Recovering magnetization distributions from their noisy diffraction data.

We study, using simulated experiments inspired by thin-film magnetic domain patterns, the feasibility of phase retrieval in x-ray diffractive imaging in the presence of intrinsic charge scattering given only photon-shot-noise limited diffraction data. We detail a reconstruction algorithm to recover the sample's magnetization distribution under such conditions and compare its performance with that of Fourier transform holography. Concerning the design of future experiments, we also chart out the reconstruction limits of diffractive imaging when photon-shot-noise and the intensity of charge scattering noise are independently varied. This work is directly relevant to the time-resolved imaging of magnetic dynamics using coherent and ultrafast radiation from x-ray free-electron lasers and also to broader classes of diffractive imaging experiments which suffer noisy data, missing data, or both.