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.

Hyperspectral images (HSIs) are of crucial importance in order to better understand features from a large number of spectral channels. Restricted by its inner imaging mechanism, the spatial resolution is often limited for HSIs. To alleviate this issue, in this work, we propose a simple and efficient architecture of deep convolutional neural networks to fuse a low-resolution HSI (LR-HSI) and a high-resolution multispectral image (HR-MSI), yielding a high-resolution HSI (HR-HSI). The network is designed to preserve both spatial and spectral information thanks to a new architecture based on: 1) the use of the LR-HSI at the HR-MSI's scale to get an output with satisfied spectral preservation and 2) the application of the attention and pixelShuffle modules to extract information, aiming to output high-quality spatial details. Finally, a plain mean squared error loss function is used to measure the performance during the training. Extensive experiments demonstrate that the proposed network architecture achieves the best performance (both qualitatively and quantitatively) compared with recent state-of-the-art HSI super-resolution approaches. Moreover, other significant advantages can be pointed out by the use of the proposed approach, such as a better network generalization ability, a limited computational burden, and the robustness with respect to the number of training samples. Please find the source code and pretrained models from https://liangjiandeng.github.io/Projects_Res/HSRnet_2021tnnls.html.

The main aim of this paper is to develop a framelet representation of the tensor nuclear norm for third-order tensor recovery. In the literature, the tensor nuclear norm can be computed by using tensor singular value decomposition based on the discrete Fourier transform matrix, and tensor completion can be performed by the minimization of the tensor nuclear norm which is the relaxation of the sum of matrix ranks from all Fourier transformed matrix frontal slices. These Fourier transformed matrix frontal slices are obtained by applying the discrete Fourier transform on the tubes of the original tensor. In this paper, we propose to employ the framelet representation of each tube so that a framelet transformed tensor can be constructed. Because of framelet basis redundancy, the representation of each tube is sparsely represented. When the matrix slices of the original tensor are highly correlated, we expect the corresponding sum of matrix ranks from all framelet transformed matrix frontal slices would be small, and the resulting tensor completion can be performed much better. The proposed minimization model is convex and global minimizers can be obtained. Numerical results on several types of multi-dimensional data (videos, multispectral images, and magnetic resonance imaging data) have tested and shown that the proposed method outperformed the other testing methods.

Hyperspectral image super-resolution (HISR) is to fuse a low-resolution hyperspectral image (LR-HSI) and a high-resolution multispectral image (HR-MSI), aiming to obtain a high-resolution hyperspectral image (HR-HSI). Recently, various convolution neural network (CNN)-based techniques have been successfully applied to address the HISR problem. However, these methods generally only consider the relation of a local neighborhood by convolution kernels with a limited receptive field, thus ignoring the global relationship in a feature map. In this letter, we design a Transformer-based architecture (called Fusformer) for the HISR problem, which is the first attempt to apply the Transformer architecture to this task to the best of our knowledge. Because of the excellent ability of feature representations, especially by the self-attention (SA) in the Transformer, our approach can globally explore the intrinsic relationship within features. Considering the specific HISR problem, since the LR-HSI holds the primary spectral information, our method estimates the spatial residual between the upsampled low-resolution multispectral image (LR-MSI) and the desired HR-HSI, reducing the burden of training the whole data in a smaller mapping space. Various experiments show that our approach outperforms current state-of-the-art (SOTA) HISR methods. The code is available at https://github.com/J-FHu/Fusformer .

Mixed noise (such as Gaussian, impulse, stripe, and deadline noises) contamination is a common phenomenon in hyperspectral imagery (HSI), greatly degrading visual quality and affecting subsequent processing accuracy. By encoding sparse prior to the spatial or spectral difference images, total variation (TV) regularization is an efficient tool for removing the noises. However, the previous TV term cannot maintain the shared group sparsity pattern of the spatial difference images of different spectral bands. To address this issue, this article proposes a group sparsity regularization of the spatial difference images for HSI restoration. Instead of using ℓ₁- or ℓ₂-norm (sparsity) on the difference image itself, we introduce a weighted ℓ2,1-norm to constrain the spatial difference image cube, efficiently exploring the shared group sparse pattern. Moreover, we employ the well-known low-rank Tucker decomposition to capture the global spatial-spectral correlation from three HSI dimensions. To summarize, a weighted group sparsity-regularized low-rank tensor decomposition (LRTDGS) method is presented for HSI restoration. An efficient augmented Lagrange multiplier algorithm is employed to solve the LRTDGS model. The superiority of this method for HSI restoration is demonstrated by a series of experimental results from both simulated and real data, as compared with the other state-of-the-art TV-regularized low-rank matrix/tensor decomposition methods.