From Simulated to Visual Data: A Robust Low-Rank Tensor Completion Approach using lp-Regression for Outlier Resistance

Abstract

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 ℓ2 -space to be robust against Gaussian noise. In this work, to tackle this issue, ℓp -regression (0<p<2) 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 ℓp -regression TT completion method (referred to ℓp -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 ℓp -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.

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Reproductions