Multi-Dimensional Image Recovery via Self-Supervised Nonlinear Transform Based a Three-Directional Tensor Nuclear Norm

Recently, the tensor nuclear norm, based on self-supervised nonlinear transformations, has gained significant attention in multidimensional image restoration. However, its primary concept involves solely nonlinear transformations along the third mode of a three-order tensor, which limits its flexibility in dealing with correlations in various modes of high-dimensional data. This paper makes three main contributions. Firstly, we introduce a novel approach called three-directional self-supervised nonlinear transform tensor nuclear norm (3DSTNN), which takes into account nonlinear transformations in all modes and can better represent the global structure of the tensor. Secondly, we suggest a model for multidimensional picture recovery that minimizes ranks by modeling the underlying tensor data as low-rank components subjected to nonlinear transformations. Thirdly, to solve the suggested model, we create an effective algorithm based on the alternating direction method of multipliers (ADMM). In low-rank tensor approximation for image restoration, our approach performs better than the state-of-the-art, according to extensive experimental results on both synthetic and actual datasets.