  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.
