TY - JOUR
T1 - Connections Between Operator-Splitting Methods and Deep Neural Networks with Applications in Image Segmentation
AU - Liu , Hao
AU - Tai , Xue-Cheng
AU - Chan , Raymond
JO - Annals of Applied Mathematics
VL - 4
SP - 406
EP - 428
PY - 2023
DA - 2023/11
SN - 39
DO - http://doi.org/10.4208/aam.OA-2023-0027
UR - https://global-sci.org/intro/article_detail/aam/22082.html
KW - Potts model, operator splitting, deep neural network, image segmentation.
AB - <p style="text-align: justify;">Deep neural network is a powerful tool for many tasks. Understanding why it is so successful and providing a mathematical explanation is
an important problem and has been one popular research direction in past
years. In the literature of mathematical analysis of deep neural networks, a
lot of works is dedicated to establishing representation theories. How to make
connections between deep neural networks and mathematical algorithms is still
under development. In this paper, we give an algorithmic explanation for deep
neural networks, especially in their connections with operator splitting. We
show that with certain splitting strategies, operator-splitting methods have the
same structure as networks. Utilizing this connection and the Potts model for
image segmentation, two networks inspired by operator-splitting methods are
proposed. The two networks are essentially two operator-splitting algorithms
solving the Potts model. Numerical experiments are presented to demonstrate
the effectiveness of the proposed networks.</p>