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

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.

Unsupervised Hyperspectral Mixed Noise Removal Via Spatial-Spectral Constrained Deep Image Prior

Hyperspectral images (HSIs) are unavoidably corrupted by mixed noise which hinders the subsequent applications. Traditional methods exploit the structure of the HSI via optimization-based models for denoising, while their capacity is inferior to the convolutional neural network (CNN)-based methods, which supervisedly learn the noisy-to-denoised mapping from a large amount of data. However, as the clean-noisy pairs of hyperspectral data are always unavailable in many applications, it is eager to build an unsupervised HSI denoising method with high model capability. To remove the mixed noise in HSIs, we suggest the spatial-spectral constrained deep image prior (S2DIP), which simultaneously capitalize the high model representation ability brought by the CNN in an unsupervised manner and does not need any extra training data. Specifically, we employ the separable 3D convolution blocks to faithfully encode the HSI in the framework of DIP, and a spatial-spectral total variation (SSTV) term is tailored to explore the spatial-spectral smoothness of HSIs. Moreover, our method favorably addresses the semi-convergence behavior of prevailing unsupervised methods, e.g., DIP 2D, and DIP 3D. Extensive experiments demonstrate that the proposed method outperforms state-of-the-art optimization-based HSI denoising methods in terms of effectiveness and robustness.