  Volumetric imaging of samples using fluorescence microscopy plays an
important role in various fields including physical, medical and life sciences.
Here we report a deep learning-based volumetric image inference framework that
uses 2D images that are sparsely captured by a standard wide-field fluorescence
microscope at arbitrary axial positions within the sample volume. Through a
recurrent convolutional neural network, which we term as Recurrent-MZ, 2D
fluorescence information from a few axial planes within the sample is
explicitly incorporated to digitally reconstruct the sample volume over an
extended depth-of-field. Using experiments on C. Elegans and nanobead samples,
Recurrent-MZ is demonstrated to increase the depth-of-field of a 63x/1.4NA
objective lens by approximately 50-fold, also providing a 30-fold reduction in
the number of axial scans required to image the same sample volume. We further
illustrated the generalization of this recurrent network for 3D imaging by
showing its resilience to varying imaging conditions, including e.g., different
sequences of input images, covering various axial permutations and unknown
axial positioning errors. Recurrent-MZ demonstrates the first application of
recurrent neural networks in microscopic image reconstruction and provides a
flexible and rapid volumetric imaging framework, overcoming the limitations of
current 3D scanning microscopy tools.
