Abstract
Abstract
Ray transforms for vector or tensor fields have been studied for a long time, also in connection with Doppler or polarization tomography. In contrast to the classical Radon transform or x-ray transform their known inversion formulae are rather complicated, and represented, for example, using series expansions or singular value decompositions. Recently, applications of the approximate inverse have been studied. In this paper we present a new class of inversion formulae for compactly supported fields similar to those of the x-ray transform. The derivation is based on two observations. First, we apply Derevtsov’s formula relating the ray transforms of vector or tensor fields to a derivative of the x-ray transform of a generating potential, [3]. Second, we apply the calculation of derivatives of a scalar function from its x-ray transform, as it is realized in feature reconstruction, [15, 16]. Generalizations complete the presentation.
Funder
Russian Foundation for Basic Research
Sino-German Center for Research Promotion
Sino-German Mobility Programme
Deutsche Forschungsgemeinschaft
Subject
Applied Mathematics,Computer Science Applications,Mathematical Physics,Signal Processing,Theoretical Computer Science
Cited by
9 articles.
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