论文标题
卷积近端神经网络和插件算法
Convolutional Proximal Neural Networks and Plug-and-Play Algorithms
论文作者
论文摘要
在本文中，我们介绍了卷积近端神经网络（CPNN），该神经网络是通过建筑平均操作员进行的。对于全长的过滤器，我们提出了在训练CPNN的Stiefel歧管的子手机上的随机梯度下降算法。如果长度有限的过滤器，我们设计了算法，以最大程度地减少近似于对操作员施加的正交性约束的函数，从而惩罚了与身份操作员的最小二乘距离。然后，我们研究了如何使用处方Lipschitz常数的缩放cpnns来定性信号和图像，在该信号和图像中，所达到的质量取决于Lipschitz常数。最后，我们将基于CPNN的DINOISER应用于即插即用（PNP）框架中，并根据Oracle构造为相应的PNP前回向拆分算法提供收敛结果。
In this paper, we introduce convolutional proximal neural networks (cPNNs), which are by construction averaged operators. For filters of full length, we propose a stochastic gradient descent algorithm on a submanifold of the Stiefel manifold to train cPNNs. In case of filters with limited length, we design algorithms for minimizing functionals that approximate the orthogonality constraints imposed on the operators by penalizing the least squares distance to the identity operator. Then, we investigate how scaled cPNNs with a prescribed Lipschitz constant can be used for denoising signals and images, where the achieved quality depends on the Lipschitz constant. Finally, we apply cPNN based denoisers within a Plug-and-Play (PnP) framework and provide convergence results for the corresponding PnP forward-backward splitting algorithm based on an oracle construction.
