Compressed Sensing: How sharp is the RIP?

Consider a measurement matrix A of size n×N, with n < N, y a signal in R^N, and b = Ay the observed measurement of the vector y. From knowledge of (b,A), compressed sensing seeks to recover the k-sparse x, k < n, which minimizes ||b-Ax||. Using various methods of analysis — convex polytopes, geometric … Read more

Phase Transitions for Greedy Sparse Approximation Algorithms

A major enterprise in compressed sensing and sparse approximation is the design and analysis of computationally tractable algorithms for recovering sparse, exact or approximate, solutions of underdetermined linear systems of equations. Many such algorithms have now been proven using the ubiquitous Restricted Isometry Property (RIP) [9] to have optimal-order uniform recovery guarantees. However, it is … Read more