Stability of Image-Reconstruction Algorithms

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.