I think identification of CRC algorithm is a better description. Reversing a compression function in the mathematical sense is simply not possible unless there are trapdoors or biases and the like. But in the reverse engineering context I think we can imply as such.
Have you tried all CRC16 possibilities on this page in Javascript?
http://www.sunshine2k.de/coding/javascript/crc/crc_js.html
Considering it could be a truncated CRC32 or CRC64 or concatenated CRC8 of subpieces or a custom CRC, it is somewhat hard to say. If its based off a polynomial may e there is a way to find it but I've not seen a technique for this but it sounds promising. Otherwise you may need to see if you can white box reverse this.
I doubt glancing at what seem to be CRC16 type values will be trivially obvious to anyone though
