Inverse polyphonic chord recognition
The problem of polyphonic music transcription has received a huge amount of attention in the research community in recent years and I would go as far as to say that for single instrument polyphonies (piano, guitar etc...) the results are very good. Here are a few papers/authors who have looked at this problem deeply. Derry Fitzgerald has done a lot in the area, a lot of his NMF work on source separation produces accurate transcriptions. Anssi Klapuri has looked even more specifically at the problem of chord detection within multi instrument polyphonies. And finally, although not published, Mikel Gainza has developed very accurate chord transcription algorithms for commercial music soon to be released in a guitar based software product Riffstation.
The publications in the linkes here should give you a good idea of how the Polyphonic music transcription landscape currently lies.