This text is a vital accessory to both students and professionals working on data compression, embedded processing and infrared astronomy. It tackles embedded data compression on-board space observatories for infrared astronomy. In the early chapter, infrared astronomy aspects are presented, including the infrared detector technologies, infrared signal characteristics and astronomical images in the infrared range. Afterwards, state-of-the-art compression is summarized as well as standardized methods for astronomical image compression are given. Designed for infrared space astronomy, the concept on-board processing is introduced to deal with the corresponding compression challenges. The complexity related aspects of the on-board processing, relevant for the DSP implementation, has been stressed. This text provides methodologies for the complexity measure of embedded applications. Finally, the PACS instrument from the ESA-Herschel space observatory is used as a case study for the demonstration of the on-board processing. Throughout the book, examples and illustrations drawn from the field of infrared astronomy illuminate the historical and technical information.