Scientific spacecraft can generate very large amounts of data. However, both the storage available onboard the spacecraft and the bandwidth available to transmit the data to ground stations are limited. Thus, data compression is needed. What algorithms have been used successfully on spacecraft?
Image data is typically compressed using standard image compression algorithms. For example, the National Imagery Transmission Format, MIL-STD-2500C, defines a standard, extensible format for the transmission of imagery data within the military. The standard calls out several types of image compression compliant with the standard (such as JPEG).
Telemetry data is often not compressed at all. One rationale is that it is often several orders of magnitude less data than what is being generated by the payload (be it imagery, communications, or data from another type of instrument or sensor), and thus in the broad scheme of things not worth compressing. Telemetry is also often sent as a stream of data (rather than a file), which limits the types of compression schemes that could be used.
In fact, radio frequency signals are often intentionally increased in size through techniques like forward error correction (FEC) and convolution coding, which are means of adding redundant data to a signal to make the transmission more robust to transmission errors endemic to space communication links.
That said, there are standards for the lossless and lossy compression of spacecraft data. The Consultative Committee for Space Data Systems (CCSDS) has published a set of standards for Space communication links. There are currently four released standards that discuss lossless data compression and image data compression.
I will focus on meteorological satellites. They're a prime example of satellites that measure very large quantities of data (and one I have personal experience with). The bottom line is: they don't really compress the data, but they might degrade/limit it. A specific property of meteorological satellites is that the users want the data fast, so that could make a difference compared to other kinds of satellites.
The Advanced Very High Resolution Radiometer (AVHRR) is a meteorological imager that has flown on meteorological satellites from NOAA and EUMETSAT since 1979. It images the entire Earth at a resolution of 1 km in five simultaneously operated channels. This resolution is so high, that the relatively short time during which it has a downlink connection is not enough for the NOAA satellites to downlink all the data. Therefore, they downlink global data only in a special format known as Global Area Coverage (GAC): 4 adjacent pixels are averaged, and 2 out of 3 scanlines are ignored. Arguably, this is a kind of lossy compression. Users that need the full-resolution data for their own region can download it directly from the satellite (and national meteorological agencies do), or pre-order full-resolution data for specific regions (but not globally).
Three properties are limited:
- computational power
With enough computational power, the NOAA satellites could compress all the data and downlink all of it. Alas, the NOAA KLM series dates from 1999 and they don't have the computational power. Since then, all the three aforementioned properties have grown, and as far as meteorological satellites are concerned, it appears bandwidth and storage have grown more than computational power. Hence, I don't think there's any advanced compression going on for the vast amounts of data measured by meteorological satellites.
Of course, there are other satellites that also collect large quantities of data. I have no expertise on those, but maybe other people can contribute with relevant answers.