Tensor Low-Rank Constraint and $l_0$ Total Variation for Hyperspectral Image Mixed Noise Removal

Conventional low-rank (LR)-based hyperspectral image (HSI) denoising models generally convert high-dimensional data into 2-D matrices or just treat this type of data as 3-D tensors. However, these pure LR or tensor low-rank (TLR)-based methods lack flexibility for considering different correlation information from different HSI directions, which leads to the loss of comprehensive structure information and inherent spatial-spectral relationship. To overcome these shortcomings, we propose a novel multidirectional LR modeling and spatial-spectral total variation (MLR-SSTV) model for removing HSI mixed noise. By incorporating the weighted nuclear norm, we obtain the weighted sum of weighted nuclear norm minimization (WSWNNM) and the weighted sum of weighted tensor nuclear norm minimization (WSWTNNM) to estimate the more accurate LR tensor, especially, to remove the dead-line noise better. Gaussian noise is further denoised and the local spatial-spectral smoothness is preserved effectively by SSTV regularization. We develop an efficient algorithm for solving the derived optimization based on the alternating direction method of multipliers (ADMM). Extensive experiments on both synthetic data and real data demonstrate the superior performance of the proposed MLR-SSTV model for HSI mixed noise removal.

The total variation (TV) model is attractive in that it is able to preserve sharp attributes in images. However, the restored images from TV-based methods do not usually stay in a given dynamic range, and hence projection is required to bring them back into the dynamic range for visual presentation or for storage in digital media. This will affect the accuracy of the restoration as the projected image will no longer be the minimizer of the given TV model. In this paper, we show that one can get much more accurate solutions by imposing box constraints on the TV models and solving the resulting constrained models. Our numerical results show that for some images where there are many pixels with values lying on the boundary of the dynamic range, the gain can be as great as 10.28 decibel in the peak signal-to-noise ratio. One traditional hindrance using the constrained model is that it is difficult to solve. However, in this paper, we propose using the alternating direction method of multipliers (ADMM) to solv...

The amount of noise included in a hyperspectral image limits its application and has a negative impact on hyperspectral image classification, unmixing, target detection, and so on. In hyperspectral images, because the noise intensity in different bands is different, to better suppress the noise in the high-noise-intensity bands and preserve the detailed information in the low-noise-intensity bands, the denoising strength should be adaptively adjusted with the noise intensity in the different bands. Meanwhile, in the same band, there exist different spatial property regions, such as homogeneous regions and edge or texture regions; to better reduce the noise in the homogeneous regions and preserve the edge and texture information, the denoising strength applied to pixels in different spatial property regions should also be different. Therefore, in this paper, we propose a hyperspectral image denoising algorithm employing a spectral-spatial adaptive total variation (TV) model, in which the spectral noise differences and spatial information differences are both considered in the process of noise reduction. To reduce the computational load in the denoising process, the split Bregman iteration algorithm is employed to optimize the spectral-spatial hyperspectral TV model and accelerate the speed of hyperspectral image denoising. A number of experiments illustrate that the proposed approach can satisfactorily realize the spectral-spatial adaptive mechanism in the denoising process, and superior denoising results are produced.

Hyperspectral images (HSIs) can finely discriminate distinct objects with a high spectral resolution, and they are widely employed in various applications. However, mixed noise severely degrades the quality of HSI and restricts the performance of subsequent tasks. As one of the critical pre-processing steps, HSI denoising has been developed rapidly, among which low-rank (LR) prior-based methods have achieved superior performance. Nevertheless, the existing approaches frequently fail to completely remove noise and reconstruct high-quality HSIs when tackling complicated mixed noise with multiple types of high-intensity stripe noise. To solve this problem, we propose an HSI denoising and destriping method based on anisotropic spatial and spectral total variation regularized double low-rank approximation (ATVDLR). The double low-rank approximation framework is devoted to separating the clean image from the mixed noise by exploiting both the global correlations of HSI tensor and the LR structure of stripe noise. Furthermore, the anisotropic spatial and spectral total variation regularization is introduced to preserve the spatial–spectral smoothness of HSI and the directional feature of stripes, thereby further suppressing high-level stripes and Gaussian noise. Finally, the alternating direction method of multipliers (ADMM) technique is designed to solve the proposed ATVDLR model. Extensive experimental results indicate that the proposed method outperforms other state-of-the-art techniques in multi-type high-intensity mixed noise reduction and image structural information protection, and has superior performance in complex mixed noise removal of real Gaofen-5 HSIs.

