On a quantitative partial imaging problem in vector tomography

Hiroshi Fujiwara; Kamran Sadiq; Alexandru Tamasan

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arXiv · 2506.16455

On a quantitative partial imaging problem in vector tomography

Hiroshi Fujiwara·Kamran Sadiq·Alexandru Tamasan

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Abstract

In two dimensions, we consider the problem of reconstructing a vector field from partial knowledge of its zeroth and first moment ray transforms. Different from existing works the data is known on a subset of lines, namely the ones intersecting a given arc. The problem is non-local and, for partial data, severely ill-posed. We present a reconstruction method which recovers the vector field in the convex hull of the arc. An algorithm based on this method is implemented on some numerical experiments. While still ill-posed the discretization stabilizes the numerical reconstruction.

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Hiroshi Fujiwara, Kamran Sadiq, Alexandru Tamasan. 2025-06-19. On a quantitative partial imaging problem in vector tomography. https://arxiv.org/abs/2506.16455

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