Overlapping Tensor Train Completion with TV Regularization for Image Reconstruction*

In this paper, we propose a novel tensor completion framework, Overlapping Tensor Train Completion with TV Regularization (OTTC-TV), which integrates the strengths of both Overlapping Ket Augmentation (OKA) and Total Variation (TV) regularization. This framework addresses two critical limitations of traditional tensor completion methods based on the Tensor Train (TT) decomposition: poor recovery performance in high missing rate scenarios and block artifacts that disrupt image continuity. By leveraging OKA, our proposal reduces block artifacts and improves inter-block smoothness, overcoming the non-smooth transitions between blocks. TV regularization further ensures smoothness across the reconstructed tensor by penalizing abrupt gradient changes. The proposed model demonstrates superior performance in completing high-missing-rate color images while also providing greater flexibility in handling varying input tensor dimensions. Extensive experiments validate the effectiveness and adaptability of OTTC-TV in color image reconstruction tasks.