L0 Gradient Regularized Low-Rank Tensor Model for Hyperspectral Image Denoising

Hyperspectral image denoising via global spatial-spectral total variation regularized nonconvex local low-rank tensor approximation

Compressive sensing (CS) has been employed to compress and store hyperspectral images (HSI) to transfer extensive data efficiently, and obtaining high-quality reconstructed images is crucial for subsequent applications. Model-based methods usually capture the priors of HSI, including sparsity, global and nonlocal low-rankness, nonlocal self-similarity and global correlation. However, it is challenging to reasonably integrate different regularizations in a united framework and exploit various priors mentioned to reconstruct high-quality images. In this paper, a tensor optimization model based on the low-rank coefficient tensor and global prior (LRCTGP) is proposed for HSI reconstruction. Complementary regularization terms are integrated into a united framework and effectively promote the reconstruction results. First, we apply the mode- tensor-matrix product to decompose the original HSI rather than employing the regularization to capture the spectral low-rankness and simultaneously constrain the original and feature HSI. Then, tensor ring decomposition is employed to constrain the coefficient tensor with fewer bands, which is more efficient in the low-rank approximation and has smaller calculation costs than applying it to the original HSI. Moreover, integrating BM3D as a regularizer is more efficient than other patch-based models. Finally, considering the smoothness and global correlation, spatial-spectral total variation (SSTV) is applied to compensate for the shortcomings after decomposing the original and feature HSI, which complements the overall structure and details of reconstructed images and improves the reconstruction quality. Alternating direction method of multipliers (ADMM) is used to optimize the proposed model. Experimental results of the LRCTGP model on different HSI datasets are better than existing state-of-the-art approaches, which proves the superiority.

Several bandwise total variation (TV) regularized low-rank (LR)-based models have been proposed to remove mixed noise in hyperspectral images (HSIs). Conventionally, the rank of LR matrix is approximated using nuclear norm (NN). The NN is defined by adding all singular values together, which is essentially a $L_{1}$ -norm of the singular values. It results in non-negligible approximation errors and thus the resulting matrix estimator can be significantly biased. Moreover, these bandwise TV-based methods exploit the spatial information in a separate manner. To cope with these problems, we propose a spatial–spectral TV (SSTV) regularized non-convex local LR matrix approximation (NonLLRTV) method to remove mixed noise in HSIs. From one aspect, local LR of HSIs is formulated using a non-convex $L_{\gamma}$ -norm, which provides a closer approximation to the matrix rank than the traditional NN. From another aspect, HSIs are assumed to be piecewisely smooth in the global spatial domain. The TV regularization is effective in preserving the smoothness and removing Gaussian noise. These facts inspire the integration of the NonLLR with TV regularization. To address the limitations of bandwise TV, we use the SSTV regularization to simultaneously consider global spatial structure and spectral correlation of neighboring bands. Experiment results indicate that the use of local non-convex penalty and global SSTV can boost the preserving of spatial piecewise smoothness and overall structural information.

Hyperspectral image (HSI) acquisitions are degraded by various noises, among which additive Gaussian noise may be the worst-case, as suggested by information theory. In this paper, we present a novel tensor-based HSI denoising approach by fully identifying the intrinsic structures of the clean HSI and the noise. Specifically, the HSI is first divided into local overlapping full-band patches (FBPs), then the nonlocal similar patches in each group are unfolded and stacked into a new third order tensor. As this tensor shows a stronger low-rank property than the original degraded HSI, the tensor weighted nuclear norm minimization (TWNNM) on the constructed tensor can effectively separate the low-rank clean HSI patches. In addition, a regularization strategy with spatial–spectral total variation (SSTV) is utilized to ensure the global spatial–spectral smoothness in both spatial and spectral domains. Our method is designed to model the spatial–spectral non-local self-similarity and global spatial–spectral smoothness simultaneously. Experiments conducted on simulated and real datasets show the superiority of the proposed method.

