论文标题
用于图像修复的深度原始偶极近端网络
A deep primal-dual proximal network for image restoration
论文作者
论文摘要
图像恢复仍然是图像处理中的一项具有挑战性的任务。许多方法解决了这个问题，通常通过最大程度地减少非平滑惩罚的共符号样式函数来解决这个问题。尽管该解决方案可以通过理论保证很容易解释，但其估计依赖于可能需要时间的优化过程。考虑到深度学习图像分类和细分的研究工作，这类方法为执行图像恢复提供了一种认真的替代方法，但在解决反问题方面保持挑战。在这项工作中，我们设计了一个名为Deeppdnet的深层网络，该网络是由与最小化标准惩罚可能性最小化的原始偶近距离迭代构建的，并以前进行了分析，从而使我们能够利用两者的优势。 我们将Condat-Vu原始双偶发梯度（PDHG）算法的特定实例重新制定为具有固定层的深网。学到的参数既是PDHG算法的台阶尺寸，又是涉及惩罚的分析线性操作员（包括正则化参数）。这些参数可以从一层到另一个参数。两种不同的学习策略：提出了“完整的学习”和“部分学习”，第一个是最有效的数值，而第二个是依靠标准约束，以确保标准PDHG迭代中的收敛性。此外，研究了全球和本地稀疏分析先验，以寻求更好的特征表示。我们将提出的方法应用于MNIST和BSD68数据集上的图像恢复，以及在BSD100和SET14数据集上的单个图像超分辨率。广泛的结果表明，所提出的DEEPPDNET在MNIST和更复杂的BSD68，BSD100和SET14数据集上表现出出色的性能，用于图像恢复和单像超级分辨率任务。
Image restoration remains a challenging task in image processing. Numerous methods tackle this problem, often solved by minimizing a non-smooth penalized co-log-likelihood function. Although the solution is easily interpretable with theoretic guarantees, its estimation relies on an optimization process that can take time. Considering the research effort in deep learning for image classification and segmentation, this class of methods offers a serious alternative to perform image restoration but stays challenging to solve inverse problems. In this work, we design a deep network, named DeepPDNet, built from primal-dual proximal iterations associated with the minimization of a standard penalized likelihood with an analysis prior, allowing us to take advantage of both worlds. We reformulate a specific instance of the Condat-Vu primal-dual hybrid gradient (PDHG) algorithm as a deep network with fixed layers. The learned parameters are both the PDHG algorithm step-sizes and the analysis linear operator involved in the penalization (including the regularization parameter). These parameters are allowed to vary from a layer to another one. Two different learning strategies: "Full learning" and "Partial learning" are proposed, the first one is the most efficient numerically while the second one relies on standard constraints ensuring convergence in the standard PDHG iterations. Moreover, global and local sparse analysis prior are studied to seek a better feature representation. We apply the proposed methods to image restoration on the MNIST and BSD68 datasets and to single image super-resolution on the BSD100 and SET14 datasets. Extensive results show that the proposed DeepPDNet demonstrates excellent performance on the MNIST and the more complex BSD68, BSD100, and SET14 datasets for image restoration and single image super-resolution task.
