论文标题
低级别和总变化正则化及其应用于图像恢复
Low-Rank and Total Variation Regularization and Its Application to Image Recovery
论文作者
论文摘要
在本文中，我们研究了从给定的部分（损坏）观察结果中恢复图像的问题。使用低级别模型恢复图像一直是数据分析和机器学习的活跃研究领域。但是通常，图像不仅是低级的，而且它们在变化的空间中也表现出稀疏性。在这项工作中，我们提出了一个新的问题制定，以使我们寻求恢复低级别且在变换的领域中稀疏的图像。我们进一步讨论了等级函数的各种非凸线非平滑替代物，导致了放松的问题。然后，我们提出了一个有效的迭代方案，以解决在每种迭代中基本上采用（加权）奇异值阈值的放松问题。此外，我们讨论了所提出的迭代方法的收敛性。我们进行了广泛的实验，表明所提出的算法在恢复图像时的表现优于最先进的方法。
In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not only of low-rank but they also exhibit sparsity in a transformed space. In this work, we propose a new problem formulation in such a way that we seek to recover an image that is of low-rank and has sparsity in a transformed domain. We further discuss various non-convex non-smooth surrogates of the rank function, leading to a relaxed problem. Then, we present an efficient iterative scheme to solve the relaxed problem that essentially employs the (weighted) singular value thresholding at each iteration. Furthermore, we discuss the convergence properties of the proposed iterative method. We perform extensive experiments, showing that the proposed algorithm outperforms state-of-the-art methodologies in recovering images.
