Advanced Search

Indexed by SCI、CA、РЖ、PA、CSA、ZR、etc .

Volume 25 Issue 1
Feb 2014
Turn off MathJax
Article Contents
Fredrik Andersson, Marcus Carlsson, Maarten V. de Hoop. Frequency Extrapolation through Sparse Sums of Lorentzians. Journal of Earth Science, 2014, 25(1): 117-125. doi: 10.1007/s12583-014-0368-z
Citation: Fredrik Andersson, Marcus Carlsson, Maarten V. de Hoop. Frequency Extrapolation through Sparse Sums of Lorentzians. Journal of Earth Science, 2014, 25(1): 117-125. doi: 10.1007/s12583-014-0368-z

Frequency Extrapolation through Sparse Sums of Lorentzians

doi: 10.1007/s12583-014-0368-z
More Information
  • Corresponding author: Fredrik Andersson, fa@maths.lth.se
  • Received Date: 12 Jun 2013
  • Accepted Date: 10 Sep 2013
  • Publish Date: 01 Feb 2014
  • Sparse sums of Lorentzians can give good approximations to functions consisting of linear combination of piecewise continuous functions. To each Lorentzian, two parameters are assigned: translation and scale. These parameters can be found by using a method for complex frequency detection in the frequency domain. This method is based on an alternating projection scheme between Hankel matrices and finite rank operators, and have the advantage that it can be done in weighted spaces. The weighted spaces can be used to partially revoke the effect of finite band-width filters. Apart from frequency extrapolation the method provides a way of estimating discontinuity locations.

     

  • loading
  • Adamjan, V. M., Arov, D. Z., Kreın, M. G., 1968. Infinite Hankel Matrices and Generalized Carathéodory-Fejér and Riesz Problems. Funkcional. Anal. iPriložen. , 2(1): 1-19 http://www.researchgate.net/publication/284678350_Infinite_hankel_matrices_and_generalized_carathodory_fejer_and_riesz_problems
    Andersson, F., Carlsson, M., 2013. Alternating Projections on Non-Tangential Manifolds. Constructive Approximation, 38(3): 489-525 doi: 10.1007/s00365-013-9213-3
    Andersson, F., Carlsson, M., de Hoop, M. V., 2011. Sparse Approximation of Functions Using Sums of Exponentials and Aak Theory. Journal of Approximation Theory, 163(2): 213-248 doi: 10.1016/j.jat.2010.09.005
    Andersson, F., Carlsson, M., 2011. A Fast Alternating Projection Method for Complex Frequency Estimation. Proceedings of the GMIG, 11: 21-36 http://gmig.math.purdue.edu/pdfs/2011/11-02.pdf
    Beylkin, G., Monzón, L., 2009. Nonlinear Inversion of a Band-Limited Fourier Transform. Applied and Computational Harmonic Analysis, 27(3): 351-366 doi: 10.1016/j.acha.2009.04.003
    Beylkin, G., Monzón, L., 2005. On Approximation of Functions by Exponential Sums. Applied and Computational Harmonic Analysis, 19(1): 17-48 doi: 10.1016/j.acha.2005.01.003
    Chartrand, R., Sidky, E. Y., Pan, X., 2011. Frequency Extrapolation by Nonconvex Compressive Sensing. In: Biomedical Imaging: From Nano to Macro, 2011. IEEE International Symposium on IEEE, 1056-1060
    Claerbout, J., 1992. Earth Soundings Analysis Processing Versus Inversion. Blackwell Scientific Publications, Cambridge
    Claerbout, J., 1998. Multidimensional Recursive Filters Via a Helix. Geophysics, 63(5): 1532-1541 doi: 10.1190/1.1444449
    Clayton, R. W., Wiggins, R. A., 1976. Source Shape Estimation and Deconvolution of Teleseismic Bodywaves. Geophysical Journal of the Royal Astronomical Society, 47(1): 151-177 doi: 10.1111/j.1365-246X.1976.tb01267.x
    Dasgupta, S., Nowack, R. L., 2008. Frequency Extrapolation to Enhance the Deconvolution of Transmitted Seismic Waves. Journal of Geophysics and Engineering, 5(1): 118-127 doi: 10.1088/1742-2132/5/1/012
    Eckart, C., Young, G., 1936. The Approximation of One Matrix by Another of Lower Rank. Psychometrika, 1(3): 211-218 doi: 10.1007/BF02288367
    Escalante, C., Gu, Y. J., Sacchi, M., 2007. Simultaneous Iterative Time-Domain Sparse Deconvolution to Teleseismic Receiver Functions. Geophysical Journal International, 171(1): 316-325 doi: 10.1111/j.1365-246X.2007.03511.x
    Horn, R. A., Johnson, C. R., 1994. Topics in Matrix Analysis. Cambridge University Press, Cambridge
    Ligorria, J. P., Ammon, C. J., 1999. Iterative Deconvolution and Receiver-Function Estimation. Bulletin of the Seismological Society of America, 89(5): 1395-1400 doi: 10.1785/BSSA0890051395
    Papoulis, A., 1975. A New Algorithm in Spectral Analysis and Band-Limited Extrapolation. Circuits and Systems, IEEE Transactionson, 22(9): 735-742 doi: 10.1109/TCS.1975.1084118
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(5)

    Article Metrics

    Article views(413) PDF downloads(97) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return