Computer-vision hospital systems can greatly assist healthcare workers and improve medical facility treatment, but often face patient resistance due to the perceived intrusiveness and violation of privacy associated with visual surveillance. We downsample video frames to extremely low resolutions to degrade private information from surveillance videos. We measure the amount of activity-recognition information retained in low resolution depth images, and also apply a privately-trained DCSCN super-resolution model to enhance the utility of our images. We implement our techniques with two actual healthcare-surveillance scenarios, hand-hygiene compliance and ICU activity-logging, and show that our privacy-preserving techniques preserve enough information for realistic healthcare tasks.