From Simulated to Visual Data: A Robust Low-Rank Tensor Completion Approach Using ℓ p -Regression for Outlier Resistance

Low-rank tensor completion (LRTC) that aims to restore the latent clean data from an incomplete and/or degraded observation, shows promising results in ubiquitous tensorial data completion applications. Most tensor completion approaches are vulnerable to outliers since their derivations are based on <tex-math notation="LaTeX">₂ </tex-math> -space to be robust against Gaussian noise. In this work, to tackle this issue, <tex-math notation="LaTeX">ₚ </tex-math> -regression <tex-math notation="LaTeX">$(0 < p < 2)$ </tex-math> is employed to achieve outlier resistance, where a factored form of tensor train (TT)-format representation is regularized by the low-TT-rank prior to exploit the inter-fibers correlation. On the basis of that, an effective iterative <tex-math notation="LaTeX">ₚ </tex-math> -regression TT completion method (referred to <tex-math notation="LaTeX">ₚ </tex-math> -TTC) is proposed, with the advantage of not requiring the hard-to-determine user-defined weights in TT rank model. Extensive experiment results are presented to demonstrate the outlier resistance of the proposed <tex-math notation="LaTeX">ₚ </tex-math> -TTC, and showing the effective and superior performance in both bistatic MIMO radar localization and color image inpainting and denoising, compared with state-of-the-art tensor completion approaches.