Hyperspectral fruit image restoration using non-convex optimization

The standard traffic assignment problem (TAP) is often augmented with additional constraints to address non-standard applications. These models are called TAP with side constraints (TAPSC). Despite the rising significance of TAPSC models, the ability to efficiently solve them to satisfactory precision remains limited in real-world applications. The purpose of this paper is to fill this gap by integrating a recently developed high performance TAP solver, known as the path-based Greedy algorithm, with the augmented Lagrangian multiplier (ALM) method. This paper examines how precisely the subproblems in the ALM method should be solved to optimize the overall convergence performance. It is found that insufficiently converged subproblem solutions sometimes lead to catastrophic failures, although pursuing extremely high precision could also be counterproductive. Accordingly, it is proposed to adjust the precision required to solve the subproblems based on an approximate gap measured by the augmented Lagrangian. Results of numerical experiments show that adaptively adjusting the subproblem precision limit produces a 25% speed-up compared with the algorithm with a fixed limit.

Hyperspectral images (HSIs) have a wealth of applications in many areas, due to their fine spectral discrimination ability. However, in the practical imaging process, HSIs are often degraded by a mixture of various types of noise, for example, Gaussian noise, impulse noise, dead pixels, dead lines, and stripe noise. Low-rank matrix decomposition theory has been widely used in HSI denoising, and has achieved competitive results by modeling the impulse noise, dead pixels, dead lines, and stripe noise as sparse components. However, the existing low-rank-based methods for HSI denoising cannot completely remove stripe noise when the stripe noise is no longer sparse. In this article, we extend the HSI observation model and propose a double low-rank (DLR) matrix decomposition method for HSI denoising and destriping. By simultaneously exploring the low-rank characteristic of the lexicographically ordered noise-free HSI and the low-rank structure of the stripe noise on each band of the HSI, the two low-rank constraints are formulated into one unified framework, to achieve separation of the noise-free HSI, stripe noise, and other mixed noise. The proposed DLR model is then solved by the augmented Lagrange multiplier (ALM) algorithm efficiently. Both simulation and real HSI data experiments were carried out to verify the superiority of the proposed DLR method.

In this paper, we propose a time-frequency analysis method to obtain instantaneous frequencies and the corresponding decomposition by solving an optimization problem. In this optimization problem, the basis that is used to decompose the signal is not known a priori. Instead, it is adapted to the signal and is determined as part of the optimization problem. In this sense, this optimization problem can be seen as a dictionary adaptation problem, in which the dictionary is adaptive to one signal rather than a training set in dictionary learning. This dictionary adaptation problem is solved by using the augmented Lagrangian multiplier (ALM) method iteratively. We further accelerate the ALM method in each iteration by using the fast wavelet transform. We apply our method to decompose several signals, including signals with poor scale separation, signals with outliers and polluted by noise and a real signal. The results show that this method can give accurate recovery of both the instantaneous frequencies and the intrinsic mode functions.

Hyperspectral images (HSIs) are frequently corrupted by various types of noise, such as Gaussian noise, impulse noise, stripes, and deadlines due to the atmospheric conditions or imperfect hyperspectral imaging sensors. These types of noise, which are also called mixed noise, severely degrade the HSI and limit the performance of post-processing operations, such as classification, unmixing, target recognition, and so on. The patch-based low-rank and sparse based approaches have shown their ability to remove these types of noise to some extent. In order to remove the mixed noise further, total variation (TV)-based methods are utilized to denoise HSI. In this paper, we propose a group low-rank and spatial-spectral TV (GLSSTV) to denoise HSI. Here, the advantage is twofold. First, group low-rank exploits the local similarity inside patches and non-local similarity between patches which brings extra structural information. Second, SSTV helps in removing Gaussian and sparse noise using the spatial and spectral smoothness of HSI. The extensive simulations show that GLSSTV is effective in removing mixed noise both quantitatively and qualitatively and it outperforms the state-of-the-art low-rank and TV-based methods.

Hyperspectral image (HSI) is often corrupted by various kinds of noises. This letter proposes an innovative HSI denoising approach by leveraging the graph signal processing (GSP) theory and the low-rank (LR) matrix recovery model. With GSP, the piecewise smoothness (PWS) property of the HSI can be efficiently characterized, leading to a new regularization for HSI denoising, termed the adaptive weight graph total variation (AWGTV) regularization. Then, the denoising problem is formulated into a constrained optimization problem that incorporates the AWGTV and the LR property of the HSI. An augmented Lagrange multiplier method is adopted to solve the problem. Numerical experiments conducted on synthetic and real-world datasets and comparisons with existing methods demonstrate the effectiveness of the proposed denoising algorithm.

