Neural networks have shown tremendous potential for reconstructing
high-resolution images in inverse problems. The non-convex and opaque nature of
neural networks, however, hinders their utility in sensitive applications such
as medical imaging. To cope with this challenge, this paper advocates a convex
duality framework that makes a two-layer fully-convolutional ReLU denoising
network amenable to convex optimization. The convex dual network not only
offers the optimum training with convex solvers, but also facilitates
interpreting training and prediction. In particular, it implies training neural
networks with weight decay regularization induces path sparsity while the
prediction is piecewise linear filtering. A range of experiments with MNIST and
fastMRI datasets confirm the efficacy of the dual network optimization problem.

本文提出了一种凸二元框架用于优化神经网络，从而解决了其在敏感应用如医学成像中的非凸和不透明性质的问题。该凸对偶网络不仅能够通过凸优化器获得最优训练，还有利于训练和预测的解释，特别是通过权重衰减正则化训练神经网络，诱导路径稀疏性的同时，预测是分段线性滤波。实验结果表明，该凸对偶网络优化问题在 MNIST 和 fastMRI 数据集上有效。