Convolutional Proximal Neural Networks and Plug-and-Play Algorithms

Abstract

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.

References in corpus (5)

• Orthogonal Weight Normalization: Solution to Optimization over Multiple Dependent Stiefel Manifolds in Deep Neural Networks
• One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Models
• Stabilizing Invertible Neural Networks Using Mixture Models
• Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transform
• Understanding and Mitigating Exploding Inverses in Invertible Neural Networks

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