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

센싱 및 계측 기술에서의 혁신: 지구물리 탐사를 위한 압축센싱 및 초고해상도 기술

  • 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))
  • 공승현 (한국과학기술원 항공우주학공과) ;
  • 한승준 (한국과학기술원 항공우주학공과)
  • Received : 2011.10.19
  • Accepted : 2011.11.17
  • Published : 2011.11.30


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.


  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.
  2. Baraniuk, R., Davenport, M., Duarte, M., and Hegde, C., 2011, An Introduction to Compressive Sensing,
  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.
  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.
  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.
  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.
  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.
  10. Donoho, D., 2006, Compressed sensing, IEEE Trans. on Information Theory, 52(4), 1289-1306.
  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.
  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.
  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.
  18. Ma, J., 2011, Improved Iterative Curvelet thresholding for Compressed Sensing and Measurement, IEEE Trans. on Instrumentation and Measurement, 60(1), 126-136.
  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.
  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.
  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.
  23. Schmidt, R., 1986, Multiple Emitter Location and Signal Parameter Estimation, IEEE Trans. on Antennas Propagation, 34(3), 276-280.
  24. Tropp, J. and Gilbert, A., 2007, Signal Recovery from Random Measurements via Orthogonal Matching Pursuit, IEEE Trans. Information Theory, 53(12), 4655-4666.
  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.