Low rank tensor ring model is powerful for image completion which recovers missing entries in data acquisition and transformation. The recently proposed tensor ring (TR) based completion algorithms generally solve the low rank optimization problem by alternating least squares method with predefined ranks, which may easily lead to overfitting when the unknown ranks are set too large and only a few measurements are available. In this paper, we present a Bayesian low rank tensor ring model for image completion by automatically learning the low rank structure of data. A multiplicative interaction model is developed for the low-rank tensor ring decomposition, where core factors are enforced to be sparse by assuming their entries obey Student-T distribution. Compared with most of the existing methods, the proposed one is free of parameter-tuning, and the TR ranks can be obtained by Bayesian inference. Numerical Experiments, including synthetic data, color images with different sizes and YaleFace dataset B with respect to one pose, show that the proposed approach outperforms state-of-the-art ones, especially in terms of recovery accuracy.

中文翻译：

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用于图像补全的贝叶斯低秩张量环模型

低秩张量环模型对于图像补全功能强大，可以恢复数据采集和转换中丢失的条目。最近提出的基于张量环（TR）的补全算法通常通过交替最小二乘法和预定义的秩来解决低秩优化问题，当未知秩设置得太大并且只有几个测量值可用时，这很容易导致过度拟合。在本文中，我们通过自动学习数据的低秩结构，提出了一种用于图像补全的贝叶斯低秩张量环模型。为低阶张量环分解开发了一个乘法交互模型，其中核心因子通过假设它们的条目服从 Student-T 分布来强制稀疏。与大多数现有方法相比，所提出的方法无需参数调整，并且可以通过贝叶斯推理获得TR等级。数值实验，包括合成数据、不同大小的彩色图像和关于一个姿势的 YaleFace 数据集 B，表明所提出的方法优于最先进的方法，尤其是在恢复精度方面。