Hyperspectral image (HSI) denoising is a fundamental task in remote sensing image processing, which is helpful for HSI subsequent applications, such as unmixing and classification. Thanks to the powerful representation ability of untrained deep neural networks, deep image prior (DIP)-based methods achieve tremendous successes in image processing (e.g., denoising and inpainting). However, DIP-based methods neglect the tensor low-rank prior of the underlying HSI which will be beneficial to capturing the global structure of the underlying HSI. To address this issue, we propose a novel model for HSI denoising, which can simultaneously take respective advantages of the tensor low-rank prior and the deep spatial-spectral prior. The tensor low-rank prior leads to a better global structure and the deep spatial-spectral prior is complementary to preserve better local details. On the one hand, we adopt low-rank tensor ring (TR) decomposition to characterize the tensor low-rank prior and capture the global structure of the underlying HSI. On the other hand, we employ untrained deep neural networks to flexibly represent the deep spatial-spectral prior and capture the local details of the underlying HSI. To solve the proposed model, we develop an efficient alternating minimization algorithm. Experimental results on simulated and real data validate the advantages of the proposed model in HSI denoising. Compared with state-of-the-art HSI denoising methods, the proposed method preserves better local details and the global structure of the underlying HSI.

This paper addresses the tensor completion problem, which aims to recover missing information of multi-dimensional images. How to represent a low-rank structure embedded in the underlying data is the key issue in tensor completion. In this work, we suggest a novel low-rank tensor representation based on coupled transform, which fully exploits the spatial multi-scale nature and redundancy in spatial and spectral/temporal dimensions, leading to a better low tensor multi-rank approximation. More precisely, this representation is achieved by using two-dimensional framelet transform for the two spatial dimensions, one/two-dimensional Fourier transform for the temporal/spectral dimension, and then Karhunen-Loéve transform (via singular value decomposition) for the transformed tensor. Based on this low-rank tensor representation, we formulate a novel low-rank tensor completion model for recovering missing information in multi-dimensional visual data, which leads to a convex optimization problem. To tackle the proposed model, we develop the alternating directional method of multipliers (ADMM) algorithm tailored for the structured optimization problem. Numerical examples on color images, multispectral images, and videos illustrate that the proposed method outperforms many state-of-the-art methods in qualitative and quantitative aspects.

Image denoising is often empowered by accurate prior information. In recent years, data-driven neural network priors have shown promising performance for RGB natural image denoising. Compared to classic handcrafted priors (e.g., sparsity and total variation), the “deep priors” are learned using a large number of training samples, which can accurately model the complex image generating process. However, data-driven priors are hard to acquire for hyperspectral images (HSIs) due to the lack of training data. A remedy is to use the so-called unsupervised deep image prior (DIP). Under the unsupervised DIP framework, it is hypothesized and empirically demonstrated that proper neural network structures are reasonable priors of certain types of images, and the network weights can be learned without training data. Nonetheless, the most effective unsupervised DIP structures were proposed for natural images instead of HSIs. The performance of unsupervised DIP-based HSI denoising is limited by a couple of serious challenges, namely network structure design and network complexity. This work puts forth an unsupervised DIP framework that is based on the classic spatiospectral decomposition of HSIs. Utilizing the so-called linear mixture model of HSIs, two types of unsupervised DIPs, that is, U-Net-like network and fully connected networks, are employed to model the abundance maps and endmembers contained in the HSIs, respectively. This way, empirically validated unsupervised DIP structures for natural images can be easily incorporated for HSI denoising. Besides, the decomposition also substantially reduces network complexity. An efficient alternating optimization algorithm is proposed to handle the formulated denoising problem. Simulated and real data experiments are employed to showcase the effectiveness of the proposed approach.

Destriping has attracted a lot of interest in the field of remote sensing images processing. Recent research works consider the characteristics of stripes, among which low-rankness and group sparsity regularizations are widely used. However, for real scenarios, these regularizations sometimes fail to work when the underlying assumptions are violated. Motivated by this observation, we propose a novel and flexible regularization, named as the reweighted block sparsity (RBS), for complex stripes (e.g., the partial stripes). RBS divides the stripe layer into several blocks along the stripe-perpendicular direction and boosts the group sparsity of each block, where the sparsity level is adaptively controlled by updating weights. Based on RBS, we further propose a destriping model by integrating RBS and unidirectional total variation regularization, which can better detect and remove complex stripes. Moreover, we develop an alternating direction method of multipliers algorithm to solve the proposed model. Experimental results demonstrate that the proposed method outperforms the state-of-the-art competitors qualitatively and quantitatively.

The transform-based tensor nuclear norm (TNN) methods have recently yielded promising results for tensor completion. The primary goal of these methods is to exploit the low-rank structure of frontal slices under the transform along the third mode. However, these methods typically neglect that the third mode fiber of a tensor is a one-dimensional signal, which is sparse under some transforms. In this study, we suggest a collaborative sparse and low-rank transforms model called CSLRT for third-order tensor completion. We simultaneously exploit the sparsity of third mode fibers and the low-rankness of frontal slices under learned transforms. In our work, the transformed sparsity is complementary to the transformed low-rankness, and they are organically combined and benefit from each other. Moreover, for tensors with limited correlation along the third mode (e.g., color images), we suggest three-directional CSLRT (3DCSLRT) to fully explore the transformed sparsity of fibers and transformed low-rankness of slices along three modes. To tackle proposed models, we develop multi-block proximal alternating minimization (PAM) algorithms and establish the theoretical guarantee. Extensive experimental results on real-world data demonstrate that proposed methods outperforms state-of-the-art competitors qualitatively and quantitatively.