Limited isometry RIP describes the similarity between a matrix and a standard orthogonal matrix and is used to describe the relationship between nearly standard orthogonal matrices when dealing with problems such as sparse vectors.

This concept was proposed by Emmanuel Candes and Terence Tao and has been used to prove several theorems in the field of compressed sensing. There are currently no known isometric constant matrices with bounded restrictions (calculating these constants is strongly NP-Hard and difficult to approximate), but many random matrices have been proven to be bounded.

It has been shown that the RIP is nearly linear in coefficients with respect to the quantity measured in exponentially high probability, random Gaussian, Bernoulli, and partial Fourier matrices.

References

【1】https://en.wikipedia.org/wiki/Restricted_isometry_property

【2】https://blog.csdn.net/jbb0523/article/details/44565647