Analysis of simultaneous inpainting and geometric separation based on sparse decomposition

Tiep, Do; Levie, Ron van und Kutyniok, Gitta (2022): Analysis of simultaneous inpainting and geometric separation based on sparse decomposition. In: Analysis and Applications, Vol. 20, No. 2: pp. 303-352

Abstract

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 an 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics; Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0219-5305
• Language: English