Restricted Isometry Property under High Correlations

Understand

Matrices satisfying the Restricted Isometry Property (RIP) play an important role in the areas of compressed sensing and statistical learning.

• RIP matrices with optimal parameters are mainly obtained via probabilistic arguments, as explicit constructions seem hard.
• It is therefore interesting to ask whether a fixed matrix can be incorporated into a construction of restricted isometries.
• In this paper, we construct a new broad ensemble of random matrices with dependent entries that satisfy the restricted isometry property.