Dual Forward-Backward Unfolded Network for Flexible Plug-and-Play
Dual Forward-Backward Unfolded Network for Flexible Plug-and-Play
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DOI：
10.23919/eusipco55093.2022.9909564
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发表时间：
2022-08
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通讯作者：
A. Repetti;M. Terris;Y. Wiaux;J. Pesquet
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作者：
A. Repetti;M. Terris;Y. Wiaux;J. Pesquet
近端方法已广泛用于从退化测量中找到未知图像的最大后验（MAP）估计。近年来，为了进一步提高重建质量，将它们与神经网络（NN）混合使用。可以区分两种方法：展开的神经网络，实现优化算法的给定迭代次数，以及即插即用（PnP）算法，将神经网络纳入现有的优化算法。展开神经网络通常在学习过程中包含测量算子，这对于具有非固定测量算子的应用可能是禁止的。PnP没有这个缺点，但是涉及到的神经网络仍然依赖于底层的统计模型（例如，测量的高噪声水平需要更强的去噪器）。在这项工作中，我们提出了一种基于前向向后（FB）迭代的PnP算法，其中学习到的去噪器是基于双FB迭代的展开NN。这个神经网络从MAP的角度模拟高斯去噪。这允许我们在模型中引入正则化参数来调整正则化强度，类似于标准变分方法。这样做的好处是使学习到的神经网络更能适应各种反问题统计模型，而不需要针对不同的噪声水平训练神经网络。
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.