  Optical diffraction tomography measures the three-dimensional refractive
index map of a specimen and visualizes biochemical phenomena at the nanoscale
in a non-destructive manner. One major drawback of optical diffraction
tomography is poor axial resolution due to limited access to the
three-dimensional optical transfer function. This missing cone problem has been
addressed through regularization algorithms that use a priori information, such
as non-negativity and sample smoothness. However, the iterative nature of these
algorithms and their parameter dependency make real-time visualization
impossible. In this article, we propose and experimentally demonstrate a deep
neural network, which we term DeepRegularizer, that rapidly improves the
resolution of a three-dimensional refractive index map. Trained with pairs of
datasets (a raw refractive index tomogram and a resolution-enhanced refractive
index tomogram via the iterative total variation algorithm), the
three-dimensional U-net-based convolutional neural network learns a
transformation between the two tomogram domains. The feasibility and
generalizability of our network are demonstrated using bacterial cells and a
human leukaemic cell line, and by validating the model across different
samples. DeepRegularizer offers more than an order of magnitude faster
regularization performance compared to the conventional iterative method. We
envision that the proposed data-driven approach can bypass the high time
complexity of various image reconstructions in other imaging modalities.
