Technical Program

Paper Detail

Paper:	SS-1.5
Session:	Statistical Inferences on Nonlinear Manifolds with Applications in Signal and Image Processing
Time:	Tuesday, May 16, 11:50 - 12:10
Presentation:	Special Session Lecture
Topic:	Special Sessions: Statistical inferences on nonlinear manifolds with applications in signal and image processing
Title:	Random Projections of Signal Manifolds
Authors:	Michael Wakin, Richard Baraniuk, Rice University, United States
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 Whitney'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, we can recover certain signals using far fewer measurements than would be required using sparsity-driven CS techniques.