It's not java but it is well-written open source -- Audacity.  Has a
pretty good noise reduction algorithm among many other things:
http://audacity.sourceforge.net/

Mathematically you would do an FFT, remove the high frequencies or
other frequencies you designated as noise then convert back.  However,
surely there must be many packages out there for doing this or
something more sophisticated.

Google for noise reduction algorithms. Don't worry about wav files.
You can always convert them to something else.

See if GoldWave or Adobe's sound editing program  has something.