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Sensors 2012, 12(10), 13034-13057; doi:10.3390/s121013034
Article

Expanding Window Compressed Sensing for Non-Uniform Compressible Signals

1,* , 1
,
1
 and
2
1 Key Lab of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China 2 Department of Electronics and Computer Engineering, Hanyang University, Seoul 133791, Korea
* Author to whom correspondence should be addressed.
Received: 7 June 2012 / Revised: 28 August 2012 / Accepted: 13 September 2012 / Published: 26 September 2012
(This article belongs to the Special Issue Ubiquitous Sensing)
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Abstract

Many practical compressible signals like image signals or the networked data in wireless sensor networks have non-uniform support distribution in their sparse representation domain. Utilizing this prior information, a novel compressed sensing (CS) scheme with unequal protection capability is proposed in this paper by introducing a windowing strategy called expanding window compressed sensing (EW-CS). According to the importance of different parts of the signal, the signal is divided into several nested subsets, i.e., the expanding windows. Each window generates its own measurements using a random sensing matrix. The more significant elements are contained by more windows, so they are captured by more measurements. This design makes the EW-CS scheme have more convenient implementation and better overall recovery quality for non-uniform compressible signals than ordinary CS schemes. These advantages are theoretically analyzed and experimentally confirmed. Moreover, the EW-CS scheme is applied to the compressed acquisition of image signals and networked data where it also has superior performance than ordinary CS and the existing unequal protection CS schemes.
Keywords: compressed sensing; image compression; networked data; non-uniform compressible signal; random projection; unequal protection compressed sensing; image compression; networked data; non-uniform compressible signal; random projection; unequal protection
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Liu, Y.; Zhu, X.; Zhang, L.; Cho, S.H. Expanding Window Compressed Sensing for Non-Uniform Compressible Signals. Sensors 2012, 12, 13034-13057.

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