Deep fully-connected tensor network decomposition for multi-dimensional signal recovery

Abstract

Fully-connected tensor network (FCTN) decomposition has garnered significant interest for processing multi-dimensional signals due to its ability to capture the all-mode correlations of a tensor. However, its representation ability is still limited, particularly for representing fine details and complex textures. To break this limitation, we propose deep fully-connected tensor network (D-FCTN) decomposition with a powerful representation ability beyond FCTN decomposition. Specifically, D-FCTN decomposition consists of two pivotal building blocks: the intrinsic low-rank representation block and the deep transform block. In the intrinsic low-rank representation block, we use FCTN decomposition to capture the all-mode correlations in the low-dimensional latent space, which implicitly regularizes the recovered signal. In the deep transform block, the latent space is transformed to the original signal space by leveraging a deep neural network due to its mighty expressive capability. The intrinsic low-rank representation boosted by the deep transform is expected to deliver a more powerful representation ability for recovering multi-dimensional signals beyond FCTN decomposition. To examine the representation ability of D-FCTN decomposition, we suggest an unsupervised D-FCTN decomposition-based multi-dimensional signal recovery model. Experiments on multi-dimensional signals demonstrate the more powerful representation ability of D-FCTN decomposition especially for recovering fine details and complex textures, compared with the state-of-the-art methods.