Self-Supervised Nonlinear Transform-Based Tensor Nuclear Norm for Multi-Dimensional Image Recovery

TL;DR

This paper introduces a self-supervised nonlinear transform neural network for tensor nuclear norm minimization, significantly improving multi-dimensional image recovery tasks over existing linear transform methods.

Contribution

It proposes a novel nonlinear multilayer neural network to learn transforms for tensor recovery, enhancing low-rank tensor approximation in various image processing applications.

Findings

Outperforms state-of-the-art methods in tensor completion

Effective in background subtraction and robust tensor recovery

Improves results in snapshot compressive imaging

Abstract

In this paper, we study multi-dimensional image recovery. Recently, transform-based tensor nuclear norm minimization methods are considered to capture low-rank tensor structures to recover third-order tensors in multi-dimensional image processing applications. The main characteristic of such methods is to perform the linear transform along the third mode of third-order tensors, and then compute tensor nuclear norm minimization on the transformed tensor so that the underlying low-rank tensors can be recovered. The main aim of this paper is to propose a nonlinear multilayer neural network to learn a nonlinear transform via the observed tensor data under self-supervision. The proposed network makes use of low-rank representation of transformed tensors and data-fitting between the observed tensor and the reconstructed tensor to construct the nonlinear transformation. Extensive experimental results on tensor completion, background subtraction, robust tensor completion, and snapshot compressive imaging are presented to demonstrate that the performance of the proposed method is better than that of state-of-the-art methods.