SPIN: Iterative signal recovery on incoherent manifolds

Chinmay Hegde; Richard G. Baraniuk

doi:10.1109/ISIT.2012.6283066

SPIN: Iterative signal recovery on incoherent manifolds

Chinmay Hegde, Richard G. Baraniuk

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

6 Scopus citations

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)
Title of host publication	2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012
Pages	1296-1300
Number of pages	5
DOIs	https://doi.org/10.1109/ISIT.2012.6283066
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
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

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10.1109/ISIT.2012.6283066

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title = "SPIN: Iterative signal recovery on incoherent manifolds",

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.",

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AB - 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.

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BT - 2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012

Y2 - 1 July 2012 through 6 July 2012

ER -

SPIN: Iterative signal recovery on incoherent manifolds

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