Low-Rank Tensor Completion with Non-Local Self-Similarity and Multidimensional Learnable Transforms

Abstract We propose a novel low-rank tensor completion framework that integrates nonlocal self-similarity and data-driven multidimensional transforms. The core of our method lies in extracting similar fully-bandwidth patches and assembling them into third-order sub-tensors. Each sub-tensor is then modeled as low-rank coding tensors under learnable multidimensional transforms, which adaptively captures intrinsic correlations across spatial, spectral, and temporal dimensions. To solve this nonconvex optimization problem, we design a multi-block proximal alternating minimization (PAM) algorithm with guaranteed global convergence. Extensive experiments on multispectral images, videos, and color images demonstrate that our method achieves significant improvements over state-of-the-art approaches.