  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 H\"{o}lder
continuity for larger $p$. They generalize well to the $L_p(\Omega)$ function
spaces.
