Transmission electron microscopes (TEM) achieve high resolution imaging by raster scanning a focused beam of electrons over the sample and measuring the transmission to form an image. While a TEM can achieve a much higher resolution than optical microscopes, they face challenges of damage to samples during the high energy processes involved. Here, we explore the possibility of applying computational ghost imaging techniques adapted from the optical regime to reduce the total, required illumination intensity. The technological lack of the equivalent high-resolution, optical spatial light modulator for electrons means that a different approach needs to be pursued. Using the optical equivalent, we show that a simple six-needle charged device to modulate the illuminating beam, alongside a novel reconstruction method to handle the resulting highly non-orthogonal patterns, is capable of producing images comparable in quality to a raster-scanned approach with much lower peak intensity.