Kronecker compressive sensing

Marco F. Duarte, Richard G. Baraniuk

Research output: Contribution to journalArticle

347 Scopus citations

Abstract

Compressive sensing (CS) is an emerging approach for the acquisition of signals having a sparse or compressible representation in some basis. While the CS literature has mostly focused on problems involving 1-D signals and 2-D images, many important applications involve multidimensional signals; the construction of sparsifying bases and measurement systems for such signals is complicated by their higher dimensionality. In this paper, we propose the use of Kronecker product matrices in CS for two purposes. First, such matrices can act as sparsifying bases that jointly model the structure present in all of the signal dimensions. Second, such matrices can represent the measurement protocols used in distributed settings. Our formulation enables the derivation of analytical bounds for the sparse approximation of multidimensional signals and CS recovery performance, as well as a means of evaluating novel distributed measurement schemes.

Original languageEnglish (US)
Article number5986706
Pages (from-to)494-504
Number of pages11
JournalIEEE Transactions on Image Processing
Volume21
Issue number2
DOIs
StatePublished - Feb 2012

Keywords

  • Compressed sensing
  • compression algorithms
  • hyperspectral imaging
  • multidimensional signal processing
  • video compression

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software

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