**Rafał Zdunek \* and Tomasz Sadowski**

Department of Electronics, Wroclaw University of Science and Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland; tomasz.sadowski@pwr.edu.pl

**\*** Correspondence: rafal.zdunek@pwr.edu.pl; Tel.: +48-71-320-3215

Received: 10 December 2019; Accepted: 20 January 2020; Published: 22 January 2020

**Abstract:** The issue of image completion has been developed considerably over the last two decades, and many computational strategies have been proposed to fill-in missing regions in an incomplete image. When the incomplete image contains many small-sized irregular missing areas, a good alternative seems to be the matrix or tensor decomposition algorithms that yield low-rank approximations. However, this approach uses heuristic rank adaptation techniques, especially for images with many details. To tackle the obstacles of low-rank completion methods, we propose to model the incomplete images with overlapping blocks of Tucker decomposition representations where the factor matrices are determined by a hybrid version of the Gaussian radial basis function and polynomial interpolation. The experiments, carried out for various image completion and resolution up-scaling problems, demonstrate that our approach considerably outperforms the baseline and state-of-the-art low-rank completion methods.

**Keywords:** image completion; tensor decomposition models; image interpolation; image up-scaling
