Signal Recovery on Incoherent Manifolds

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 submanifold of a high-dimensional ambient space. We introduce successive projections onto incoherent manifolds (SPIN), a first-order p...

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Bibliographic Details
Published in:IEEE transactions on information theory 2012-12, Vol.58 (12), p.7204-7214
Main Authors: Hegde, C., Baraniuk, R. G.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Approximation algorithms
Approximation methods
Compressed sensing
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Information theory
Information, signal and communications theory
Inverse problems
Manifolds
Mathematics
Measurement
Noise measurement
Operators
Projection
Recovery
sampling theory
Sampling, quantization
Signal and communications theory
signal deconvolution
Signal, noise
Sparse matrices
State of the art
Telecommunications and information theory
Vectors
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Summary: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 submanifold of a high-dimensional ambient space. We introduce successive projections 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 recovery models and algorithms for low-dimensional linear inverse problems and matches (or exceeds) the current state of the art in terms of performance.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2012.2210860