New Analysis of Manifold Embeddings and Signal Recovery From Compressive Measurements
Compressive Sensing (CS) exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive, often random linear measurements of that signal. Strong theoretical guarantees have been established concerning the embedding of a sparse signal family under a random measurement operator and on the accuracy to which sparse signals can be recovered from noisy compressive measurements. In this paper, the authors address similar questions in the context of a different modeling framework. Instead of sparse models, they focus on the broad class of manifold models, which can arise in both parametric and non-parametric signal families.