TY - JOUR
T1 - Kronecker compressive sensing
AU - Duarte, Marco F.
AU - Baraniuk, Richard G.
N1 - Funding Information:
Manuscript received December 16, 2009; revised November 12, 2010, March 18, 2011 and July 28, 2011; accepted August 09, 2011. Date of publication August 18, 2011; date of current version January 18, 2012. This work was supported in part by the National Science Foundation under Grant CCF-0431150 and Grant CCF-0728867, by the Defense Advanced Research Projects Agency/ Office of Naval Research (ONR) under Grant N66001-08-1-2065, by the ONR under Grant N00014-07-1-0936 and Grant N00014-08-1-1112, by the Air Force Office of Scientific Research under Grant FA9550-07-1-0301, by the Multidisciplinary University Research Initiatives of the Army Research Office under Grant W911NF-07-1-0185 and Grant W911NF-09-1-0383, and by the Texas Instruments Leadership Program. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Ying Wu.
PY - 2012/2
Y1 - 2012/2
N2 - 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.
AB - 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.
KW - Compressed sensing
KW - compression algorithms
KW - hyperspectral imaging
KW - multidimensional signal processing
KW - video compression
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U2 - 10.1109/TIP.2011.2165289
DO - 10.1109/TIP.2011.2165289
M3 - Article
C2 - 21859622
AN - SCOPUS:84856295286
VL - 21
SP - 494
EP - 504
JO - IEEE Transactions on Image Processing
JF - IEEE Transactions on Image Processing
SN - 1057-7149
IS - 2
M1 - 5986706
ER -