AUTHOR=Boßmann Florian , Sauer Tomas , Sissouno Nada 

TITLE=Modeling Variational Inpainting Methods With Splines

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=5

YEAR=2019

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2019.00027

DOI=10.3389/fams.2019.00027

ISSN=2297-4687

ABSTRACT=<p>Mathematical methods of image inpainting often involve the discretization of a given continuous model. Typically, this is done by a pointwise discretization. We present a method that avoids this by modeling known variational approaches using a finite dimensional spline space. The way we build our algorithm we are able to prove that the basis of the spline space is stable. Further, due to the compact supports and structure of the basis the model involves a sparse system matrix allowing a fast and memory efficient implementation. Besides the analysis of the resulting model, we present a numerical implementation based on the alternating method of multipliers. We compare the results numerically with classical TV inpainting and give examples of applications, such as text removal, restoration, and noise removal.</p>