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A semiconductor Compton camera that combines silicon (Si) and cadmium telluride (CdTe) detectors was developed, and its imaging capability was examined with various kinds of gamma-ray targets such as a point source, arranged point sources and an extended source. The camera consists of one double-sided Si strip detector and four layers of CdTe pad detectors, and was designed to minimize the distance between a scatterer and the target. This is because the spatial resolution with Compton imaging improves as the target approaches the scatterer. This new camera realizes a minimum distance of 25 mm. By placing the target at a distance of 30 mm from the detector, resolving power better than 3 mm was demonstrated experimentally for a 364 keV (131I) gamma-ray. Positional determination with accuracy of 1 mm was also demonstrated. As a deconvolution method, we selected the iteration algorithm (called List-Mode Expectation-Maximizing Maximum Likelihood), and applied it to several kinds of experimental data. The Compton back projection images of the arranged point sources and an extended object were successfully deconvolved.