Sparse ptychographical coherent diffractive imaging from noisy measurements.

Ptychography is a lensless coherent diffractive imaging that uses intensity measurements of multiple diffraction patterns collected with a localized illumination probe from overlapping regions of an object. An iterative algorithm is proposed that is targeted on optimal processing noisy measurements. The noise suppression is enabled by two instruments: first, the maximum-likelihood technique formulated for Poissonian (photon-counting) measurements, and, second, sparse approximation of the phase and magnitude of the object and probe. It is shown that the maximum-likelihood estimate of the wavefield at the sensor plane for noisy measurements is essentially different 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.