Hyperspectral image denoising by total variation-regularized bilinear factorization

Hyperspectral (HS) and multispectral (MS) image fusion aims at producing high-resolution HS (HRHS) images. However, the existing methods could not simultaneously consider the structures in both the spatial and spectral domains of the HS cube. In order to effectively preserve spatial–spectral structures in HRHS images, we propose a new low-resolution HS (LRHS) and high-resolution MS (HRMS) image fusion method based on spatial–spectral-graph-regularized low-rank tensor decomposition (SSGLRTD) in this paper. First, we reformulate the image fusion problem as a low-rank tensor decomposition model to utilize the low-rank property in the HS image. Then, two graphs are constructed in spatial and spectral domains, respectively. One of them is derived from the HRMS image for the spatial consistency, and the other is inferred from the LRHS image for spectral smoothness. Finally, the SSGLRTD fusion framework is established by combining all regularizers. With these two graphs, the spatial correlation and the spectral structure in the fused HRHS images are efficiently preserved. The experimental results on different datasets reveal that the proposed fusion method outperforms several existing fusion methods in terms of visual analysis and numerical comparison.

Hyperspectral video sequences (HVSs) are well suited for gas plume detection (GPD). The high spectral resolution allows the detection of chemical clouds even when they are optically thin. Processing this new type of video sequences is challenging and requires advanced image and video analysis algorithms. In this paper, we propose a novel method for GPD recorded in HVSs. Based on the assumption that the background is stationary and the gas plume is moving, the proposed method separates the background from the gas plume via a low-rank and sparse decomposition. Furthermore, taking into consideration that the gas plume is continuous in both spatial and temporal dimensions, we include total variation regularization in the constrained minimization problem, which we solve using the augmented Lagrangian multiplier method. After applying the above process to each extracted feature, a novel fusion strategy is proposed to combine the information into a final detection result. Experimental results using real data sets indicate that the proposed method achieves very promising GPD performance.

The majority of existing hyperspectral (HS) image denoising methods exploit local similarity in HS images by rearranging them into the matrix or vector forms. As the typical 3-D data, the inherent spatial and spectral properties in HS images should be simultaneously explored for denoising. Therefore, a 3-D geometrical kernel (3DGK) is developed in this article to describe the local structure. The proposed method assumes that the pixel can be represented by other pixels within a 3-D block efficiently owing to the local similarity with adjacent positions. Then, the HS image is modeled by the 3-D kernel regression with <italic>L</italic>₁-norm constraint, in which the local similarity is captured by the proposed 3DGK. To efficiently compute the parameters in 3DGK, geometrical structures, such as scale, shape, and orientation in the 3-D block, are estimated from the gradient information approximately. Finally, the noises are effectively removed while preserving the structures in HS images. Moreover, experimental results on simulated and real datasets demonstrate that the performance of 3DGK is better than those of the methods based on local similarity prior.

The hyperspectral and multispectral image fusion process, commonly known as the multisharpening process (also known as the hypersharpening process), results in the creation of unobservable high spectral and spatial resolution hyperspectral remote sensing data, by combining (or fusing) a hyperspectral image, characterized by a high spectral resolution, with, especially, a high spatial resolution multispectral one. There are several approaches in the literature performing such a process, in particular, those based on the spectral unmixing concept. The latter fusion methods aim to extract pure-material spectra from the high spectral resolution hyperspectral image and combine them with their corresponding proportions extracted from the high spatial resolution multispectral image. However, most of these methods, which mainly consider the standard linear mixing model, do not address the spectral variability phenomenon, precisely due to the considered data mixing model, which does not handle variations in illumination and atmospheric conditions or material composition inducing spectral variability. Neglecting such a phenomenon may lead to errors in the fusion process, thus decreasing the spatial and spectral qualities of sharpened products. In this paper, a new hyperspectral and multispectral data fusion method, based on the linear spectral unmixing concept that deals with spectral variability, is proposed. This approach, based on a multiplicative Nonnegative Matrix Factorization (NMF) technique, substantially extends the multiplicative Coupled NMF (CNMF) algorithm by considering a linear data mixing model that addresses the considered phenomenon. Indeed, the introduced approach minimizes new cost functions involving matrices with specific structures in order to deal with the spectral variability phenomenon. The proposed method is applied to synthetic and real data, and its effectiveness is evaluated with established performance criteria. Experimental results show that the designed algorithm globally yields sharpened hyperspectral data with fine spectral and spatial fidelities. Also, these results demonstrate that the proposed technique globally outperforms the tested literature approaches.