Norms in sinogram space and stability estimates for the Radon transform

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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.