Stability of Image-Reconstruction Algorithms

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.

11 pages, 6 figures, 1 appendix