Rank-1 accelerated illumination recovery in scanning diffractive imaging by transparency estimation

We consider the problem of blind ptychography, that is the joint estimation of an unknown object and an illumination function from diffraction intensity measurements. In ptychography, diffraction measurements from neighboring regions of the same object are related to each other by a pairwise relationship between overlapping frames. When the illumination is well known, the relationship among frames is given by a linear projection operator. We propose a power iteration-projection algorithm that minimizes the global pairwise discrepancy among frames. We accelerate the convergence of power method by subtracting the estimated localized average transparency of the unknown object. The method is effective for weakly scattering and low contrast objects or piecewise smooth specimens.