Remarks on the general
Funk transform and thermoacoustic tomography
Pages: 693  702,
Volume 4,
Issue 4,
November
2010
doi:10.3934/ipi.2010.4.693 Abstract
References
Full text (168.2K)
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Victor Palamodov  School of Mathematical Sciences, Tel Aviv University, Ramat Aviv Tel Aviv 69978, Israel (email)
1 
M. Agranovsky, P. Kuchment and E. T. Quinto, Range descriptions for the spherical mean Radon transform, J. Funct. Anal., 248 (2007), 344386. 

2 
J. Boman, On stable inversion of the attenuated Radon transform with half data, in "Integral Geometry and Tomography," 1926, Amer. Math. Soc., Providence, RI, 2006. 

3 
D. Finch and Rakesh, The range of the spherical mean value operator for functions supported in a ball, Inverse Problems, 22 (2006), 923938. 

4 
P. Funk, Über Flächen mit lauter geschlossenen geodätischen Linien, Math. Ann., 74 (1913), 278300. 

5 
V. Guillemin, On some results of Gelfand in integral geometry, in "Pseudodifferential Operators and Applications," 149155, Proc. Sympos.Pure Math., 43, Amer. Math. Soc., Provindence, RI, 1985. 

6 
L. Hörmander, "The Analysis of Linear Partial Differential Operators IV. Fourier Integral Operators," Springer, 1985. 

7 
M. M. Lavrent'ev and A. L. Buhgeim, A certain class of problems of integral geometry, Dokl. Akad. Nauk SSSR, 211 (1973), 3839. 

8 
R. G. Mukhometov, On a problem of integral geometry on the plane, in "Methods of Functional Analysis in Problems of Mathematical Physics (Russian)," 3037, Akad. Nauk Ukrain. SSR, 180, Inst. Mat., Kiev, 1978. 

9 
F. Natterer, "The Mathematics of Computerized Tomography," B.G.Teubner, John Wiley & Sons, Stuttgart, 1986. 

10 
S. K. Patch, Moment conditions indirectly improve image quality, in "Radon Transform and Tomography," 193205, Amer. Math. Soc., Providence, RI, 2001. 

11 
S. K. Patch and O. Scherzer, Photo and thermoacoustic imaging, Inverse Problems, 23 (2007), S1S10. 

12 
D. A. Popov, The generalized Radon transform on the plane, its inversion, and the Cavalieri conditions, Funct. Anal. Appl., 35 (2001), 270283. 

13 
D. A. Popov and D. V. Sushko, Image restoration in opticalacoustic tomography, Probl. Inf. Transm., 40 (2004), 254278. 

14 
E. T. Quinto, The dependence of the generalized Radon transform on defining measures, Trans. Amer. Math. Soc., 257 (1980), 331346. 

15 
H. Rullgård, Stability of the inverse problem for the attenuated Radon transform with 180 $^\circ$ data, Inverse Problems, 20 (2004), 781797. 

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