEM or tomography.