论文标题
一种新型的可学习梯度下降类型算法，用于非凸线非平滑逆问题
A Novel Learnable Gradient Descent Type Algorithm for Non-convex Non-smooth Inverse Problems
论文作者
论文摘要
用于解决非凸逆问题的优化算法最近引起了重大兴趣。但是，现有方法要求NonConvex正则化是平滑或简单以确保收敛的。在本文中，我们提出了一种新颖的梯度下降型算法，它利用残留学习和Nesterov的平滑技术的思想来解决由一般的非凸和非平滑正规化组成的反问题，并具有可证明的融合。此外，我们开发了一种神经网络体系结构，该神经网络体系结构暗示该算法从训练数据中自适应地学习非线性稀疏性转换，这也继承了融合以适应这种学识渊博的转换的一般非凸结构。数值结果表明，在效率和准确性方面，提出的网络在各种不同图像重建问题上的最新方法优于最先进的方法。
Optimization algorithms for solving nonconvex inverse problem have attracted significant interests recently. However, existing methods require the nonconvex regularization to be smooth or simple to ensure convergence. In this paper, we propose a novel gradient descent type algorithm, by leveraging the idea of residual learning and Nesterov's smoothing technique, to solve inverse problems consisting of general nonconvex and nonsmooth regularization with provable convergence. Moreover, we develop a neural network architecture intimating this algorithm to learn the nonlinear sparsity transformation adaptively from training data, which also inherits the convergence to accommodate the general nonconvex structure of this learned transformation. Numerical results demonstrate that the proposed network outperforms the state-of-the-art methods on a variety of different image reconstruction problems in terms of efficiency and accuracy.
