Stability of Image-Reconstruction Algorithms

Pol del Aguila Pla, Sebastian Neumayer, Michael Unser

Abstract: Robustness and stability of image-reconstruction algorithms have recently come under scrutiny. Their importance to medical imaging cannot be overstated. We review the known results for the topical variational regularization strategies ( $\ell _{2}$ and $\ell _{1}$ regularization) and present novel stability results for $\ell _{p}$ -regularized linear inverse problems for $p\in (1,\infty)$ . Our results guarantee Lipschitz continuity for small $p$ and Hölder continuity for larger $p$ . They generalize well to the $L_{p}(\Omega)$ function spaces.