Kronecker Compressive Sensing

Authors:
Marco F. Duarte;Richard G. Baraniuk
Affiliations:
Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA, USA;Department of Electrical and Computer Engineering, Rice University, Houston, TX, USA
Venue:
IEEE Transactions on Image Processing
Year:
2012

Citing 0
Cited 3

Total variation minimization with separable sensing operator

ICISP'10 Proceedings of the 4th international conference on Image and signal processing
Block-Based Compressed Sensing of Images and Video

Foundations and Trends in Signal Processing
Computing sparse representations of multidimensional signals using kronecker bases

Neural Computation

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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.