TY - GEN
T1 - Random projections of signal manifolds
AU - Wakin, Michael B.
AU - Baraniuk, Richard G.
PY - 2006
Y1 - 2006
N2 - 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 ℝN. 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 Whitney's Embedding Theorem, which states that a A'-dimensional manifold can be embedded in ℝ2K+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, we can recover certain signals using far fewer measurements than would be required using sparsity-driven CS techniques.
AB - 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 ℝN. 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 Whitney's Embedding Theorem, which states that a A'-dimensional manifold can be embedded in ℝ2K+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, we can recover certain signals using far fewer measurements than would be required using sparsity-driven CS techniques.
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M3 - Conference contribution
AN - SCOPUS:33947665032
SN - 142440469X
SN - 9781424404698
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - V941-V944
BT - 2006 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings
T2 - 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006
Y2 - 14 May 2006 through 19 May 2006
ER -