Hyperspectral Imagery Denoising via Reweighed Sparse Low-Rank Nonnegative Tensor Factorization

Efficient denoising of hyperspectral imagery (HSI) relies on an representational model that is capable of capturing the spatial and spectral correlation in HSI. Recently, an intrinsic representation (IR) approach based on the linear spectral mixture model (LSMM) was proposed for unsupervised feature extraction. The IR model constitutes a sound representational model due to its ability to account for the physical data generation process of HSI, the spatial correlation effect, and the noise variance heterogeneity effect. In this paper, we explore the potential of IR for the denoising of HSI. A noisy pixel in HSI is expressed as a nonnegative linear combination of several endmembers, plus some Gaussian noise with heterogeneous noise variances. In order to perform denoising, the IR approach is used to adaptively estimate both the endmembers and the nonnegative coefficients (i.e., the abundances), which are finally used to reconstruct the clean image. The experiments on both simulated and real hyperspectral images demonstrate that the IR approach not only can resist the influence of noise, but also can preserve the image details.

Hyperspectral imagery (HSI) denoising is a popular research topic in remote sensing. In this paper, we propose a novel method for HSI denoising by performing Minimum Noise Fraction (MNF) to the original HSI data cube, thresholding the noisy output bands with the Video Non-Local Bayes (VNLB) algorithm, and then conducting the inverse MNF transform to obtain the denoised data cube. Our experiments demonstrate that the proposed method usually achieves the best denoising results among several existing denoising methods for two HSI data cubes. In addition, it is much faster for HSI denoising than the VNLB algorithm which was originally developed for video denoising.

Sparse coding based noise reduction algorithms have been extensively applied on hyperspectral imagery (HSI) denoising. Dictionary learning schemes are strongly suggested for sparse reconstruction in many researches, aiming at a smaller error between the underlying clean image and the reconstruction result. In previous researches, the training samples (patches) are selected from either unrelated clean images or the noised image itself. The dictionaries learned form unrelated clean images can not perfectly represent the underlying clean target image, while the dictionaries learned form the noised image itself may be affected by the noise existing in training samples. In this paper, we propose a novel dictionary learning scheme that depends on a panchromatic image from the same or similar scene with HSI. Considering the fact that the noise level of a panchromatic image is always much lower than HSI, we take the patches from panchromatic image as training samples. Taking the multi-scale image representation into consideration, we construct the dictionary from different scales via Gaussian pyramid. The proposed dictionary shows its good denoising performance in our experiments.

In this paper, we conduct a study for the effects of principal component analysis (PCA) on hyperspectral imagery denoising. Our previous works combined PCA with wavelet shrinkage, block matching and 3D filtering (BM3D), and block matching and 4D filtering (BM4D), respectively, and very good denoising results have been obtained for hyperspectral imagery with very little noise. To demonstrate if these methods are the best for other noise scenarios, we combine PCA with video BM3D (VBM3D) and video BM4D (VBM4D), and non-local means (NL-Means) as well. Experimental results show that the PCA+VBM3D is the best denoising method for moderate and high noise levels, and PCA+BM4D is preferred for very low noise levels. KeywordsHyperspectral imagery denoisingBM3DBM4DVBM3DVBM4DPrincipal component analysis (PCA)

For the instrument limitation and imperfect imaging optics, it is difficult to acquire high spatial resolution hyperspectral imagery. Low spatial resolution will result in a lot of mixed pixels and greatly degrade the detection and recognition performance, affect the related application in civil and military fields. As a powerful statistical image modeling technique, sparse representation can be utilized to analyze the hyperspectral image efficiently. Hyperspectral imagery is intrinsically sparse in spatial and spectral domains, and image super-resolution quality largely depends on whether the prior knowledge is utilized properly. In this article, we propose a novel hyperspectral imagery super-resolution method by utilizing the sparse representation and spectral mixing model. Based on the sparse representation model and hyperspectral image acquisition process model, small patches of hyperspectral observations from different wavelengths can be represented as weighted linear combinations of a small number of atoms in pre-trained dictionary. Then super-resolution is treated as a least squares problem with sparse constraints. To maintain the spectral consistency, we further introduce an adaptive regularization terms into the sparse representation framework by combining the linear spectrum mixing model. Extensive experiments validate that the proposed method achieves much better results.

In this paper, we study the sparse nonnegative tensor factorization and completion problem from partial and noisy observations for third-order tensors. Because of sparsity and nonnegativity, the underlying tensor is decomposed into the tensor-tensor product of one sparse nonnegative tensor and one nonnegative tensor. We propose to minimize the sum of the maximum likelihood estimation for the observations with nonnegativity constraints and the tensor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{0}$ </tex-math></inline-formula> norm for the sparse factor. We show that the error bounds of the estimator of the proposed model can be established under general noise observations. The detailed error bounds under specific noise distributions including additive Gaussian noise, additive Laplace noise, and Poisson observations can be derived. Moreover, the minimax lower bounds are shown to be matched with the established upper bounds up to a logarithmic factor of the sizes of the underlying tensor. These theoretical results for tensors are better than those obtained for matrices, and this illustrates the advantage of the use of nonnegative sparse tensor models for completion and denoising. Numerical experiments are provided to validate the superiority of the proposed tensor-based method compared with the matrix-based approach.

