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A new type of soft X-ray source, i.e. a plasma-based X-ray laser, is found to be promising to conduct transient measurement. By means of picosecond X-ray laser speckles, the dynamic microscopic polarization clusters within cubic (paraelectric) BaTiO3 was directly observed and characterized in a microscopic scale for the first time.This opens a way to study this type of clusters, which usually manifest large exteal-field response for ferroelectric materials.