Sparse Optimization of Vibration Signal by ADMM
In this paper, the alternating direction method of multipliers (ADMM) algorithm is applied to the compressed sensing theory to realize the sparse optimization of vibration signal. Solving the basis pursuit problem for minimizing the L1 norm minimization under the equality constraints, the sparse mat...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2017/4612853 |
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| author | Song Wanqing |
| author_facet | Song Wanqing |
| author_sort | Song Wanqing |
| collection | DOAJ |
| description | In this paper, the alternating direction method of multipliers (ADMM) algorithm is applied to the compressed sensing theory to realize the sparse optimization of vibration signal. Solving the basis pursuit problem for minimizing the L1 norm minimization under the equality constraints, the sparse matrix obtained by the ADMM algorithm can be reconstructed by inverse sparse orthogonal matrix inversion. This paper analyzes common sparse orthogonal basis on the reconstruction results, that is, discrete Fourier orthogonal basis, discrete cosine orthogonal basis, and discrete wavelet orthogonal basis. In particular, we will show that, from the point of view of central tendency, the discrete cosine orthogonal basis is more suitable, for instance, at the vibration signal data because its error is close to zero. Moreover, using the discrete wavelet transform in signal reconstruction there still are some outliers but the error is unstable. We also use the time complex degree and validity, for the analysis of the advantages and disadvantages of the ADMM algorithm applied to sparse signal optimization. The advantage of this method is that these abnormal values are limited in the control range. |
| format | Article |
| id | doaj-art-a523cf461a7a4c8a889545e0e2546427 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-a523cf461a7a4c8a889545e0e25464272025-02-03T06:00:03ZengWileyJournal of Applied Mathematics1110-757X1687-00422017-01-01201710.1155/2017/46128534612853Sparse Optimization of Vibration Signal by ADMMSong Wanqing0School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, ChinaIn this paper, the alternating direction method of multipliers (ADMM) algorithm is applied to the compressed sensing theory to realize the sparse optimization of vibration signal. Solving the basis pursuit problem for minimizing the L1 norm minimization under the equality constraints, the sparse matrix obtained by the ADMM algorithm can be reconstructed by inverse sparse orthogonal matrix inversion. This paper analyzes common sparse orthogonal basis on the reconstruction results, that is, discrete Fourier orthogonal basis, discrete cosine orthogonal basis, and discrete wavelet orthogonal basis. In particular, we will show that, from the point of view of central tendency, the discrete cosine orthogonal basis is more suitable, for instance, at the vibration signal data because its error is close to zero. Moreover, using the discrete wavelet transform in signal reconstruction there still are some outliers but the error is unstable. We also use the time complex degree and validity, for the analysis of the advantages and disadvantages of the ADMM algorithm applied to sparse signal optimization. The advantage of this method is that these abnormal values are limited in the control range.http://dx.doi.org/10.1155/2017/4612853 |
| spellingShingle | Song Wanqing Sparse Optimization of Vibration Signal by ADMM Journal of Applied Mathematics |
| title | Sparse Optimization of Vibration Signal by ADMM |
| title_full | Sparse Optimization of Vibration Signal by ADMM |
| title_fullStr | Sparse Optimization of Vibration Signal by ADMM |
| title_full_unstemmed | Sparse Optimization of Vibration Signal by ADMM |
| title_short | Sparse Optimization of Vibration Signal by ADMM |
| title_sort | sparse optimization of vibration signal by admm |
| url | http://dx.doi.org/10.1155/2017/4612853 |
| work_keys_str_mv | AT songwanqing sparseoptimizationofvibrationsignalbyadmm |