A noninvasive high resolving power quantum microscope would facilitate progress in the areas of research and development in biosciences as well as in the area of biomedical technology. Longer-wavelength microscopes, i.e., visible or near-infrared, can provide noninvasive features. On the other hand, shorter wavelengths, i.e., in the ultraviolet, can provide better resolving power. We propose the development of both a noninvasive and high resolving power quantum microscope by using two-color entangled photon ghost imaging technology.