Graph Regularized Tensor Train Completion (GraphTTC)

Introduction

This is a matlab implemenation of the graph regularized tensor train completion, which optimizes one TT core fiber in each subproblem instead of a TT core. Both GraphTT-opt and GraphTT-vi are included, along with a demo on image completion. An illustration of our methods:

Data and noise

Recovery under 40% sampling rate

Recovery under 20% sampling rate

Update

We also included the modeling for outliers.

Functions

• demo_image_completion.m

  Run this demo to test GraphTT-opt/vi on image completion. The adopted image is "TestImages/airplane.mat".

• f_graphTT_opt/

  Includes functions implementing GraphTT-opt.

  • ttc_graph.m

    Use this function to run GraphTT-opt.

• f_graphTT_vi/

  Includes functions implementing GraphTT-VI.

  • VITTC_gh.m

    Use this function to run GraphTT-VI.

• rely/

  Includes an implementation on khatrirao product from MATLAB Tensor Toolbox.

• f_perfevaluate/

  Includes functions that evaluate the performance of the recovered tensor.

• TestImages/

  An 'airplane' image.

• ExperimentResults/

  A folder used for storing results.

Reference

Xu, L., Cheng, L., Wong, N., & Wu, Y. C. (2025). To Fold or Not to Fold: Graph Regularized Tensor Train for Visual Data Completion. IEEE Transactions on Pattern Analysis and Machine Intelligence. Paper link: https://arxiv.org/abs/2306.11123