Yes. I know of a person trading profitably with about $200k capital. The company I work for started off this way as well, and it's considerably larger than $200k. I also know of a person who went this route and had trading profits but his trading profits didn't cover expenses (he lost something in the neighborhood of $50-100k).
You'll typically need to buy a server and colocate it at your broker's datacenter.
Brokers to talk to:
http://www.limebrokerage.com/offerings/by_role_highfrequency... (This is the same Lime as LimeWire.)
http://www.interactivebrokers.com/ibg/main.php
Unless you are very rich, you probably can't afford to do latency arbitrage, which is only a subset of high frequency. The capital expenses (custom routers and the like) are probably too high for individuals.