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arXiv · 1801.05838

Revisiting the Problem of Recovering Functions in $\Bbb R^{n}$ by Integration on $k$ Dimensional Planes

Yehonatan Salman
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Abstract

The aim of this paper is to present inversion methods for the classical Radon transform which is defined on a family of $k$ dimensional planes in $\Bbb R^{n}$ where $1\leq k\leq n - 2$. For these values of $k$ the dimension of the set $\mathcal{H}(n,k)$, of all $k$ dimensional planes in $\Bbb R^{n}$, is greater than $n$ and thus in order to obtain a well-posed problem one should choose proper subsets of $\mathcal{H}(n,k)$. We present inversion methods for some prescribed subsets of $\mathcal{H}(n,k)$ which are of dimension $n$.

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Yehonatan Salman. 2018-01-17. Revisiting the Problem of Recovering Functions in $\Bbb R^{n}$ by Integration on $k$ Dimensional Planes. https://arxiv.org/abs/1801.05838

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