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On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data

Chunguang Liu Jinan University Zuoqiang Shi Tsinghua University Thomas Y. Hou Caltech

Numerical Analysis and Scientific Computing mathscidoc:1709.25009

SIAM: Multiscale Modeling & Simulation, 13, (3), 790-811, 2015
In this paper, we analyze the uniqueness of the sparse time frequency decomposition and investigate the eciency of the nonlinear matching pursuit method. Under the assumption of scale separation, we show that the sparse time frequency decomposition is unique up to an error that is determined by the scale separation property of the signal. We further show that the unique decomposition can be obtained approximately by the sparse time frequency decomposition using nonlinear matching pursuit.
sparse time frequency decomposition; scale separation; nonlinear matching
[ Download ] [ 2017-09-27 10:07:43 uploaded by shizqi ] [ 885 downloads ] [ 0 comments ] 
@inproceedings{chunguang2015on,
  title={On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data},
  author={Chunguang Liu, Zuoqiang Shi, and Thomas Y. Hou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170927100743375909828},
  booktitle={SIAM: Multiscale Modeling & Simulation},
  volume={13},
  number={3},
  pages={790-811},
  year={2015},
}
Chunguang Liu, Zuoqiang Shi, and Thomas Y. Hou. On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data. 2015. Vol. 13. In SIAM: Multiscale Modeling & Simulation. pp.790-811. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170927100743375909828.
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