  Errors in data are usually unwelcome and so some means to correct them is
useful. However, it is difficult to define, detect or correct errors in an
unsupervised way. Here, we train a deep neural network to re-synthesize its
inputs at its output layer for a given class of data. We then exploit the fact
that this abstract transformation, which we call a deep transform (DT),
inherently rejects information (errors) existing outside of the abstract
feature space. Using the DT to perform probabilistic re-synthesis, we
demonstrate the recovery of data that has been subject to extreme degradation.
