## Abstract

Random projections have recently found a surprising niche in signal processing. The key revelation is that the relevant structure in a signal can be preserved when that signal is projected onto a small number of random basis functions. Recent work has exploited this fact under the rubric of Compressed Sensing (CS): signals that are sparse in some basis can be recovered from small numbers of random linear projections. In many cases, however, we may have a more specific low-dimensional model for signals in which the signal class forms a nonlinear manifold in ℝ^{N}. This paper provides preliminary theoretical and experimental evidence that manifold-based signal structure can be preserved using small numbers of random projections. The key theoretical motivation comes from Whitney's Embedding Theorem, which states that a A'-dimensional manifold can be embedded in ℝ^{2K+1}. We examine the potential applications of this fact. In particular, we consider the task of recovering a manifold-modeled signal from a small number of random projections. Thanks to our more specific model, we can recover certain signals using far fewer measurements than would be required using sparsity-driven CS techniques.

Original language | English (US) |
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Title of host publication | 2006 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings |

Volume | 5 |

State | Published - Dec 1 2006 |

Event | 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006 - Toulouse, France Duration: May 14 2006 → May 19 2006 |

### Other

Other | 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006 |
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Country | France |

City | Toulouse |

Period | 5/14/06 → 5/19/06 |

## ASJC Scopus subject areas

- Software
- Signal Processing
- Electrical and Electronic Engineering