A Reconstruction Method for Compressed Sampling in Shift-Invariant Spaces


  • Junyi Luo School of Electronic Information Engineering, Chengdu University, Chengdu City
  • Yuting Yang School of Foreign Language, Chengdu University, Chengdu City




A traditional sampling method is that the signal should be sampled at a rate exceeding twice the highest frequency. This is based on the assumption that the signal occupies the entire bandwidth. In practice, however, many signals are sparse so that only part of the bandwidth is used. Compressed sampling has been developed for low-rate sampling of continuous time sparse signals in shift-invariant spaces generated by m kernels with period T. However, in general the reconstruction of compressed sampling signals is unstable. To reconstruct the signal, continuous reconstruction is replaced by generalized inverse. In this paper, periodic non-uniform sampling and the reconstruction of functions in shift-invariant spaces are discussed, the unique sparse expression is obtained by using the minimal L1 norm. Also, necessary condition and error of reconstruction were analyzed. Finally, the method was validated via simulation and it was shown that the method was effective.


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Baraniuk, R., A Lecture on Compressive Sensing, IEEE Signal Processing Magazine, 6(3), pp. 88-97, 2007.

Cands, E.J., An Introduction To Compressive Sampling, IEEE Signal Processing Magazine, (3), pp. 20-30, 2008.

Nguyen, H.T. & Do, M.N., Signal Reconstruction from a Periodic Nonuniform Set of Samples Using Ha?? Optimization, IEEE Trans. Signal Proc., 53(5), pp. 1731-1738, 2005.

Meng, C. & Tuqan , J., Generalized Periodic Non-uniform Sampling of Non-bandlimited Signals[C], IEEE International Conference ICASSP Madrid, Spain, pp. 1-3, 2006.

Donoho, D., Compressed Sensing, IEEE Trans. Inform. Theory, 52(4) pp. 1289-1306, 2006

Cands, E.J., Compressive Sampling, Proceedings of the International Congress of Mathematicians, Seattle, U.S.A. pp. 524-526, 2006.

Cotter, S.F. Sparse Solutions to Linear Inverse Problems with Multiple Measurement Vectors, IEEE Transactions on Signal Processing, 53(7) pp. 2477-2489, 2005.

Rebollo-Neira, L. & Lowe, D., Optimized Orthogonal Matching Pursuit Approach, IEEE Signal Processing Letters, 9(4), pp. 137-140, 2002.




How to Cite

Luo, J., & Yang, Y. (2016). A Reconstruction Method for Compressed Sampling in Shift-Invariant Spaces. Journal of Engineering and Technological Sciences, 48(2), 183-199. https://doi.org/10.5614/j.eng.technol.sci.2016.48.2.5