Full reconstruction of a vector field from restricted Doppler and first integral moment transforms in \(\mathbb{R}^n\). (English) Zbl 1446.44001
Summary: We show that a vector field in \(\mathbb{R}^n\) can be reconstructed uniquely from the knowledge of restricted Doppler and first integral moment transforms. The line complex we consider consists of all lines passing through a fixed curve \(\gamma \subset \mathbb{R}^n\). The question of reconstruction of a symmetric \(m\)-tensor field from the knowledge of the first \(m+1\) integral moments was posed by V. A. Sharafutdinov [Integral geometry for tensor fields. Transl. from the Russian. Utrecht: VSP (1994; Zbl 0883.53004); p. 78]. In this work, we provide an answer to Sharafutdinov’s question for the case of vector fields from restricted data comprising of the first two integral moment transforms.
Citations:
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