Compressive ptychographical coherent diffractive imaging based on Poissonian maximum likelihood and sparse approximations for phase and magnitude

1 Ptychography is a lensless coherent di¤ractive imaging that uses intensity measurements of multiple di¤raction patterns collected with a localized illumination probe from overlapping regions of an object. A novel iterative algorithm is proposed targeted on optimal processing noisy measurements. The noise suppression is enabled by two instruments. First, by the maximum likelihood technique formulated for Poissonian (photon counting) measurements, and second, by sparse approximation of phase and magnitude of object and probe. It is shown in particular, that for noisy data the maximum likelihood estimate of the wave…eld at the sensor plane is essentially di¤erent from the famous Gerchberg-Saxton-Fienup solution, where the magnitude of the estimate is replaced by the square root of the intensity measurement. The simulation experiments demonstrate the state-of-the-art performance of the proposed algorithm both numerically and visually.