Convolutional Proximal Neural Networks and Plug-and-Play Algorithms
This work addresses denoising challenges in signal and image processing, presenting an incremental advancement in neural network-based operator design.
The paper tackles the problem of designing averaged operators for signal and image denoising by introducing convolutional proximal neural networks (cPNNs), with results including training algorithms for filters and convergence guarantees for Plug-and-Play frameworks.
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.