The Helium Ion Microscope (HIM) is a new tool capable of imaging at resolutions not possible in the ubiquitous Scanning Electron Microscope (SEM). However, along with this improvement in imaging, the helium ions used in HIM cause greater damage to samples. Reducing ion doses decreases the amount of damage incurred at the expense of increased noise in the final image. Motivated by the damage to samples inherent in HIM imaging, the possibility of imaging at low ion doses is investigated. A two-parameter Neyman Type A model of pixelwise Ion induced Secondary Electron (iSE) emission is introduced. This model takes into account randomness in both the Poisson emission of helium ions and the Poisson emission of iSE per each incident helium ion. HIM images are simulated for low ion doses. Using the Neyman Type A model, an image formation algorithm is developed using maximum likelihood (ML) estimation. This estimation procedure is regularized by sparsity in the wavelet domain to account for spatial correlations inherent in real world samples.