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Two-dimensional Doppler tomography. (English. Russian original) Zbl 0915.65132
Comput. Math. Math. Phys. 36, No. 11, 1591-1598 (1996); translation from Zh. Vychisl. Mat. Mat. Fiz. 36, No. 11, 126-133 (1996).
Summary: The problem of reconstructing a two-dimensional vector function of two variables which is equal to zero outside a bounded domain \({\mathfrak D}\) is considered. The information from which this function is determined is a known function of the parameter \(\omega\) for any oriented straight line, which defines the measure of the set of points of the line belonging to \({\mathfrak D}\) at which the scalar product of the required function and the unit vector of the line is not greater than \(\omega\). An example to demonstrate that the solution of the problem is not unique is constructed. A system of nonlinear partial differential equations for the components of the function required is derived. The non-classical problem for Poisson’s equation which arises in the case where the vector function has zero divergence is considered.

MSC:
65R10 Numerical methods for integral transforms
44A12 Radon transform
92C55 Biomedical imaging and signal processing
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