Robust Tensor CUR

This repository is for our paper:

[1] HanQin Cai, Zehan Chao, Longxiu Huang, and Deanna Needell. Robust Tensor CUR: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruptions. SIAM Journal on Imaging Sciences, 17(1): 225–247, 2024.

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Introduction

A fast non-convex optimization algorithm, called RTCUR, for tensor robust principal component analysis (TRPCA) problem. We provide four verisons of this generalization.

Environment

This repo is developed with Tensor Toolbox v3.1. A future verison of this toolbox may also increase the peformance of our code; however, we cannot guarantee their compatibility.

Syntex

All functions in the algorithm folder follow the same syntax. For example:

RTCUR with fixed Chidori CUR

[L_core,X_sub_mat,timer,err ] = RTCUR_fc(D, r, para)

RTCUR with resampling Fiber CUR

[L_core,X_sub_mat,timer,err ] = RTCUR_rf(D, R, para)

Input Description

1. D : Inputed tensor.
2. R : Targeted multilinear rank.
3. (optional) para.max_iter, para.epsilon, para.zeta, para.gamma, para.CI: parameters described in our paper. All have defalut values.

• See paper for the details of constant selection.

Output Description

1. L_core : Core tensor, i.e., $\mathcal{R}$.
2. X_sub_mat : Fiber CUR components, i.e., {$C_i U_i^\dagger$}.

To obtain the full estimated tensor, call

L_est = ttm(L_core,X_sub_mat);

Demo

Clone the codes as well as Tensor Toolbox v3.1 and run simpleRPCAtest.m for a test demo.