论文标题
可学习的下降算法，用于非平滑非凸图像重建
Learnable Descent Algorithm for Nonsmooth Nonconvex Image Reconstruction
论文作者
论文摘要
我们提出了一个基于一般学习的框架，用于解决非平滑和非凸图像重建问题。我们将正则函数建模为$ l_ {2,1} $ norm的组成，并且将光滑但非convex功能映射参数化为深卷积神经网络。我们通过利用Nesterov的平滑技术和残留学习的概念来开发一种可证明的收敛性下降型算法来解决非平滑的非convex最小化问题，并学习网络参数，以使算法的输出与培训数据中的参考匹配。我们的方法用途广泛，因为人们可以将各种现代网络结构用于正规化，而所得网络继承了算法的保证收敛性。我们还表明，所提出的网络是参数有效的，其性能与实践中各种图像重建问题中最新方法相比有利。
We propose a general learning based framework for solving nonsmooth and nonconvex image reconstruction problems. We model the regularization function as the composition of the $l_{2,1}$ norm and a smooth but nonconvex feature mapping parametrized as a deep convolutional neural network. We develop a provably convergent descent-type algorithm to solve the nonsmooth nonconvex minimization problem by leveraging the Nesterov's smoothing technique and the idea of residual learning, and learn the network parameters such that the outputs of the algorithm match the references in training data. Our method is versatile as one can employ various modern network structures into the regularization, and the resulting network inherits the guaranteed convergence of the algorithm. We also show that the proposed network is parameter-efficient and its performance compares favorably to the state-of-the-art methods in a variety of image reconstruction problems in practice.
