Stability of Image-Reconstruction Algorithms
This addresses stability issues in image-reconstruction algorithms, which are critical for medical imaging, but is incremental as it builds on existing variational regularization strategies.
The paper tackles the problem of stability in image-reconstruction algorithms, particularly for medical imaging, by presenting novel stability results for ℓp-regularized linear inverse problems, showing Lipschitz continuity for small p and Hölder continuity for larger p.
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 $L_p(Ω)$ function spaces.