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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