Low-dimensional models for dimensionality reduction and signal recovery: A geometric perspective

Richard G. Baraniuk, Volkan Cevher, Michael B. Wakin

Research output: Contribution to journalReview article

110 Scopus citations

Abstract

We compare and contrast from a geometric perspective a number of low-dimensional signal models that support stable information-preserving dimensionality reduction. We consider sparse and compressible signal models for deterministic and random signals, structured sparse and compressible signal models, point clouds, and manifold signal models. Each model has a particular geometrical structure that enables signal information to be stably preserved via a simple linear and nonadaptive projection to a much lower dimensional space; in each case the projection dimension is independent of the signal's ambient dimension at best or grows logarithmically with it at worst. As a bonus, we point out a common misconception related to probabilistic compressible signal models, namely, by showing that the oft-used generalized Gaussian and Laplacian models do not support stable linear dimensionality reduction.

Original languageEnglish (US)
Article number5456163
Pages (from-to)959-971
Number of pages13
JournalProceedings of the IEEE
Volume98
Issue number6
DOIs
StatePublished - Jun 2010

Keywords

  • Compression
  • Compressive sensing
  • Dimensionality reduction
  • Manifold
  • Point cloud
  • Sparsity
  • Stable embedding

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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