I have been looking for the origin of the restricted isometry property (RIP). Many papers cite the origin of the RIP in the following paper
- Emmanuel Candès, Terence Tao, Decoding by Linear Programming, February 2005.
but I cannot understand where the definition came from. Some others papers say that the RIP is very similar to the Johnson-Lindenstrauss lemma (JL), and in fact it is, but I am not sure that that it is the origin of the RIP. However, I haven't been able to find this origin, mathematically.
On the other hand, how can the RIP be proved with certain matrices? Let's say for example Gaussian matrices or a Fourier matrix?