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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A fast non-convex optimization algorithm, called RTCUR, for tensor robust principal component analysis (TRPCA) problem. We provide four verisons of this generalization.
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.
All functions in the algorithm folder follow the same syntax. For example:
[L_core,X_sub_mat,timer,err ] = RTCUR_fc(D, r, para)
[L_core,X_sub_mat,timer,err ] = RTCUR_rf(D, R, para)
- D : Inputed tensor.
- R : Targeted multilinear rank.
- (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.
- L_core : Core tensor, i.e.,
$\mathcal{R}$ . - X_sub_mat : Fiber CUR components, i.e., {$C_i U_i^\dagger$}.
L_est = ttm(L_core,X_sub_mat);
Clone the codes as well as Tensor Toolbox v3.1 and run simpleRPCAtest.m
for a test demo.