Long Zhen, Zhu Ce, Liu Jiani, Liu Yipeng
IEEE Trans Image Process. 2021;30:3568-3580. doi: 10.1109/TIP.2021.3062195. Epub 2021 Mar 11.
Low rank tensor ring based data recovery can recover missing image entries in signal 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 article, we present a Bayesian low rank tensor ring completion method for image recovery by automatically learning the low-rank structure of data. A multiplicative interaction model is developed for low rank tensor ring approximation, where sparsity-inducing hierarchical prior is placed over horizontal and frontal slices of core factors. 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, real-world color images and YaleFace dataset, show that the proposed method outperforms state-of-the-art ones, especially in terms of recovery accuracy.
基于低秩张量环的数据恢复能够在信号采集与变换过程中恢复缺失的图像数据项。最近提出的基于张量环（TR）的补全算法通常通过具有预定义秩的交替最小二乘法来解决低秩优化问题，当未知秩设置得过大且仅有少量测量数据时，这很容易导致过拟合。在本文中，我们提出一种用于图像恢复的贝叶斯低秩张量环补全方法，该方法通过自动学习数据的低秩结构来实现。我们为低秩张量环逼近开发了一种乘法交互模型，其中在核心因子的水平切片和正面切片上放置了诱导稀疏性的分层先验。与大多数现有方法相比, 所提出的方法无需进行参数调整，并且可以通过贝叶斯推理获得张量环的秩。数值实验，包括合成数据、真实世界彩色图像和耶鲁人脸数据集，表明所提出的方法优于现有方法，特别是在恢复精度方面。
