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

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.

References in corpus (14)

• Adam: A Method for Stochastic Optimization
• Deep Convolutional Neural Network for Inverse Problems in Imaging
• Rank Minimization for Snapshot Compressive Imaging
• Weighted Schatten $p$-Norm Minimization for Image Denoising and Background Subtraction
• Framelet Representation of Tensor Nuclear Norm for Third-Order Tensor Completion
• Low-rank Matrix Factorization under General Mixture Noise Distributions
• A New Convex Relaxation for Tensor Completion
• The Universal Approximation Property
• Robust Low-Rank Tensor Ring Completion
• Hyperspectral Denoising Using Unsupervised Disentangled Spatio-Spectral Deep Priors
• Combining Weighted Total Variation and Deep Image Prior for natural and medical image restoration via ADMM
• A variational approach to stable principal component pursuit
• PLU: The Piecewise Linear Unit Activation Function
• A Fast Algorithm for Cosine Transform Based Tensor Singular Value Decomposition

Cited by in corpus (1)

• T2LR-Net: An unrolling network learning transformed tensor low-rank prior for dynamic MR image reconstruction