MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

The compressive sensing theory of Candes and Tao (See 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.

share|cite|improve this question

@Daniel: Can you make your question more precise? In traditional CS, the signal is $k$-sparse but their locations are typically uniformly distributed, i.e., there are $n\choose k$ possibilities. I am a bit confused as to what you mean by "data follow some distribution".

share|cite|improve this answer

This paper may be related:

V. Cevher, “Learning with compressible priors,” in NIPS, Vancouver, BC, Canada, 2008, p. 7--12.

From the abstract:

We describe a set of probability distributions, dubbed compressible priors, whose independent and identically distributed (iid) realizations result in p-compressible signals. [...] We show that the membership of generalized Pareto, Student’s t, log-normal, Frechet, and log-logistic distributions to the set of compressible priors depends only on the distribution parameters and is independent of N. In contrast, we demonstrate that the membership of the generalized Gaussian dis- tribution (GGD) depends both on the signal dimension and the GGD parameters

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.