Inpainting of Cyclic Data using First and Second Order Differences

TL;DR

This paper presents a novel variational inpainting model for cyclic data, employing absolute cyclic second order differences and a cyclic proximal point algorithm, with demonstrated effectiveness on synthetic and real data.

Contribution

It introduces a new inpainting model for cyclic data using absolute cyclic second order differences and develops an efficient cyclic proximal point algorithm for its minimization.

Findings

Effective inpainting on synthetic data

Successful application to real-world cyclic data

Competitive performance demonstrated

Abstract

Cyclic data arise in various image and signal processing applications such as interferometric synthetic aperture radar, electroencephalogram data analysis, and color image restoration in HSV or LCh spaces. In this paper we introduce a variational inpainting model for cyclic data which utilizes our definition of absolute cyclic second order differences. Based on analytical expressions for the proximal mappings of these differences we propose a cyclic proximal point algorithm (CPPA) for minimizing the corresponding functional. We choose appropriate cycles to implement this algorithm in an efficient way. We further introduce a simple strategy to initialize the unknown inpainting region. Numerical results both for synthetic and real-world data demonstrate the performance of our algorithm.