The majority of the work done by imlocalbrighten() is handled by imreducehaze(). The rest is just input parsing, inversion, and output compositing (if selected). So open it up and look through it. Open up imreducehaze() and look through it too. There may be some private functions that get called internally, but they should be under toolbox/images/images/private/ or somewhere therabouts. For what it's worth, imreducehaze() has a lot of descriptive comments, so that should help.
As far as which of the papers have been used, I imagine all three were used to at least some extent that would warrant citing them. I don't have copies of them, so it's not immediately apparent which papers contribute to certain features of the code as written.
