Stable Manifold Embeddings with Operators Satisfying the Restricted Isometry Property (bibtex)

by H.L. Yap, M.B. Wakin and C.J. Rozell

Abstract:

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.

Reference:

Stable Manifold Embeddings with Operators Satisfying the Restricted Isometry PropertyH.L. Yap, M.B. Wakin and C.J. Rozell. In Proceedings of the Conference on Information Sciences and Systems (CISS), March 2011.

Bibtex Entry:

@InProceedings{yap.11, author = {Yap, H.L. and Wakin, M.B. and Rozell, C.J.}, title = {Stable Manifold Embeddings with Operators Satisfying the Restricted Isometry Property}, booktitle = {{Proceedings of the Conference on Information Sciences and Systems (CISS)}}, year = 2011, month = {March}, address = {Baltimore, MD}, abstract={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. }, url = {http://siplab.gatech.edu/pubs/yapCISS2011.pdf} }

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