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Phase retrieval reconstruction is a central problem in digital holography, with various applications in microscopy, biomedical imaging, fluid mechanics. In an in-line configuration, the particular difficulty is the non-linear relation between the object phase and the recorded intensity of the holograms, leading to high indeterminations in the reconstructed phase. Thus, only efficient constraints and a priori information, combined with a finer model taking into account the non-linear behaviour of image formation, will allow to get a relevant and quantitative phase reconstruction. Inverse problems approaches are well suited to address these issues, only requiring a direct model of image formation and allowing the injection of priors and constraints on the objects to reconstruct, and hence offer good warranties on the optimality of the expected solution. In this context, following our previous works in digital in-line holography, we propose a regularized reconstruction method that includes several physicallygrounded constraints such as bounds on transmittance values, maximum/minimum phase, spatial smoothness or the absence of any object in parts of the field of view. To solve the non-convex and non-smooth optimization problem induced by our modeling, a variable splitting strategy is applied and the closed-form solution of the sub-problem (the so-called proximal operator) is derived. The resulting algorithm is efficient and is shown to lead to quantitative phase estimation of micrometric objects on reconstructions of in-line holograms simulated with advanced models using Mie theory. Then we discuss the quality of reconstructions from experimental inline holograms obtained from two different applications of in-line digital holography: tracking of an evaporating droplet (size~100μm) and microscopy of bacterias (size~1μm). The reconstruction algorithm and the results presented in this proceeding have been initially published in [Jolivet et al., 2018].1
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