We present a diffuser-based computational X-ray coherent imaging method using a speckle-correlation scattering matrix (SSM), which is based on the spatial pseudorandomness of generated speckle patterns. An X-ray diffuser was introduced to ensure the generation of pseudorandom speckle patterns on the detector. Using the SSM method, we achieved 13.9 nm image resolution, which surpasses the feature size of the diffuser (300 nm). We also apply our method to the shot-by-shot pulse characterization of an X-ray free-electron laser; and analyze the statistical properties of each pulse in intensity, position, angle, and shape.
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