The work involves comparative analysis for solving cross-well tomography problem in spaces L2, L1 and L0. There is short overview of techniques which allow to solve conditional minimization problem in space Lp, where p<1. It is also presented results of numerical experiments for reconstruction sparse solution in case of “checkerboard” model.


Article metrics loading...

Loading full text...

Full text loading...


  1. Beck, A., Teboulle, M., Potra, F., and CarmichaelG.
    , [2009] A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Image Sciences, 1, 183–202.
    [Google Scholar]
  2. Candes, E., Wakin, M.
    , [2008] An introduction to compressive sampling. IEEE Signal Process. Magazine, 21, 21–30.
    [Google Scholar]
  3. Chen, C, Huang, J., He, L., Li, H.
    , [2014] Preconditioning for accelerated iteratively reweighted least squares in structured sparsity reconstruction. Proc. IEEE Conf. Computer Vision and Pattern Recognition. 2713–2720.
    [Google Scholar]
  4. Cheverda. V., Kostin. V.
    , [2010] R-pseudo inverse for compact operator. Siberian Electronic Mathematical Reports, 7, 258. (In Russian)
    [Google Scholar]
  5. Daubechies, I., DeVore, R., Fornasier, M., and Gunturk, C.
    , [2010] Iteratively reweighted least squares minimization for sparse recovery. Comman. Pure Appl. Math., 63(1), 1–38.
    [Google Scholar]
  6. Donoho, D.
    , [2006] Compressed sensing. IEEE Trans. Inform. Theory, 53(4), 1289–1306.
    [Google Scholar]
  7. Engan, K., Rao, В., Kreutz-DelgadoK.
    , [2000] Regularized FOCUSS for subset selection in noise. Proc. of NORGSIG, 247–250.
    [Google Scholar]
  8. Godunov, S., Antonov, A., Kiriluk, O., Kostin, V.
    , [1988] Guaranteed accuracy for linear equations systems solving in Euclidean space. NovosibirskIzdatel Nauka. (In Russian)
    [Google Scholar]
  9. Gorodnitsky, I., Rao, В.
    , [1997] Sparse signal reconstructions from limited data using FOCUSS: A re-weighted minimum norm algorithm. IEEE Trans. Signal Processing, 45, 600–616.
    [Google Scholar]
  10. Kabanic, A., Orlov, U., Cheverda, V.
    , [2004] Numerical solution of linear seismic tomography on transmitted rays: case of incomplete data. Siberian journal of industrial mathematics, 2, 54–67. (In Russian)
    [Google Scholar]
  11. Lavrentyev, M., Romanov, V.
    , [1966] About three linearized inverse problems for hyperbolic equations. Report AS USSR, 6, 1279–1281. (In Russian)
    [Google Scholar]
  12. Rao, В., Kreutz-Delgado, K.
    , [1999] An affine scaling methodology for best basis selection. IEEE Trans. Signal Process., 1, 187–200.
    [Google Scholar]
  13. Tikhonov, A., Goncharsky, A., Stepanov, V., and Yagola, A.
    , [1990] Numerical methods for the solution of ill-posed problems. MoscowIzdatel Nauka. (In Russian)
    [Google Scholar]

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error