Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition

Hyperspectral images (HSIs) are often corrupted by a mixture of several types of noise during the acquisition process, e.g., Gaussian noise, impulse noise, dead lines, stripes, and many others. Such complex noise could degrade the quality of the acquired HSIs, limiting the precision of the subsequent processing. In this paper, we present a novel tensor-based HSI restoration approach by fully identifying the intrinsic structures of the clean HSI part and the mixed noise part respectively. Specifically, for the clean HSI part, we use tensor Tucker decomposition to describe the global correlation among all bands, and an anisotropic spatial-spectral total variation (SSTV) regularization to characterize the piecewise smooth structure in both spatial and spectral domains. For the mixed noise part, we adopt the $\ell_1$ norm regularization to detect the sparse noise, including stripes, impulse noise, and dead pixels. Despite that TV regulariztion has the ability of removing Gaussian noise, the Frobenius norm term is further used to model heavy Gaussian noise for some real-world scenarios. Then, we develop an efficient algorithm for solving the resulting optimization problem by using the augmented Lagrange multiplier (ALM) method. Finally, extensive experiments on simulated and real-world noise HSIs are carried out to demonstrate the superiority of the proposed method over the existing state-of-the-art ones.Comment: 15 pages, 20 figure

Constrained low-tubal-rank tensor recovery for hyperspectral images mixed noise removal by bilateral random projections

In this paper, we propose a novel low-tubal-rank tensor recovery model, which directly constrains the tubal rank prior for effectively removing the mixed Gaussian and sparse noise in hyperspectral images. The constraints of tubal-rank and sparsity can govern the solution of the denoised tensor in the recovery procedure. To solve the constrained low-tubal-rank model, we develop an iterative algorithm based on bilateral random projections to efficiently solve the proposed model. The advantage of random projections is that the approximation of the low-tubal-rank tensor can be obtained quite accurately in an inexpensive manner. Experimental examples for hyperspectral image denoising are presented to demonstrate the effectiveness and efficiency of the proposed method.Comment: Accepted by IGARSS 201

Denoising of Hyperspectral Images Using Group Low-Rank Representation

Hyperspectral images (HSIs) have been used in a wide range of fields, such as agriculture, food safety, mineralogy and environment monitoring, but being corrupted by various kinds of noise limits its efficacy. Low-rank representation (LRR) has proved its effectiveness in the denoising of HSIs. However, it just employs local information for denoising, which results in ineffectiveness when local noise is heavy. In this paper, we propose an approach of group low-rank representation (GLRR) for the HSI denoising. In our GLRR, a corrupted HSI is divided into overlapping patches, the similar patches are combined into a group, and the group is reconstructed as a whole using LRR. The proposed method enables the exploitation of both the local similarity within a patch and the nonlocal similarity across the patches in a group simultaneously. The additional nonlocallysimilar patches can bring in extra structural information to the corrupted patches, facilitating the detection of noise as outliers. LRR is applied to the group of patches, as the uncorrupted patches enjoy intrinsic low-rank structure. The effectiveness of the proposed GLRR method is demonstrated qualitatively and quantitatively by using both simulated and real-world data in experiments

Interpretable Hyperspectral AI: When Non-Convex Modeling meets Hyperspectral Remote Sensing

Hyperspectral imaging, also known as image spectrometry, is a landmark technique in geoscience and remote sensing (RS). In the past decade, enormous efforts have been made to process and analyze these hyperspectral (HS) products mainly by means of seasoned experts. However, with the ever-growing volume of data, the bulk of costs in manpower and material resources poses new challenges on reducing the burden of manual labor and improving efficiency. For this reason, it is, therefore, urgent to develop more intelligent and automatic approaches for various HS RS applications. Machine learning (ML) tools with convex optimization have successfully undertaken the tasks of numerous artificial intelligence (AI)-related applications. However, their ability in handling complex practical problems remains limited, particularly for HS data, due to the effects of various spectral variabilities in the process of HS imaging and the complexity and redundancy of higher dimensional HS signals. Compared to the convex models, non-convex modeling, which is capable of characterizing more complex real scenes and providing the model interpretability technically and theoretically, has been proven to be a feasible solution to reduce the gap between challenging HS vision tasks and currently advanced intelligent data processing models

A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems

Non-Local Total Variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the Structure Tensor (ST) resulting from the gradient of a multicomponent image. The proposed approach allows us to penalize the non-local variations, jointly for the different components, through various $\ell_{1,p}$ matrix norms with $p \ge 1$. To facilitate the choice of the hyper-parameters, we adopt a constrained convex optimization approach in which we minimize the data fidelity term subject to a constraint involving the ST-NLTV regularization. The resulting convex optimization problem is solved with a novel epigraphical projection method. This formulation can be efficiently implemented thanks to the flexibility offered by recent primal-dual proximal algorithms. Experiments are carried out for multispectral and hyperspectral images. The results demonstrate the interest of introducing a non-local structure tensor regularization and show that the proposed approach leads to significant improvements in terms of convergence speed over current state-of-the-art methods