  In this paper, we propose the SPR (sparse phase retrieval) method, which is a
new phase retrieval method for coherent x-ray diffraction imaging (CXDI).
Conventional phase retrieval methods effectively solve the problem for high
signal-to-noise ratio measurements, but would not be sufficient for single
biomolecular imaging which is expected to be realized with femto-second x-ray
free electron laser pulses. The SPR method is based on the Bayesian statistics.
It does not need to set the object boundary constraint that is required by the
commonly used hybrid input-output (HIO) method, instead a prior distribution is
defined with an exponential distribution and used for the estimation.
Simulation results demonstrate that the proposed method reconstructs the
electron density under a noisy condition even some central pixels are masked.
