Bayesian Low Rank Tensor Ring Model for Image Completion

TL;DR

This paper introduces a Bayesian tensor ring model that automatically learns the low-rank structure of data for improved image completion, avoiding overfitting and parameter tuning issues present in existing methods.

Contribution

The paper proposes a Bayesian low rank tensor ring model with automatic rank determination and sparse core factors, enhancing image completion performance over existing methods.

Findings

Outperforms state-of-the-art methods in image recovery accuracy.

Automatically learns tensor ranks via Bayesian inference.

Effective on synthetic and real-world image datasets.

Abstract

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.