论文标题
Fista-net：学习成像中的反问题的快速迭代收缩阈值网络
FISTA-Net: Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging
论文作者
论文摘要
逆问题对于成像应用至关重要。在本文中，我们通过结合基于模型的快速迭代收缩/阈值算法（FISTA）以及强大的正则化和数据驱动的神经网络的无调优势来结合基于模型的深度学习网络，称为Fista-NET。通过将Fista展开到一个深网络中，Fista-Net的架构由级联中的多个梯度下降，近端映射和动量模块组成。与FISTA不同，在迭代期间可以更新Fista-NET中的梯度矩阵，并为非线性阈值开发了近端操作员网络，可以通过端到端培训来学习。 Fista-NET的关键参数，包括梯度步长，阈值值和动量标量，从训练数据而不是手工制作中学习。我们进一步对这些参数施加了积极和单调的约束，以确保它们正确收敛。实验结果在视觉和定量上均评估，表明Fista-NET可以优化不同成像任务的参数，即电磁层析成像（EMT）（EMT）和X射线计算机断层扫描（X射线CT）。它的表现优于基于最先进的模型和深度学习方法，并且在不同的噪声水平下，基于其他竞争性学习的方法具有良好的概括能力。
Inverse problems are essential to imaging applications. In this paper, we propose a model-based deep learning network, named FISTA-Net, by combining the merits of interpretability and generality of the model-based Fast Iterative Shrinkage/Thresholding Algorithm (FISTA) and strong regularization and tuning-free advantages of the data-driven neural network. By unfolding the FISTA into a deep network, the architecture of FISTA-Net consists of multiple gradient descent, proximal mapping, and momentum modules in cascade. Different from FISTA, the gradient matrix in FISTA-Net can be updated during iteration and a proximal operator network is developed for nonlinear thresholding which can be learned through end-to-end training. Key parameters of FISTA-Net including the gradient step size, thresholding value and momentum scalar are tuning-free and learned from training data rather than hand-crafted. We further impose positive and monotonous constraints on these parameters to ensure they converge properly. The experimental results, evaluated both visually and quantitatively, show that the FISTA-Net can optimize parameters for different imaging tasks, i.e. Electromagnetic Tomography (EMT) and X-ray Computational Tomography (X-ray CT). It outperforms the state-of-the-art model-based and deep learning methods and exhibits good generalization ability over other competitive learning-based approaches under different noise levels.
