Stable manifold embeddings with operators satisfying the Restricted Isometry Property

Signals of interests can often be thought to come from a low dimensional signal model. The exploitation of this fact has led to many recent interesting advances in signal processing, one notable example being in the field of compressive sensing (CS). The literature on CS has established that many matrices satisfy the Restricted Isometry Property (RIP), which guarantees a stable (i.e., distance-preserving) embedding of a sparse signal model from an undersampled linear measurement system. In this work, we study the stable embedding of manifold signal models using matrices that satisfy the RIP. We show that by paying reasonable additional factors in the number of measurements, all matrices that satisfy the RIP can also be used (in conjunction with a random sign sequence) to obtain a stable embedding of a manifold.