  We present an algorithm for coherent diffractive imaging with phaseless
measurements. It treats the forward model as a combination of coherent and
incoherent waves. The algorithm reconstructs absorption and phase contrast that
quantifies the attenuation and the refraction of the waves propagating through
an object. It requires coherent or partially coherent illuminations, and
several detectors to record the intensity of the distorted wave that passes
through the object under inspection. The diversity of illuminations, obtained
by putting masks between the source and the object, provides enough information
for imaging. The computational cost of our algorithm is linear in the number of
pixels of the image. Therefore, it is efficient for high-resolution imaging.
Our algorithm guarantees exact recovery if the image is sparse for a given
basis. Numerical experiments in the setting of phaseless diffraction imaging of
sparse objects validate the efficiency and the precision of the suggested
algorithm.