The problem for image restoration is usually reduced to a constraint optimization problem. Different choice of optimization operator leads to various restoration models, e.g. least squares model and original total variation (TV) model. The TV model and its modified version can efficiently preserve the edge of the restored image well, but there exist obvious staircases in smooth area of the restored image. To reduce those staircases, we propose a new modified TV model, by adding a constraint term for smooth area protection as a penalty function. The numerical experiment shows our model can not only preserve the edge as well as TV model, but also efficiently reduce the staircase appearing in the smooth areas. Furthermore, It is shown that the restored image by our model has higher signal-to-noise ratio, less mean square error and better visual effect than those by the least squares model and by the TV models.

Image restoration is a key step in the field of image processing. Total Variation (TV) model is widely applied in image denoising because it preserves edges and image details. However, TV model has some shortcomings, such as staircase artifacts and excessive smoothing of image texture area. Then we purpose a truncated L1-L2 Total Variational model, which is nonconvex and nonsmooth, for image restoration with impulse noise. In this proper, two algorithms, the alternating direction method of multiplier (ADMM) and the penalty-Gaussian Seidel type inertial proximal alternating linearized minimization (P-GiPALM), are designed to solve the nonconvex optimization. The subproblems are solved by the proximal difference-of -convex algorithm with extrapolation (pDCAe) and GiPALM with global convergence, respectively. The experimental results show that the new model has higher peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) values than those of median filter and the cutting-edge Cauchy denoising method.

Purpose. The total variation (TV) minimization algorithm is an effective image reconstruction algorithm capable of accurately reconstructing images from sparse and/or noisy data. The TV model consists of two terms: a data fidelity term and a TV regularization term. Two constrained TV models, data divergence-constrained TV minimization (DDcTV) and TV-constrained data divergence minimization (TVcDM), have been successfully applied to computed tomography (CT) and electron paramagnetic resonance imaging (EPRI). In this work, we propose a new constrained TV model, a doubly constrained TV (dcTV) model, which has the potential to further improve the reconstruction accuracy for the two terms which are both of constraint forms. Methods. We perform an inverse crime study to validate the model and its Chambolle-Pock (CP) solver and characterize the performance of the dcTV-CP algorithm in the context of CT. To demonstrate the superiority of the dcTV model, we compare the convergence rate and the reconstruction accuracy with the DDcTV and TVcDM models via simulated data. Results and Conclusions. The performance-characterizing study shows that the dcTV-CP algorithm is an accurate and convergent algorithm, with the model parameters impacting the reconstruction accuracy and the algorithm parameters impacting the convergence path and rate. The comparison studies show that the dcTV-CP algorithm has a relatively fast convergence rate and can achieve higher reconstruction accuracy from sparse projections or noisy projections relative to the other two single-constrained TV models. The knowledge and insights gained in the work may be utilized in the application of the new model in other imaging modalities including divergence-beam CT, magnetic resonance imaging (MRI), positron emission tomography (PET), and EPRI.

Although the traditional TV (Total Variation) model owns excellent image denoising ability, there are staircase effect problems for TV model. In this article, two detection operators for staircase effect problem are proposed. The staircase effect problem can be solved effectively by introducing two operators into traditional TV model. On the basis, it proposes an adaptive total variation model for image denoising. When dealing with image edge, it can still use the traditional TV model. Its purpose is to maintain the advantages in edge protection for TV model. When it is in the smooth area of image, linear diffusion is used to avoid the staircase effect.

An [formula omitted]-overlapping group sparse total variation for impulse noise image restoration

The total variation model performs very well for removing noise while preserving edges. However, it gives a piecewise constant solution which often leads to the staircase effect, consequently small details such as textures are filtered out in the denoising process. Fractional‐order total variation method is one of the major approaches to overcome such drawbacks. Unlike their good quality of fractional order, all these methods use a fixed fractional order for the whole of the image. In this paper, a novel variable‐order total fractional variation model is proposed for image denoising, in which the order of fractional derivative will be allocated automatically for each pixel based on the context of the image. This kind of selection is able to capture the edges and texture of the image simultaneously. In this regard, we prove the existence and uniqueness of the presented model. The split Bregman method is adapted to solve the model. Finally, the results illustrate the efficiency of the proposed model that yielded good visual effects and a better signal‐to‐noise ratio.

