Smooth PARAFAC Decomposition for Tensor Completion

TL;DR

This paper introduces a novel tensor completion method called smooth PARAFAC tensor completion (SPC) that combines low-rank approximation with smoothness constraints, significantly improving visual data recovery especially with high missing data ratios.

Contribution

The paper proposes an innovative tensor completion algorithm integrating smoothness constraints with low-rank models, enhancing performance on visual data with high missing data ratios.

Findings

Significant improvements in prediction accuracy over state-of-the-art methods.

Enhanced efficiency in tensor completion tasks.

Effective handling of high missing data ratios in visual datasets.

Abstract

In recent years, low-rank based tensor completion, which is a higher-order extension of matrix completion, has received considerable attention. However, the low-rank assumption is not sufficient for the recovery of visual data, such as color and 3D images, where the ratio of missing data is extremely high. In this paper, we consider "smoothness" constraints as well as low-rank approximations, and propose an efficient algorithm for performing tensor completion that is particularly powerful regarding visual data. The proposed method admits significant advantages, owing to the integration of smooth PARAFAC decomposition for incomplete tensors and the efficient selection of models in order to minimize the tensor rank. Thus, our proposed method is termed as "smooth PARAFAC tensor completion (SPC)." In order to impose the smoothness constraints, we employ two strategies, total variation (SPC-TV) and quadratic variation (SPC-QV), and invoke the corresponding algorithms for model learning. Extensive experimental evaluations on both synthetic and real-world visual data illustrate the significant improvements of our method, in terms of both prediction performance and efficiency, compared with many state-of-the-art tensor completion methods.