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Lens-free microscopy aims at recovering sample image from diffraction measurements. The acquisitions are usually processed with an inverse problem approach to retrieve the sample image (phase and absorption). The perfect reconstruction of the sample image is however difficult to achieve. Mostly because of the lack of phase information in the recording process. Recently, deep learning has been used to circumvent this challenge. Convolutional neural networks can be applied to the reconstructed image as a single pass to improve e.g. the signal-to noise ratio or the spatial resolution. Here as an alternative, we propose to alternate between the two classes of algorithms, between the inverse problem approach and the data driven approach. In doing so we intend to improve the reconstruction results but also and importantly try to address the concerns associated with the use of deep learning, namely the generalization and hallucination problems. To demonstrate the applicability of our novel approach we choose to address the case of floating cells sample acquired by means of lens-free microscopy. This is a challenging case with a lot of phase wrapping artifacts that has never been solved using inverse problem approaches only. We demonstrate that our approach is successful in performing the phase unwrapping and that it can next be applied to a very different cell sample, namely the cultures of adherent mammalian cell lines.
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