The total variation (TV) regularization has been widely used in various applications related to hyperspectral (HS) signal and image processing due to its potential in modeling the underlying smoothness of HS data. However, most existing TV norms usually tend to generate spatial oversmoothing or artifacts. To this end, we propose a novel l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> - l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> hybrid TV ( l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> - l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> HTV) regularization with the applications to HS mixed noise removal and compressed sensing (CS). More specifically, l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> - l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> HTV can be regarded as a globally and locally integrated TV regularizer, where the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> gradient constraint is incorporate into the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> spatial-spectral TV ( l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -SSTV). l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -SSTV is capable of exploiting the local structure information across both spatial and spectral domains, while the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> gradient can promote a globally spectral-spatial smoothness by directly controlling the number of nonzero gradients of HS images. This efficient combination considers more comprehensive prior knowledge of HS images, yielding sharper edge preservation and resolving the above drawbacks of existing pure TV norms. More significantly, l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> - l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> HTV can be easily injected into HS-related processing models, and an effective algorithm based on the alternating direction method of multipliers (ADMM) is developed to solve the optimization problems. Extensive experiments conducted on several HS data sets substantiate the superiority and effectiveness of the proposed method in comparison with many state-of-the-art methods.

Recently, deep learning-based methods are proposed for hyperspectral images (HSIs) denoising. Among them, unsupervised methods such as deep image prior (DIP)-based methods have received much attention because these methods do not require any training data. However, DIP-based methods suffer from the semi-convergence behavior, i.e., the iteration of DIP-based methods needs to terminate by referring to the ground-truth image at the optimal iteration point. In this paper, we propose the spatial-spectral constrained deep image prior (S2DIP) for the HSI mixed noise removal. Specifically, we integrate the DIP, the spatial-spectral total variation regularization term, and the l1-norm sparse term to respectively capture the deep prior of the clean HSI, the spatial-spectral local smooth prior of the clean HSI, and the sparse prior of noise. The proposed S2DIP jointly leverages the expressive power brought from the deep convolutional neural network without any training data and exploits the HSI and noise structures via hand-crafted priors. Thus, our method avoids the semi-convergence behavior of DIP-based methods. Meanwhile, our method largely enhances the HSI denoising ability of DIP-based methods. To tackle the corresponding model, we utilize the alternating direction multiplier method algorithm. Extensive experiments demonstrate that our method outperforms model-based and deep learning-based state-of-the-art HSI denoising methods.

Hyperspectral imaging and laser technology both rely on different wavelengths of light to analyze the characteristics of materials, revealing their composition, state, or structure through precise spectral data. In hyperspectral image (HSI) classification tasks, the limited number of labeled samples and the lack of feature extraction diversity often lead to suboptimal classification performance. Furthermore, traditional convolutional neural networks (CNNs) primarily focus on local features in hyperspectral data, neglecting long-range dependencies and global context. To address these challenges, this paper proposes a novel model that combines CNNs with an average pooling Vision Transformer (ViT) for hyperspectral image classification. The model utilizes three-dimensional dilated convolution and two-dimensional convolution to extract multi-scale spatial–spectral features, while ViT was employed to capture global features and long-range dependencies in the hyperspectral data. Unlike the traditional ViT encoder, which uses linear projection, our model replaces it with average pooling projection. This change enhances the extraction of local features and compensates for the ViT encoder’s limitations in local feature extraction. This hybrid approach effectively combines the local feature extraction strengths of CNNs with the long-range dependency handling capabilities of Transformers, significantly improving overall performance in hyperspectral image classification tasks. Additionally, the proposed method holds promise for the classification of fiber laser spectra, where high precision and spectral analysis are crucial for distinguishing between different fiber laser characteristics. Experimental results demonstrate that the CNN-Transformer model substantially improves classification accuracy on three benchmark hyperspectral datasets. The overall accuracies achieved on the three public datasets—IP, PU, and SV—were 99.35%, 99.31%, and 99.66%, respectively. These advancements offer potential benefits for a wide range of applications, including high-performance optical fiber sensing, laser medicine, and environmental monitoring, where accurate spectral classification is essential for the development of advanced systems in fields such as laser medicine and optical fiber technology.

Although the Total Variation (TV) model has good performance in the image inpainting including both maintaining damaged images' edge and reducing numerical calculation, it should be improved in the inpainting domain with rich texture. In this paper, an image multi-level-inpainting method based on TV model and texture synthesis scheme is proposed. It is the main research topic to improve the visual result of inpainted images with scratches including rich texture. At the first inpainting level, damaged images are calculated following the TV model, and then the patch-based texture synthesis scheme is used to improve the inpainted results of rich texture domain in the first level. Experimental results prove that the method has better performance in restoring an incomplete 2-D image in every detail that it looks more `complete' and `natural'.

Hyperspectral image classification with discriminative manifold broad learning system