Norms in sinogram space and stability estimates for the Radon transform

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.

33 pages, 5 figures