Developing a fast and robust THz time-domain imaging system that is low cost is essential for future commercial uses of such systems. Single-pixel imaging techniques are compatible with THz time-domain detectors and the combination of being a movement-free imaging system with undersampling capabilities gives them the potential of having fast acquisition rates. However, most undersampling algorithms have been designed for visible light imaging technology which is very different from THz technology. Here, we optimize the equipment and algorithms used for time-domain THz single-pixel imaging.