2024/03/12 by Stefan Kindermann, Kindermann, Stefan, Simon Hubmer +1 · 1 citation
Earth and Planetary Sciences · Mathematics · Medicine · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.2403.07466
openalex publication_date 2024/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.