Entanglement and correlation are at the basis of quantummechanicsand have been used in optics to create a framework for "ghostimaging". We propose that a similar scheme can be used in anelectron microscope to exploit the correlation of electrons with thecoincident detection of collective mode excitations in a sample. Inthis way, an image of the sample can be formed on an electron cameraeven if electrons never illuminated the region of interest directly.This concept, which can be regarded as the inverse of photon-inducednear-field electron microscopy, can be used to probe delicate moleculeswith a resolution that is beyond the wavelength of the collectivemode.