<p>Recently, tensor network decomposition has gained significant attention for its promising performance in multi-dimensional image recovery, which has allowed for a customized low-rank representation of the given tensor. However, the different frequency components of the original tensor are mixed together, while the standard tensor network decompositions attempt to treat these components equally, which limits their ability to capture different components during image recovery simultaneously. To address this issue, we propose a frequency-aware tensor network (FA-TN) decomposition, which allows us to flexibly characterize each unique frequency component. Specifically, FA-TN decomposition factorizes a tensor into different frequency components, which are flexibly captured by an exclusive tensor network decomposition. Compared to the standard tensor network decompositions, FA-TN decomposition more flexibly respects the characterization of each frequency, leading to more favorable recovery for the different frequency components. On the basis of the proposed FA-TN decomposition, we build a multi-dimensional image recovery model. To address the resulting highly non-convex optimization problem, we develop an efficient proximal alternating minimization (PAM)-based algorithm and establish its theoretical convergence guarantee. Extensive experimental results on color videos and light field data demonstrate the remarkable improvement of FA-TN over several state-of-the-art tensor decomposition-based methods.</p>