  Ptychography is a popular technique to achieve diffraction limited resolution
images of a two or three dimensional sample using high frame rate detectors. We
introduce a relaxation of common projection algorithms to account for
instabilities given by intensity and background fluctuations, position errors,
or poor calibration using multiplexing illumination. This relaxation introduces
an additional phasing optimization at every step that enhances the convergence
rate of common projection algorithms. Numerical tests exhibit the exact
recovery of the object and the noise when there is high redundancy in the data.
