지구물리와물리탐사 (Geophysics and Geophysical Exploration)

  • 제14권4호
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  • Pages.335-341
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  • 2011
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  • 1229-1064(pISSN)
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  • 2384-051X(eISSN)
한국지구물리·물리탐사학회 (Korean Society of Earth and Exploration Geophysicists)
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센싱 및 계측 기술에서의 혁신: 지구물리 탐사를 위한 압축센싱 및 초고해상도 기술

A Breakthrough in Sensing and Measurement Technologies: Compressed Sensing and Super-Resolution for Geophysical Exploration

  • 공승현 (한국과학기술원 항공우주학공과) ;
  • 한승준 (한국과학기술원 항공우주학공과)
  • Kong, Seung-Hyun (Dept. of Aerospace Engineering, Korea Advanced Institute of Science and Technology (KAIST)) ;
  • Han, Seung-Jun (Dept. of Aerospace Engineering, Korea Advanced Institute of Science and Technology (KAIST))
  • Received : 2011.10.19
  • Accepted : 2011.11.17
  • Published : 2011.11.30
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⟨ 이전 논문 다음 논문 ⟩

Abstract

탐사 시스템을 포함하여 대부분의 센싱 및 계측 시스템은 중요한 정보를 놓치지 않기 위하여 필요한 정보 보다 높은 샘플주기로 정보를 수집 한다. 이는 경우에 따라 센싱 및 계측 시스템이 비효율적일 수 있음을 의미한다. 본 논문에서는 적은 샘플자료로부터 높은 정밀도의 정보 취득에 관한 새로운 두 가지 연구분야를 소개하고자 한다. 하나는 가능한 적은 샘플로 원래의 정보를 복원하는 압축센싱(Compressed Sensing)기술이며, 또 다른 하나는 이미 얻어진 한정된 샘플로부터 높은 해상도의 정보를 추정하는 초고해상도(Super-Resolution)기술이다. 본 논문에서는 압축센싱 기술의 기본이론과 복원기술에 대해 설명하고, 탐사분야의 적용 사례, 초고해상도 기술의 배경 및 최근의 기술인 FRI (Finite Rate of Innovation) 개념과 LIMS (Least-squares based Iterative Multipath Super-resolution)기술의 적용사례를 소개한다. 결론으로는 이러한 새로운 기술들이 지구물리 탐사분야에 어떻게 활용될 수 있는지 논의한다.

Most sensing and instrumentation systems should have very higher sampling rate than required data rate not to miss important information. This means that the system can be inefficient in some cases. This paper introduces two new research areas about information acquisition with high accuracy from less number of sampled data. One is Compressed Sensing technology (which obtains original information with as little samples as possible) and the other is Super-Resolution technology (which gains very high-resolution information from restrictively sampled data). This paper explains fundamental theories and reconstruction algorithms of compressed sensing technology and describes several applications to geophysical exploration. In addition, this paper explains the fundamentals of super-resolution technology and introduces recent research results and its applications, e.g. FRI (Finite Rate of Innovation) and LIMS (Least-squares based Iterative Multipath Super-resolution). In conclusion, this paper discusses how these technologies can be used in geophysical exploration systems.

