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Nonlinear regularization of inversion of exponential Radon transform. (English, Russian) Zbl 1157.65511

Mosc. Univ. Comput. Math. Cybern. 2006, No. 1, 23-28 (2006); translation from Vestn. Mosk. Univ., Ser. XV 2006, No. 1, 23-28 (2006).
Summary: The paper deals with the problem of inversion of exponential Radon transform. The incorrectness of the problem of function reconstruction from its exponential Radon transform is investigated and a method of expansion of a function in wavelet-series is proposed with a subsequent threshold processing of wavelet coefficients.

MSC:

65R10 Numerical methods for integral transforms
65R30 Numerical methods for ill-posed problems for integral equations
65T60 Numerical methods for wavelets
44A12 Radon transform
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[1] X. D. Wang, G. Pang, Y. J. Ku, X. Y. Xie, G. Stoica, and L.-H. V. Wang, ”Noninvasive Laser-Induced Photoacoustic Tomography for Structural and Functional in Vivo Imaging of the Brain,” Nature Biotechn. 21, 803–806 (2003. · doi:10.1038/nbt839
[2] R. A. Kruger, K. D. Miller, H. E. Reynolds, W. L. Kiser, D. R. Reinecke, and G. A. Kruger, ”Breast Cancer in vivo: Contrast Enhancement with Thermoacoustic CT at 434 MHz-Feasibility Study,” Radiology 216, 279–283 (2000. · doi:10.1148/radiology.216.1.r00jl30279
[3] S. J. Norton, ”Reconstruction of a Two-Dimensional Reflecting Medium Over a Circular Domain: Exact Solution,” J. Acoust. Soc. Am. 67, 1266–1273 (1980. · Zbl 0422.76049 · doi:10.1121/1.384168
[4] D. Finch and M. Haltmeier, ”Inversion of Spherical Means and the Wave Equation in Even Dimensions,” SIAM J. Appl. Math. 68, 392–412 (2007. · Zbl 1159.35073 · doi:10.1137/070682137
[5] L. A. Khalfin and L. B. Klebanov, ”A Solution of the Computer Tomography Paradox and Estimating the Distances between the Densities of Measures with the Same Marginals,” Ann. Prob. 22, 2235–2241 (1994. · Zbl 0834.60017 · doi:10.1214/aop/1176988502
[6] O. V. Shestakov and T. Yu. Savenkov, ”Estimation of the Distance Between Densities of Probability Measures Having Close Projections,” Vestn. Mosk. Univ., Ser. 15: Vychisl. Mat. Kibern., No. 4, 44–46 (2001. · Zbl 1054.60016
[7] S. Helgason, The Radon Transform (Birkhäuser, Boston, 1980; Mir, Moscow, 1983. · Zbl 0453.43011
[8] F. Natterer, ”Inversion of the Attenuated Radon Transform,” Inverse Probl. 17, 113–119 (2001). · Zbl 0980.44006 · doi:10.1088/0266-5611/17/1/309
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