Acta mathematica scientia, Series B >
NON-UNIQUENESS OF THE RECONSTRUCTION FOR CONNECTED AND SIMPLY CONNECTED SETS IN THE PLANE BY THEIR FIXED#br# FINITE PROJECTIONS
Received date: 2009-02-12
Revised date: 2011-03-07
Online published: 2012-07-20
We discuss a problem to reconstruct the measurable sets in the plane from their fixed finite projections. In the main theorem, we construct an example of connected and simply connected polygons which are not uniquely reconstructed by their fixed finite projections. We also make a comparison between our main theorem and the known results on this problem.
Key words： Radon transform; inverse problem
Takashi Takiguchi . NON-UNIQUENESS OF THE RECONSTRUCTION FOR CONNECTED AND SIMPLY CONNECTED SETS IN THE PLANE BY THEIR FIXED#br# FINITE PROJECTIONS[J]. Acta mathematica scientia, Series B, 2012 , 32(4) : 1637 -1646 . DOI: 10.1016/S0252-9602(12)60130-1
[1] Lorentz G G. A problem of plane measure. Amer J Math, 1949, 71: 417–426
[2] Gardner R J. X-rays of polygons. Discrete Comput Geom, 1992, 7: 281–293
[3] Kuba A, Volˇciˇc A. Characterization of measurable plane sets which are reconstructable from their two projections. Inverse Problems, 1988, 4: 513–527
[4] Takiguchi T. Reconstruction of the measurable sets in the two dimensional plane by two projections. Journal of Physics, Conference Series, 2007, 73: 012022
[5] Huang L, Takiguchi T. The reconstruction of uniquely determined plane sets from two projections. J Inv Ill-Posed Problems, 1998, 6: 217–242
[6] Kaneko A, Huang L. Reconstruction of plane figures from two projections//Herman G T, Kuba A, eds. Discrete Tomography. Boston: Birkhauser, 1999: 115–135
[7] Takiguchi T. Reconstruction of measurable plane sets from their orthogonal projections. Contemporary Mathematics, 2004, 348: 199–208
/
| 〈 |
|
〉 |