# Seismic Signal Compression Using Nonparametric Bayesian Dictionary Learning via Clustering
## 3 Seismic Signal Compression Using Nonparametric Bayesian Dictionary Learning via Clustering
### Online Testing
For compression, the nonzero coefficients are quantized and coded with an adaptive arithmetic coding algorithm. The quantization step in this experiment is 1024. The experimental results are shown in Figure 7. Curvelet performs better than DCT in most situations--especially in higher rates. OffDL, DLOD and the proposed method outperformed DCT and Curvelet. The compression performance of OffDL highly depends on the correlation between the training data and the testing data. For example, for sensor 3, its performance could be close to DLOD, yet its performance deteriorated for sensor 1. The performance of the proposed method is made better than OffDL and OLOD by the use of clustering. Although the rate will increase by transmission for the information of clustering, the distortion could be efficiently reduced--especially when the rate is high. For example, the rate gain of the proposed method could be approximately 22.4% and 77.8% when \(SNR\) is about 28 dB for the seismic signals of sensor 1. Then, we could conclude that the proposed method is an efficient method for seismic signal compression. Figure 6: Experimental result of dictionary learning. ## 5 Conclusions

In this paper, we have shown how to compress seismic signals efficiently by using a clustering-based nonparametric Bayesian dictionary learning method. The previous transmitted data is used to train the dictionary for sparse representation. After clustering by their structural similarities, each cluster could have its own dictionary. Then, the seismic signals of each cluster could be well represented. A nonparametric Bayesian dictionary learning method is used to train the dictionary, which infers an adaptive dictionary size. Experimental results demonstrate better rate-distortion performance over other seismic signal compression schemes, validating the effectiveness of the proposed method. This work is supported by the Basic Research (Free Exploration) Project from Commission on Innovation and Technology of Shenzhen, the Nature Science Foundation of China, under grants 61102064, and Key Laboratory of Satellite Mapping Technology and Application, National Administration of Surveying, Mapping and Geoinformation. All of the authors contributed to the content of this paper. [PERSON] wrote the paper and conceived the experiments. [PERSON] performed the theoretical analysis. The authors declare no conflict of interest. ## References

* [PERSON] et al. (2015) [PERSON]; [PERSON] [PERSON]; [PERSON] Use of composite higher order spectra for faults diagnosis of rotating machines with different foundation flexibilities. _Measurement_**2015**, _70_, 47-61. * [PERSON] et al. (2016) [PERSON]; [PERSON] Sensitivity analysis of higher order coherent spectra in machine faults diagnosis. _Struct. Health Monit._**2016**, _15_, 555-567, doi:10.1177/1475921716651394. * [PERSON] et al. (1991) [PERSON]; [PERSON]; [PERSON] Transform Methods for Seismic Data Compression. _IEEE Trans. Geosci. Remote Sens._**1991**, _29_, 407-416. Figure 7: Compression performance comparison of seismic signals from different sensors. * [PERSON] and [PERSON] (2006) [PERSON]; [PERSON] Adaptive Local Cosine transform for Seismic Image Compression. In Proceedings of the 2006 International Conference on Advanced Computing and Communications, Surathkal, India, 20-23 December 2006. * [PERSON] [PERSON] (2007) [PERSON]; [PERSON] [PERSON] Leading-order Seismic Imaging Using Curvelets. _Geophysics_**2007**, _72_, S231-S248. * [PERSON] et al. (2008) [PERSON]; [PERSON]; [PERSON]; [PERSON] Curvelet-based seismic data processing: A multiscale and nonlinear approach. _Geophysics_**2008**, _73_, A1-A5, doi:10.1190/1.2799517. * [PERSON] and [PERSON] (2011) [PERSON]; [PERSON] Image compression using learned dictionaries by RLS-DLA and compared with K-SVD. In Proceedings of the 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic, 22-27 May 2011; pp. 1517-1520. * [PERSON] et al.