Unsupervised regularized inverse method for 3D reconstruction in tomographic diffractive microscopy

Regularized inverse approaches are now widely used for the three dimensional reconstructions in Tomographic Diffractive Microscopy. This family of methods consists in the minimization, under some constraints, of a cost function often composed with a data fidelity term and one or several regularization terms. On one hand, the data fidelity term is based on the likelihood of the data. On the other hand, the regularization terms are based on physical a priori (morphology, values,…). It is important to keep a good trade off between data fidelity and regularization. The contribution of these last ones is weighted through hyperparameters which require a precise tuning. The minimization of the Generalized Stein’s Unbiased Risk Estimator (GSURE) is efficient to select a set of optimal hyperparameters however it requires an accurate approximation of the data formation. In this work, we compare the efficiency of an unsupervised regularized approach using GSURE depending of the data model approximation. We compare the optimal reconstructions obtained using the first Born approximation on one side and the Beam Propagation Method on the other side. We chose the regularization of the Total Variation, which favor piece-wise constant structures. For the reconstruction, we used the Primal-Dual Condat-Vũ algorithm with backtracking. We apply both reconstruction methods on experimental data. Our results show that our unsupervised regularized method manages in both cases to find an optimal reconstruction