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.

UR - http://www.scopus.com/inward/record.url?scp=33947665032&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33947665032&partnerID=8YFLogxK

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 -