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Title:
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Random Projections of Signal Manifolds |
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Author:
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Wakin, Michael; Baraniuk, Richard G.
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Type:
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Conference Paper |
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Keywords:
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random projections; signal manifolds |
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Citation:
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M. Wakin and R. G. Baraniuk,"Random Projections of Signal Manifolds," in IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP),, pp. V-941 - V-944. |
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Abstract:
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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 Whitneyâ s Embedding Theorem, which states
that a K-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, the ability to recover the signal can be far superior to
existing techniques in CS. |
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Date Published:
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2006-05-01 |
