A small-sized soft x-ray (energy ≤ 1 keV) source based on a high-voltage vacuum discharge with a current of 20 kA and an ultrashort pulse duration of about 10 ps has been developed. It was shown that the radiation was emitted by a micropinch, which was formed in the discharge plasma and had a size of the order of a micrometer. In a single shot, an image of the test object was obtained with a resolution of several micrometers.