Physical Sciences and Mathematics Commons^™

Restricted Isometric Projections For Differentiable Manifolds And Applications, Vasile Pop

USF Tampa Graduate Theses and Dissertations

The restricted isometry property (RIP) is at the center of important developments in compressive sensing. In R^N, RIP establishes the success of sparse recovery via basis pursuit for measurement matrices with small restricted isometry constants δ_2s < 1=3. A weaker condition, δ_2s < 0:6246, is actually sufficient to guarantee stable and robust recovery of all s-sparse vectors via l₁-minimization. In infinite Hilbert spaces, a random linear map satisfies a general RIP with high probability and allow recovering and extending many known compressive sampling results. This thesis extends the known restricted isometric projection of sparse datasets of vectors embedded in the Euclidean spaces RN down into low-dimensional subspaces R^m ,m << N …