Multidimensional nonlinear transform-based tensor representation for high-dimensional image reconstruction

Zhi-Wei Shi, Yu-Bang Zheng, Yi Zhang, Heng-Chao Li

Abstract: The transform-based tensor nuclear norm (TNN) methods have achieved great performance on high-dimensional image reconstruction. In particularly, the nonlinear transform can achieve a lower-rank representation due to their ability to better model real data. However, the existing nonlinear transform-based TNN methods ignore the strong local neighboring correlations and lack the flexibility to handle correlations between different dimensions. To tackle these issues, we propose a novel multidimensional nonlinear transform-based tensor representation. Specifically, we use the structure of multiple convolution layers and activation layers to design a novel nonlinear transform. Different from pixel-to-pixel nonlinear transform, the proposed transform is a pixel block fusion nonlinear transform, and thus can integrate the strong local neighboring correlations to achieve a lower-rank representation. Also, to flexibly treat different correlations among different dimensions in high-dimensional images, we apply the designed nonlinear transform on different dimensions. Building on this, we define a novel three-dimensional convolution-based nonlinear transform tensor nuclear norm (3DCNTNN), construct a high-dimensional image reconstruction model, and develop a corresponding solving algorithm. Extensive experimental results show that the proposed method outperforms state-of-the-art transform-based tensor methods.