Journal
IEEE TRANSACTIONS ON IMAGE PROCESSING
Volume 21, Issue 2, Pages 494-504Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIP.2011.2165289
Keywords
Compressed sensing; compression algorithms; hyperspectral imaging; multidimensional signal processing; video compression
Funding
- National Science Foundation [CCF-0431150, CCF-0728867]
- Defense Advanced Research Projects Agency/Office of Naval Research (ONR) [N66001-08-1-2065]
- ONR [N00014-07-1-0936, N00014-08-1-1112]
- Air Force Office of Scientific Research [FA9550-07-1-0301]
- Multidisciplinary University Research Initiatives of the Army Research Office [W911NF-07-1-0185, W911NF-09-1-0383]
- Texas Instruments Leadership Program
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [0926127] Funding Source: National Science Foundation
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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 themeasurement 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.
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