Computational inverse problems always rely on regularization to overcome ill-conditionedness and ill-posedness. The utility of machine learning, at least of the supervised kind is therefore, in retrospect, obvious: given typical object-measurement pairs, the supervised architecture is supposed to learn the regularizing priors. The story, however, is more complicated than that: for example, should one include the physics captured in the forward operator explicitly into the learning architecture, or build a black box encompassing everything? And what if the forward operator itself is only partially known, or the cost of obtaining sufficient training pairs experimentally is prohibitive? While not claiming to have the ultimate answers, in my talk I will discuss what we learnt from implementations of machine learning-aided inverses in three classical inverse problems: retrieval of the phase of the electromagnetic field from intensity, retrieval of a 3D dielectric structure from limited-angle intensity projections, and quantitative analysis of highly scattering surfaces. The structure of such problems points to interesting directions for future joint optimization of the forward operators and machine learning inverse for better robustness to noise and other uncertainties (e.g. in the forward operator.)
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