  It is time-consuming and expensive to take high-quality or high-resolution
electron microscopy (EM) and fluorescence microscopy (FM) images. Taking these
images could be even invasive to samples and may damage certain subtleties in
the samples after long or intense exposures, often necessary for achieving
high-quality or high resolution in the first place. Advances in deep learning
enable us to perform image-to-image transformation tasks for various types of
microscopy image reconstruction, computationally producing high-quality images
from the physically acquired low-quality ones. When training image-to-image
transformation models on pairs of experimentally acquired microscopy images,
prior models suffer from performance loss due to their inability to capture
inter-image dependencies and common features shared among images. Existing
methods that take advantage of shared features in image classification tasks
cannot be properly applied to image reconstruction tasks because they fail to
preserve the equivariance property under spatial permutations, something
essential in image-to-image transformation. To address these limitations, we
propose the augmented equivariant attention networks (AEANets) with better
capability to capture inter-image dependencies, while preserving the
equivariance property. The proposed AEANets captures inter-image dependencies
and shared features via two augmentations on the attention mechanism, which are
the shared references and the batch-aware attention during training. We
theoretically derive the equivariance property of the proposed augmented
attention model and experimentally demonstrate its consistent superiority in
both quantitative and visual results over the baseline methods.
