Random Projections of Signal Manifolds

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Title: Random Projections of Signal Manifolds
Author: Wakin, Michael; Baraniuk, Richard G.
Type: Conference paper
Keywords: random projections; signal manifolds
Citation: M. Wakin and R. G. Baraniuk, "Random Projections of Signal Manifolds," vol. 5, pp. V-941 - V-944, 2006.
Abstract: 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.
Date Published: 2006-05-01

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  • ECE Publications [1048 items]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students
  • DSP Publications [508 items]
    Publications by Rice Faculty and graduate students in digital signal processing.