Random Projections of Signal Manifolds
Author
Wakin, Michael; Baraniuk, Richard G.
Date
2006-01-01Abstract
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.
Description
Conference Paper
Citation
Published Version
Keyword
random projections; signal manifolds; Multiscale geometry processing; random projections; signal manifolds
Type
Conference paper
Citable link to this page
https://hdl.handle.net/1911/20434Metadata
Show full item recordCollections
- DSP Publications [508]
- ECE Publications [1468]