<p>Robust tensor completion (RTC), which aims to recover a clean latent tensor from incomplete and corrupted observations, has found broad applications in various fields. However, existing RTC methods often neglect the piecewise smoothness of tensors and rely on second-order statistics or Lasso-type penalties, which significantly limit their effectiveness in noise suppression and accurate recovery. To address these challenges, this paper proposes a novel two-stage RTC method termed enhanced global recovery with local patch-level refinement (EGRLPR). In the global recovery stage, we introduce weighted tensor correlation total variation (t-CTV) minimization with an outlier projection scheme (WTCTVOP) to jointly capture low-rank structure and piecewise smoothness while suppressing sparse noise and outliers. In the subsequent local patch-level refinement stage, an M-estimator-based tensor recovery method is utilized to further eliminate residual noise and enhance reconstruction quality. Extensive experiments on real-world visual datasets demonstrate that the proposed method consistently outperforms several state-of-the-art RTC approaches in both accuracy and robustness.</p>