Stability of Image-Reconstruction Algorithms

2022/06/14 by Pla, Pol del Aguila, Neumayer, Sebastian, Unser, Michael
#FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Image and Video Processing (eess.IV) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Signal Processing (eess.SP) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2206.07128

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 (ℓ₂ and ℓ₁ regularization) and present novel stability results for ℓ_p-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 L_p(Ω) function spaces.

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