  We propose a constrained linear data-feature-mapping model as an
interpretable mathematical model for image classification using a convolutional
neural network (CNN). From this viewpoint, we establish detailed connections
between the traditional iterative schemes for linear systems and the
architectures of the basic blocks of ResNet- and MgNet-type models. Using these
connections, we present some modified ResNet models that compared with the
original models have fewer parameters and yet can produce more accurate
results, thereby demonstrating the validity of this constrained learning
data-feature-mapping assumption. Based on this assumption, we further propose a
general data-feature iterative scheme to show the rationality of MgNet. We also
provide a systematic numerical study on MgNet to show its success and
advantages in image classification problems and demonstrate its advantages in
comparison with established networks.
