The compressive sensing theory of Candes and Tao (See http://en.wikipedia.org/wiki/Compressed_sensing) relies highly on the fact that the underlying data (such as a signal or an image) is sparse or compressible under some basis.

Now we suppose that the underlying data is probabilistic, namely the data follow some distribution. And we want to know with how much probability that the samples from the distribution would be sparse or compressive under some basis.

Is there any relevant literature? Thanks.