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In the context of machine learning for uncertainty quantification (UQ) of inverse problems: we propose to first transform input observations using the adjoint. We demonstrate with two imaging examples (photoacoustic imaging and CT) that firstly: the adjoint partially undoes the physics of the problem resulting in faster convergence of the learning phase and secondly: the final algorithm is now robust to changes in observations such as changing transducer subsampling in photoacoustic imaging and angles in CT. Our adjoint-based method gives point estimates faster than traditional baselines and with higher SSIM metrics, while also providing validated UQ.
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Rafael Orozco, Ali Siahkoohi, Gabrio Rizzuti, Tristan van Leeuwen, Felix J. Herrmann, "Adjoint operators enable fast and amortized machine learning based Bayesian uncertainty quantification," Proc. SPIE 12464, Medical Imaging 2023: Image Processing, 124641L (3 April 2023); https://doi.org/10.1117/12.2651691