论文标题
分析基于稀疏分解的同时镶嵌和几何分离
Analysis of simultaneous inpainting and geometric separation based on sparse decomposition
论文作者
论文摘要
自然图像通常是不同几何特征的各个部分的叠加。例如，图像可能是卡通和纹理结构的混合物。此外，通常会给图像带有丢失的数据。在本文中，我们开发了一种将图像同时分解为其两个基础部分并介绍丢失数据的方法。我们的分离授课方法是基于$ l_1 $最小化方法，使用两个词典，每个词典都占用了一个图像部分之一，而不是另一个。我们在一般环境中介绍了我们的方法的全面收敛分析，利用关节浓度，聚类稀疏性和聚类相干性的概念。作为我们理论的主要应用，我们考虑了将图像分开和介绍到卡通和纹理部分的问题。
Natural images are often the superposition of various parts of different geometric characteristics. For instance, an image might be a mixture of cartoon and texture structures. In addition, images are often given with missing data. In this paper, we develop a method for simultaneously decomposing an image to its two underlying parts and inpainting the missing data. Our separation inpainting method is based on and $l_1$ minimization approach, using two dictionaries, each sparsifying one of the image parts but not the other. We introduce a comprehensive convergence analysis of our method, in a general setting, utilizing the concepts of joint concentration, clustered sparsity, and cluster coherence. As the main application of our theory, we consider the problem of separating and inpainting an image to a cartoon and texture parts.
