Abstract Seismic data regularization is an important preprocessing step in seismic signal processing. Traditional seismic acquisition methods follow the Shannon–Nyquist sampling theorem, whereas compressive sensing (CS) provides a fundamentally new paradigm to overcome limitations in data acquisition. Besides the sparse representation of seismic signal in some transform domain and the 1-norm reconstruction algorithm, the seismic data regularization quality of CS-based techniques strongly depends on random undersampling schemes. For 2D seismic data, discrete uniform-based methods have been investigated, where some seismic traces are randomly sampled with an equal probability. However, in theory and practice, some seismic traces with different probability are required to be sampled for satisfying the assumptions in CS. Therefore, designing new undersampling schemes is imperative. We propose a Bernoulli-based random undersampling scheme and its jittered version to determine the regular traces that are randomly sampled with different probability, while both schemes comply with the Bernoulli process distribution. We performed experiments using the Fourier and curvelet transforms and the spectral projected gradient reconstruction algorithm for 1-norm (SPGL1), and ten different random seeds. According to the signal-to-noise ratio (SNR) between the original and reconstructed seismic data, the detailed experimental results from 2D numerical and physical simulation data show that the proposed novel schemes perform overall better than the discrete uniform schemes.
This paper was financially supported by The 2011 Prospective Research Project of SINOPEC (P11096).
Cite this article:
CAI Rui,ZHAO Qun,SHE De-Ping et al. Bernoulli-based random undersampling schemes for 2D seismic data regularization[J]. APPLIED GEOPHYSICS, 2014, 11(3): 321-330.
[1]
Baraniuk, R. G., 2007, Compressive sensing: IEEE Signal Processing Magazine, 24(4), 118-121.
[2]
Baraniuk, R. G., 2011, More is less: signal processing and the data deluge: Science, 331(6018), 717-719.
[3]
Berg, E. V. D., and Friedlander, M. P., 2008, Probing the Pareto frontier for basis pursuit solutions: SIAM Journal on Scientific Computing, 31(2), 890-912.
[4]
Berg, E. V. D., Friedlander, M. P., Hennenfent, G., Herrmann, F. J., Saab, R., and Yilmaz, O., 2009, Algorithm 890: Sparco: a testing framework for sparse reconstruction: ACM Transactions on Mathematical Software, 35(4), 1-16.
[5]
Billingsley, P., 1986, Probability and measure (2nd Edition): Wiley press.
[6]
Candes, E. J., 2006, Compressive sampling: International Congress of Mathematics, 3, 1433-1452.
[7]
Davenport, M., Duarte, M., Eldar, Y. C., and Kutyniok, G., 2012, Introduction to compressed sensing, In Eldar, Y. C., and Kutyniol, G., Eds., Compressed Sensing: Theory and Applications: Cambridge University Press.
[8]
Donoho, D., 2006, Compressed sensing: IEEE Transactions on Information Theory, 52(4), 1289-1306.
[9]
Fornasier, M., 2010, Theoretical foundations and numerical methods for sparse recovery: de Gruyter Press.
[10]
Hennenfent, G., and Herrmann, F. J., 2008, Simply denoise: wavefield reconstruction via jittered undersampling: Geophysics, 73(3), V19-V28.
[11]
Herrmann, F. J., Wang, D., Hennenfent, G., and Moghaddam, P. P., 2008, Curvelet-based seismic data processing: a multiscale and nonlinear approach: Geophysics, 73(1), A1-A5.
[12]
Herrmann, F. J., and Hennenfent, G., 2008, Nonparametric seismic data recovery with curvelet frames: Geophysical Journal International, 173(1), 233-248.
[13]
Herrmann, F. J., 2010, Randomized sampling and sparsity: getting more information from fewer samples: Geophysics, 75(6), WB172-WB187.
[14]
Li, C., Mosher C. C., Shan, S., and Brewer, J. D., 2013, Marine towed streamer data reconstruction based on compressive sensing: 83th Ann. Soc. Expl. Geophys. Mtg., Expanded Abstracts, 3597-3602.
[15]
Mansour, H., Herrmann, F.J., and Yilmaz, O, 2013, Improved wavefield reconstruction from randomized sampling via weighted one-norm minimization: Geophysics, 78(5), V193-V206
[16]
Patel, V. M., and Chellappa, R., 2013, Sparse representations and compressive sensing for imaging and vision, Springer press.
Wang, S., Li, J., Chiu, S. K., and Anno, P. D., 2010, Seismic data compression and regularization via wave packets: 80th Ann. Soc. Expl. Geophys. Mtg., Expanded Abstracts, 3650-3655.
[19]
Wang, Y., Cao, J., and Yang, C., 2011, Recovery of seismic wavefield-based on compressive sensing by an l1-norm constrained trust region method and the piecewise random subsampling: Geophysical Journal International, 187(1), 199-213.
[20]
Wu, R.-S., Geng, Y. and Ye, L., 2013, Preliminary study on dreamlet-based compressive sensing data recovery: 83th Ann. Soc. Expl. Geophys. Mtg., Expanded Abstracts, 3585-3590.
2014, Vol. 11 