In this paper, we propose a method that not only reduces the dimensionality of a hyperspectral data cube but also removes noise in the data cube by combining the bivariate wavelet thresholding with principal component analysis (PCA). The data cube thus obtained is applied to mineral endmember extraction and mineral detection. The reason why we incorporate bivariate wavelet denoising into PCA dimensionality reduction is because the dimensionality-reduced channels using PCA often contain significant amounts of noise. By reducing noise in the data cube, we can get better dimensionality-reduced output channels for hyperspectral data analysis and processing. Experiments reported in this paper confirm that the proposed method outperforms PCA for endmember extraction and mineral detection using the Cuprite data cube.

Anomaly is generally defined as an object that strays away from the background clutter. As for hyperspectral anomaly detection, most of the previous methods fail to fully take advantage of the knowledge in both spatial and spectral domain. In this paper, we propose a novel method based on tensor recovery in which spatial structures and spectral characters are reasonably considered to separate the hypercube into a low-rank background and sparse anomalies. Since background is highly consistent not only in spectral domain, but also in spatial domain, we impose low-rank constraints on three unfolding matrix of the hypercube respectively to capture the global structure together. To better describe the local irregularities with low probability, a general l 1 norm constraint and an extra sparse regularization are imposed on pixels in the spectral mode alone, for that we consider each spectrum as an entirety. Extensive experiments on two real datasets show outstanding anomaly detection performance of the proposed method in comparison with the state-of-the-art methods.

Many spectral unmixing approaches ranging from geometry, algebra to statistics have been proposed, in which nonnegative matrix factorization (NMF)-based ones form an important family. The original NMF-based unmixing algorithm loses the spectral and spatial information between mixed pixels when stacking the spectral responses of the pixels into an observed matrix. Therefore, various constrained NMF methods are developed to impose spectral structure, spatial structure, and spectral-spatial joint structure into NMF to enforce the estimated endmembers and abundances preserve these structures. Compared with matrix format, the third-order tensor is more natural to represent a hyperspectral data cube as a whole, by which the intrinsic structure of hyperspectral imagery can be losslessly retained. Extended from NMF-based methods, a matrix-vector nonnegative tensor factorization (NTF) model is proposed in this paper for spectral unmixing. Different from widely used tensor factorization models, such as canonical polyadic decomposition CPD) and Tucker decomposition, the proposed method is derived from block term decomposition, which is a combination of CPD and Tucker decomposition. This leads to a more flexible frame to model various application-dependent problems. The matrix-vector NTF decomposes a third-order tensor into the sum of several component tensors, with each component tensor being the outer product of a vector (endmember) and a matrix (corresponding abundances). From a formal perspective, this tensor decomposition is consistent with linear spectral mixture model. From an informative perspective, the structures within spatial domain, within spectral domain, and cross spectral-spatial domain are retreated interdependently. Experiments demonstrate that the proposed method has outperformed several state-of-the-art NMF-based unmixing methods.

Hyperspectral imagery (HSI) consists of hundred or thousand of spectral bands and provides a wealth of spectral information. Although several parametric and non-parametric classifiers have been built with the purpose of efficiently and fully utilizing the spectral information in HSI, few of them are designed to exploit the underlying sparsity in HSI. In recent work, a joint sparsity model (JSM) based on the sparse representation theory was developed for HSI classification. In JSM, contextual information of HSI was exploited, where a rectangular window is employed to select neighboring pixels of a test pixel with the goal of providing spatial context to traditional per-pixel spectral classification. In this work, we propose a region growing approach to select the neighboring pixels of a test sample instead of the rectangular window and hence further improve the performance of such sparse representation classifiers. Experimental results with two different types of real-world hyperspectral datasets are reported to quantify the efficacy of the proposed approach.

The production of a high spatial resolution (HR) hyperspectral image (HSI) through the fusion of a low spatial resolution (LR) HSI with an HR multispectral image (MSI) has underpinned much of the recent progress in HSI super-resolution. The premise of these signs of progress is that both the degeneration from the HR HSI to LR HSI in the spatial domain and the degeneration from the HR HSI to HR MSI in the spectral domain are assumed to be known in advance. However, such a premise is difficult to achieve in practice. To address this problem, we propose to incorporate degeneration estimation into HSI super-resolution and present an unsupervised deep framework for "blind" HSIs super-resolution where the degenerations in both domains are unknown. In this framework, we model the latent HR HSI and the unknown degenerations with deep network structures to regularize them instead of using handcrafted (or shallow) priors. Specifically, we generate the latent HR HSI with an image-specific generator network and structure the degenerations in spatial and spectral domains through a convolution layer and a fully connected layer, respectively. By doing this, the proposed framework can be formulated as an end-to-end deep network learning problem, which is purely supervised by those two input images (i.e., LR HSI and HR MSI) and can be effectively solved by the backpropagation algorithm. Experiments on both natural scene and remote sensing HSI data sets show the superior performance of the proposed method in coping with unknown degeneration either in the spatial domain, spectral domain, or even both of them.

