Structural Sparse Tensor Robust PCA Method Based on Cross-Entropy for Vehicular Network Data Recovery

Existing works mostly use tensor robust principal component analysis (TRPCA) with $\ell _{1}$ norm to effectively recover clean low-rank traffic data from the Laplacian distributed outliers polluted data. However, in some traffic applications, the outliers are more likely to obey structural sparse distribution, which may lead to significant recovery performance degradation, especially under the coexistence of noise and structural outliers. Therefore, this paper proposes an effective structural sparse TRPCA method based on cross-entropy to recover traffic data from mixed pollution cases. In the proposed method, the global characteristics of the low-rank traffic data and the structural sparsity of the outliers are captured by the tensor nuclear norm and $\ell _{2,2,1}$ norm, respectively. Moreover, two new sets (noise probability set $\mathcal {P}_{N}$ and structural outlier probability set $\mathcal {P}_{S}$) are defined to clearly describe the uncertainty of different pollution types for each element. Then, a noise regularization term and a structural outlier regularization term with $\ell _{F}$ norm constrained are established via $\mathcal {P}_{N}$ and $\mathcal {P}_{S}$, respectively, to accurately quantify the element-wise corrupted level of different pollution types. Furthermore, a new cross-entropy (CE) with $\mathcal {P}_{N}$ and $\mathcal {P}_{S}$ is constructed as a regularization term to delicately distinguish the difference between noise and structural outliers. Via the defined CE regularization term, not only can the effects of different pollution types be distinctly quantified and separated, but also the values in the probability sets can be adaptively corrected during TRPCA optimization. Theoretical analysis and simulation results indicate that the proposed method can offer lower recovery error ratio and root mean square error with lower computational complexity in comparison to related works.