Implicit neural representation (INR) has emerged as a powerful representation for data (e.g., multispectral images and videos). Previously, most INR methods directly represent data in the original space. However, since different frequency components are mixed in the original space, it is difficult to capture these frequency components simultaneously and accurately. To alleviate this limitation, we suggest a new frequency-aware implicit neural representation (FA-INR) working in a physically interpretable and learnable frequency space by cleverly introducing an extra frequency dimension, which allows us to readily decouple and modulate different frequency components, leading to a more accurate characterization of different frequency components in a divide-and-conquer manner. Specifically, the FA-INR consists of two important modules, i.e., the frequency module and the integration module. In the frequency module, we propose a new low-rank tensor frequency function to compactly and continuously represent the latent frequency space. In the integration module, different frequency components are adaptively integrated back to the original space. Extensive experiments on various multi-dimensional data, including multispectral images, color videos, and light field data, demonstrate that the proposed FA-INR significantly outperforms the state-of-the-art INR methods, especially for characterizing high-frequency components (e.g., textures and edges).

Recently, the transform-based tensor representation has attracted increasing attention in multimedia data (e.g., images and videos) recovery problems, which consists of two indispensable components, i.e., the transform and the characterization. Previously, the development of transform-based tensor representation has focused mainly on the transform perspective. Although several attempts have considered shallow matrix factorization (e.g., singular value decomposition and nonnegative matrix factorization) for characterizing the frontal slices of the transformed tensor (termed the latent tensor), the faithful characterization perspective has been underexplored. To address this issue, we propose a unifiedDeepTensorRepresentation (DTR) framework by synergistically combining the deep latent generative module and the deep transform module. Especially, the deep latent generative module can faithfully generate the latent tensor as compared with shallow matrix factorization. The new DTR framework not only allows us to better understand the classical shallow representations but also leads us to explore new representations. To examine the representation capability of the proposed DTR, we consider the representative multidimensional data recovery task and suggest an unsupervised DTR-based multidimensional data recovery model. Extensive experiments demonstrate that DTR achieves superior performance compared to the state-of-the-art methods from both quantitative and qualitative aspects, especially for fine detail recovery.