Dual Forward-Backward Unfolded Network for Flexible Plug-and-Play

Proximal methods have been extensively used to find maximum a posteriori (MAP) estimates of unknown images from degraded measurement. Recently, they have been mixed with neural networks (NN) to further improve the reconstruction quality. Two approaches can be distinguished: unfolded NNs, implementing a given iteration number of an optimisation algorithm, and plug-and-play (PnP) algorithms, incorporating NNs in existing optimisation algorithms. Unfolded NNs usually incorporate the measurement operator in the learning process, which can be prohibitive for applications with non-fixed measurement operators. PnP do not have this drawback, but involved NNs still depend on the underlying statistical models (e.g., higher noise level on the measurements requires stronger denoisers). In this work, we propose a PnP algorithm based on forward-backward (FB) iterations, where the learned denoiser is an unfolded NN based on dual-FB iterations. This NN is built to mimic a Gaussian denoiser from a MAP viewpoint. This allows us to introduce a regularisation parameter in the model to tune the regularization strength, similarly to standard variational approaches. This has the advantage of making the learned NN more adaptive to a variety of inverse problem statistical models, without requiring to train the NN for different noise levels.