The low-rank tensor factorization (LRTF) technique has received increasing attention in many computer vision applications. Compared with the traditional matrix factorization technique, it can better preserve the intrinsic structure information and thus has a better low-dimensional subspace recovery performance. Basically, the desired low-rank tensor is recovered by minimizing the least square loss between the input data and its factorized representation. Since the least square loss is most optimal when the noise follows a Gaussian distribution, -norm-based methods are designed to deal with outliers. Unfortunately, they may lose their effectiveness when dealing with real data, which are often contaminated by complex noise. In this paper, we consider integrating the noise modeling technique into a generalized weighted LRTF (GWLRTF) procedure. This procedure treats the original issue as an LRTF problem and models the noise using a mixture of Gaussians (MoG), a procedure called MoG GWLRTF. To extend the applicability of the model, two typical tensor factorization operations, i.e., CANDECOMP/PARAFAC factorization and Tucker factorization, are incorporated into the LRTF procedure. Its parameters are updated under the expectation-maximization framework. Extensive experiments indicate the respective advantages of these two versions of MoG GWLRTF in various applications and also demonstrate their effectiveness compared with other competing methods.

Various existing anomaly detection (AD) technologies focus on the background feature extraction and suppression, which serves as a crucial step to extrude anomalies from the hyperspectral imagery (HSI). In this article, motivated by the advantages of the joint sparse representation (JSR) model for adaptive background base selection, a robust background feature extraction method through homogeneous region-based JSR is proposed and used for AD. By segmenting the scene from the spatial domain through an eight-connected region division operation based on the clustering result, a series of nonoverlapping homogeneous regions each sharing a common sparsity pattern are obtained. After discarding small regions, JSR is performed on each region with the dictionary constituted by the overall spectral items in the corresponding cluster. By calculating the usage frequency of dictionary atoms, the most representative background bases describing each background cluster are adaptively selected and then combined into the global background bases. In addition, considering the interference of noise on detection accuracy, an energy deviation-based noise estimation strategy is presented by analyzing the residual obtained from JSR. Finally, the anomaly response of each pixel is measured by comparing its projection energy obtained from the background orthogonal subspace projection with the noise energy in its corresponding region. The proposed method overcomes the shortcomings of traditional neighborhood-based JSR in the common sparsity pattern and anomaly proportion. The spatial characteristics of HSI are fully explored. Furthermore, the interference of noise on detection accuracy is eliminated. Experiments on four HSI data sets demonstrate the superiority of the proposed method.

Infrared target detection technology is indispensable in precision guidance and infrared warning systems. It faces grant challenges under complex scenes, such as poor robustness against a variety of scenes, inaccurate separation of the target from similar goals, etc. To solve these problems, we present a novel small target detection method based on spatial–temporal information of infrared imageries. A nonoverlapping patch spatial–temporal tensor (NPSTT) model is established by sliding a window to obtain nonoverlapping patches in adjacent images. Moreover, the tensor capped nuclear norm (TCNN) is introduced, which approximates the tensor rank more accurately for local infrared images. TCNN regularization and NPSTT (TCNN-NPSTT) are adopted to detect the potential targets. Essentially, the procedure of extracting targets from the background is converted to the low rank and sparse tensor factorization. Besides, an efficient optimization scheme utilizing the alternating direction multiplier method (ADMM) is introduced to solve the proposed model. Experiments in various scenes show that NPSTT can obtain better performance against complex backgrounds than state-of-the-art baselines, using the evaluating indicators include the receiver operating characteristic curve (ROC), signal-to-clutter ratio gain (SCRG), and background suppression factor (BSF).

Although hyperspectral remotely sensed data are believed to be nonlinear, they are often modeled and processed by algorithms assuming that the data are realizations of some linear stochastic processes. This is likely due to the reason that either the nonlinearity of the data may not be strong enough, and the algorithms based on linear data assumption may still do the job, or the effective algorithms that are capable of dealing with nonlinear data are not widely available. The simplification on data characteristics, however, may compromise the effectiveness and accuracy of information extraction from hyperspectral imagery. In this paper, we are investigating the existence of non- linearity in hyperspectral data represented by a 4-m Airborne Visible/Infrared Imaging Spectrometer image acquired over an area of coastal forests on Vancouver Island. The method employed for the investigation is based on the statistical test using surrogate data, an approach often used in nonlinear time series analysis. In addition to the high-order autocorrelation, spectral angle is utilized as the discriminating statistic to evaluate the differences between the hyperspectral data and their surrogates. To facilitate the statistical test, simulated data sets are created under linear stochastic constraints. Both simulated and real hyperspectral data are rearranged into a set of spectral series where the spectral and spatial adjacency of the original data is maintained as much as possible. This paper reveals that the differences are statistically significant between the values of discriminating statistics derived from the hyperspectral data and their surrogates. This indicates that the selected hyperspectral data are nonlinear in the spectral domain. Algorithms that are capable of explicitly addressing the nonlinearity are needed for processing hyperspectral remotely sensed data.