Stability of image-reconstruction algorithms
Pol del Aguila Pla (EPFL - CIBM); Sebastian Neumayer (EPFL); Michael Unser (EPFL)
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09 Jun 2023
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 (ℓ₂ and ℓ₁ regularization) and present novel stability results for ℓₚ-regularized linear inverse problems for p∈(1,∞). Our results guarantee Lipschitz continuity for small p and Hölder continuity for larger p. They generalize well to the Lₚ(Ω) function spaces.
