  Deep learning (DL) has been applied extensively in many computational imaging
problems, often leading to superior performance over traditional iterative
approaches. However, two important questions remain largely unanswered: first,
how well can the trained neural network generalize to objects very different
from the ones in training? This is particularly important in practice, since
large-scale annotated examples similar to those of interest are often not
available during training. Second, has the trained neural network learnt the
underlying (inverse) physics model, or has it merely done something trivial,
such as memorizing the examples or point-wise pattern matching? This pertains
to the interpretability of machine-learning based algorithms. In this work, we
use the Phase Extraction Neural Network (PhENN), a deep neural network (DNN)
for quantitative phase retrieval in a lensless phase imaging system as the
standard platform and show that the two questions are related and share a
common crux: the choice of the training examples. Moreover, we connect the
strength of the regularization effect imposed by a training set to the training
process with the Shannon entropy of images in the dataset. That is, the higher
the entropy of the training images, the weaker the regularization effect can be
imposed. We also discover that weaker regularization effect leads to better
learning of the underlying propagation model, i.e. the weak object transfer
function, applicable for weakly scattering objects under the weak object
approximation. Finally, simulation and experimental results show that better
cross-domain generalization performance can be achieved if DNN is trained on a
higher-entropy database, e.g. the ImageNet, than if the same DNN is trained on
a lower-entropy database, e.g. MNIST, as the former allows the underlying
physics model be learned better than the latter.
