In this paper, we propose a unified framework of denoising score-based models in the context of graduated non-convex energy minimization. We show that for sufficiently large noise variance, the associated negative log density -- the energy -- becomes convex. Consequently, denoising score-based models essentially follow a graduated non-convexity heuristic. We apply this framework to learning generalized Fields of Experts image priors that approximate the joint density of noisy images and their associated variances. These priors can be easily incorporated into existing optimization algorithms for solving inverse problems and naturally implement a fast and robust graduated non-convexity mechanism.

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Using mathematical image processing, scientists at the BioTechMed-Graz research cooperation have found a way to create digital twins from human hearts. The method opens up completely new possibilities in clinical diagnostics. Although treatment options are constantly improving, cardiovascular diseases are still one of the most frequent causes of death in Europe. The success of the treatment varies from patient to patient and depends on the individual clinical picture, as Gernot Plank, researcher at the Institute of Biophysics at the Medical University of Graz explains using an example: "For example, pacemaker therapy is not successful in about 30 per cent of cardiac patients who have had a pacemaker implanted for mechanical resynchronization of the heartbeat." In order to be able to rule out such interventions in advance, Plank has developed a computer model together with the mathematicians Gundolf Haase and Kristian Bredies from the University of Graz and computer scientist Thomas Pock from the Institute of Computer Vision and Representation at Graz University of Technology, respectively, with which doctors can pre-simulate the optimal therapy and dramatically improve the success of treatment.