Methods of solving certain two-dimensional problems of Doppler tomography. (English) Zbl 0944.44003
Summary: In the development of methods of recovering a vector field using radiolocation systems by continuous unmodulated radiation the problem arises of recovering a vector-valued function from information determined by a family of oriented lines. In the two-dimensional case this problem has a nonunique solution in the class of continuous functions of compact support. In the present paper the problem is studied on the set of solenoidal functions and the set of piecewise-constant functions. We give a method of solving the problem and study its stability.
MSC:
| 44A12 | Radon transform |
| 65R10 | Numerical methods for integral transforms |
| 65R32 | Numerical methods for inverse problems for integral equations |
| 86A10 | Meteorology and atmospheric physics |
| 86A22 | Inverse problems in geophysics |
Keywords:
Radon transform; Doppler tomography; Doppler spectra; radiometeorology; Doppler radiolocators; problem of nonuniqueness; reconstructive tomography; radiolocation systems; solenoidal functions; piecewise-constant functions; stabilityReferences:
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| [3] | A. M. Denisov and A. A. Popov, ”The two-dimensional problem of Doppler tomography,”Zh. Vychisl. Mat. Mat. Fiz.,36, No. 11, 126–133 (1996). · Zbl 0915.65132 |
| [4] | A. M. Denisov,Introduction to the Theory of Inverse Problems [in Russian], Moscow University Press (1994). · Zbl 0861.35135 |
| [5] | S. Helgason,The Radon Transform, Birkhäuser, Boston (1980). · Zbl 0453.43011 |
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