Keywords

References

  1. Baboulaz, L. and Dragatti, P., 2009, Exact Feature Extraction Using Finite Rate of Innovation Principles With and Application to Image Super-Resolution, IEEE Trans. On Image Processing, 18(2), 281-298. https://doi.org/10.1109/TIP.2008.2009378
  2. Baraniuk, R., Davenport, M., Duarte, M., and Hegde, C., 2011, An Introduction to Compressive Sensing, http://cnx.org/content/col11133/1.5
  3. Berinde, R. and Indyk, P. 2009, Sequential Sparse Matching Pursuit, 47th Annual Allerton Conference on Communication, Control and Computing, Allerton 2009., IEEE, 36-43.
  4. Blumensath, T. and Davies, M., 2009, Iterative Hard Thresholding for Compressed Sensing, Applied and Computational Harmonic Analysis, 27(3), 265-274. https://doi.org/10.1016/j.acha.2009.04.002
  5. Calderbank, R., Howard, S., and Jafarpour, S., 2010, Construction of a Large Class of Deterministic Sensing Matrices that Satisfy a Statistical Isometry Property, IEEE Journal of Selected Topics in Signal Processing, 4(2), 358-374. https://doi.org/10.1109/JSTSP.2010.2043161
  6. Candes, E. and Donoho, D., 2004, New Tight Frames of Curvelets and Optimal Representations of Objects with Piecewise C2 Singularities, Communications on Pure and Applied Mathematics, 57(2), 219-266. https://doi.org/10.1002/cpa.10116
  7. Candes, E., Romberg, J., and Tao, T., 2006, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information, IEEE Trans. On information theory, 52, pp. 489-509. https://doi.org/10.1109/TIT.2005.862083
  8. Candes, E., Rudelson, M., Tao, T., and Vershynin. R., 2005, Error correction via linear programming, 46th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2005. IEEE, 295-308.
  9. Candes, E.,Demanet, L. Donoho, D., and Ying, L., 2006, Fast Discrete Curvelet Transforms, Multiscale Modeling and Simulation, 5(3), 861-899. https://doi.org/10.1137/05064182X
  10. Donoho, D., 2006, Compressed sensing, IEEE Trans. on Information Theory, 52(4), 1289-1306. https://doi.org/10.1109/TIT.2006.871582
  11. Donoho, D., Drori, I., Tsaig, Y., and Stark, J. L., 2006, Sparse Solution of Underdetermined Linear Equations by Stagewise Orthogonal Matching Pursuit, Technical Report 2006-2, Department of Statistics, Stanford University.
  12. Duarte, M., Davenport, M., Takhar, D., Laska, J., Sun, T., Kelly, K., and Baraniuk, R., 2008, Single-pixel Imaging via Compressive Sampling, IEEE Signal Process. Magazine, 25(2), 83-91. https://doi.org/10.1109/MSP.2007.914730
  13. Duarte, M., Wakin, M., and Baraniuk. R., 2005, Fast Reconstruction of Piecewise Smooth Signals from Incoherent Projections. In Proc. Work. Struc. Parc. Rep. Adap. Signaux (SPARS), Rennes, France, Nov. 2005.
  14. Fessler, J. and Hero, A., 1994, Space Alternating Generalized Expectation-Maximization Algorithm, IEEE Trans. on Signal Processing, 42(10), 2664-2677. https://doi.org/10.1109/78.324732
  15. Gilbert, A., Strauss, M., Tropp, J., and Vershynin, R., 2007, One sketch for all: Fast Algorithms for Compressed Sensing, In Proceedings of the thirty-ninth annual ACM symposium on Theory of computing, 237-246.
  16. Herrmann, F., 2010, Randomized Sampling and Sparsity: Getting More Information from Fewer Samples, UBC-EOS Technical Report. TR-2010-01. Geophysics, 173(75).
  17. Hua, Y. and Sarkar, T. K., 1990, Matrix Pencil Method for Estimating Parameters of Exponentially Damped/Undamped Sinusoids in Noise, IEEE Trans. on Acoustics, Speech, and Signal Processing, 38(5), 814-824. https://doi.org/10.1109/29.56027
  18. Ma, J., 2011, Improved Iterative Curvelet thresholding for Compressed Sensing and Measurement, IEEE Trans. on Instrumentation and Measurement, 60(1), 126-136. https://doi.org/10.1109/TIM.2010.2049221
  19. Manabe, T. and Takai, H., 1992, Superresolution of Multipath Delay Profiles Measured by PN Correlation Method, IEEE Trans. on Antennas and Propagation, 40(5), 500-509. https://doi.org/10.1109/8.142624
  20. Nam, W. and Kong, S., 2011, Modified Least-Squares based Iterative Multipath Super-Resolution Algorithm, Proceedings of the 2011 International Technical Meeting of The Institute of Navigation, San Diego, CA, January 2011. 591-595.
  21. Needell, D. and Tropp, J., 2009, CoSaMP: Iterative Signal Recovery from Incomplete and Inaccurate Samples. Applied and Computational Harmonic Analysis, 26(3), 301-321. https://doi.org/10.1016/j.acha.2008.07.002
  22. Roy, R. and Kailath, T., 1989, ESPRIT-Estimation of Signal Parameters Via Rotational Invariance Techniques, IEEE Trans. On Acoustics, Speech, and Signal Processing, 37(7), 984-995. https://doi.org/10.1109/29.32276
  23. Schmidt, R., 1986, Multiple Emitter Location and Signal Parameter Estimation, IEEE Trans. on Antennas Propagation, 34(3), 276-280. https://doi.org/10.1109/TAP.1986.1143830
  24. Tropp, J. and Gilbert, A., 2007, Signal Recovery from Random Measurements via Orthogonal Matching Pursuit, IEEE Trans. Information Theory, 53(12), 4655-4666. https://doi.org/10.1109/TIT.2007.909108
  25. Vetterli, M., Marziliano, P., and Blu, T., 2002, Sampling Signals With Finite Rate of Innovation, IEEE Trans. on Signal Processing, 50(6), 1417-1428. https://doi.org/10.1109/TSP.2002.1003065