  Purpose: Probe-based Confocal Laser Endomicroscopy (pCLE) enables performing
an optical biopsy, providing real-time microscopic images, via a probe. pCLE
probes consist of multiple optical fibres arranged in a bundle, which taken
together generate signals in an irregularly sampled pattern. Current pCLE
reconstruction is based on interpolating irregular signals onto an over-sampled
Cartesian grid, using a naive linear interpolation. It was shown that
Convolutional Neural Networks (CNNs) could improve pCLE image quality. Although
classical CNNs were applied to pCLE, input data were limited to reconstructed
images in contrast to irregular data produced by pCLE. Methods: We compare pCLE
reconstruction and super-resolution (SR) methods taking irregularly sampled or
reconstructed pCLE images as input. We also propose to embed a Nadaraya-Watson
(NW) kernel regression into the CNN framework as a novel trainable CNN layer.
Using the NW layer and exemplar-based super-resolution, we design an NWNetSR
architecture that allows for reconstructing high-quality pCLE images directly
from the irregularly sampled input data. We created synthetic sparse pCLE
images to evaluate our methodology. Results: The results were validated through
an image quality assessment based on a combination of the following metrics:
Peak signal-to-noise ratio, the Structural Similarity Index. Conclusion: Both
dense and sparse CNNs outperform the reconstruction method currently used in
the clinic. The main contributions of our study are a comparison of sparse and
dense approach in pCLE image reconstruction, implementing trainable generalised
NW kernel regression, and adaptation of synthetic data for training pCLE SR.
