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arXiv · 2403.07466

Norms in sinogram space and stability estimates for the Radon transform

Stefan Kindermann·Simon Hubmer
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Abstract

We consider different norms for the Radon transform $Rf$ of a function $f$ and investigate under which conditions they can be estimated from above or below by some standard norms for $f$. We define Fourier-based norms for $Rf$ which can be related to Bessel-potential space norms for $f$. Furthermore, we define a variant of a total-variation norm for $Rf$ and provide conditions under which it is equivalent to the total-variation norm of $f$. To illustrate potential applications of these results, we propose a novel nonlinear backprojection method for inverting the Radon transform and present numerical results on simulated and experimental data.

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Stefan Kindermann, Simon Hubmer. 2024-03-12. Norms in sinogram space and stability estimates for the Radon transform. https://arxiv.org/abs/2403.07466

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