Abstract
Suppose that we observe noisy linear measurements of an unknown signal that can be modeled as the sum of two component signals, each of which arises from a nonlinear sub-manifold of a high-dimensional ambient space. We introduce Successive Projection onto INcoherent manifolds (SPIN), a first-order projected gradient method to recover the signal components. Despite the nonconvex nature of the recovery problem and the possibility of underdetermined measurements, SPIN provably recovers the signal components, provided that the signal manifolds are incoherent and that the measurement operator satisfies a certain restricted isometry property. SPIN significantly extends the scope of current signal recovery models and algorithms for low-dimensional linear inverse problems, and matches (or exceeds) the current state of the art in terms of performance.
Original language | English (US) |
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Title of host publication | 2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012 |
Pages | 1296-1300 |
Number of pages | 5 |
DOIs | |
State | Published - Oct 22 2012 |
Event | 2012 IEEE International Symposium on Information Theory, ISIT 2012 - Cambridge, MA, United States Duration: Jul 1 2012 → Jul 6 2012 |
Other
Other | 2012 IEEE International Symposium on Information Theory, ISIT 2012 |
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Country/Territory | United States |
City | Cambridge, MA |
Period | 7/1/12 → 7/6/12 |
ASJC Scopus subject areas
- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics