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Journal of Applied Mathematics
Volume 2013, Article ID 715848, 6 pages
http://dx.doi.org/10.1155/2013/715848
Research Article

Exact CS Reconstruction Condition of Undersampled Spectrum-Sparse Signals

1Institute of Information and Navigation, Air Force Engineering University, Xi’an 710077, China
2Key Laboratory for Information Science of Electromagnetic Waves, Ministry of Education, Fudan University, Shanghai 200433, China
3Institute of Science, Air Force Engineering University, Xi’an 710051, China

Received 15 August 2013; Accepted 18 November 2013

Academic Editor: Feng Gao

Copyright © 2013 Ying Luo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Compressive sensing (CS) reconstruction of a spectrum-sparse signal from undersampled data is, in fact, an ill-posed problem. In this paper, we mathematically prove that, in certain cases, the exact CS reconstruction of a spectrum-sparse signal from undersampled data is impossible. Then we present the exact CS reconstruction condition of undersampled spectrum-sparse signals, which is valuable for digital signal compression.