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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 (
Inverse problems are at the core of computational imaging. Medical imaging critically depends on the guarantees provided by established image-reconstruction methodologies to inform diagnostic and treatment decisions. New techniques based on artificial intelligence and deep neural networks offer major average performance improvements in most applications , , , , at the cost of poor practical stability ,  and a lack in theoretical guarantees. In particular, seemingly small perturbations of the measurements can produce large errors in the resulting image. Insidiously, these errors may incorporate deceptive patterns that look realistic because they were learnt from the training database (hallucination) .
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