  In this paper, we demonstrate how deep autoencoders can be generalized to the
case of inpainting and denoising, even when no clean training data is
available. In particular, we show how neural networks can be trained to perform
all of these tasks simultaneously. While, deep autoencoders implemented by way
of neural networks have demonstrated potential for denoising and anomaly
detection, standard autoencoders have the drawback that they require access to
clean data for training. However, recent work in Robust Deep Autoencoders
(RDAEs) shows how autoencoders can be trained to eliminate outliers and noise
in a dataset without access to any clean training data. Inspired by this work,
we extend RDAEs to the case where data are not only noisy and have outliers,
but also only partially observed. Moreover, the dataset we train the neural
network on has the properties that all entries have noise, some entries are
corrupted by large mistakes, and many entries are not even known. Given such an
algorithm, many standard tasks, such as denoising, image inpainting, and
unobserved entry imputation can all be accomplished simultaneously within the
same framework. Herein we demonstrate these techniques on standard machine
learning tasks, such as image inpainting and denoising for the MNIST and
CIFAR10 datasets. However, these approaches are not only applicable to image
processing problems, but also have wide ranging impacts on datasets arising
from real-world problems, such as manufacturing and network processing, where
noisy, partially observed data naturally arise.
