I think there's at least three different experiences here, and they're all valid, but I don't know what you really want.
A) remote desktop --- connect to a fully formed desktop environment (with SSH to authenticate, I guess?), possibly persisted and/or shared so you can connect back and get into the same place or share with another user?
B) run a program remotely and display it on your local terminal; essentially remote X, but I gather you're looking for more performance and maybe some other nice to haves? Maybe you want to transport audio too... Maybe you don't want the crap experience remote X has become since app developers don't spend any effort on it and you kind of get what you get, which is a lot of jank.
C) images in the terminal, with high performance. PNG should be ok for that, right? Maybe an extension for lossy compression might be nice depending.