Sparse Unmixing Research Articles

Spectral–Spatial Weighted Sparse Regression for Hyperspectral Image Unmixing

Spectral unmixing aims at estimating the fractional abundances of a set of pure spectral materials (endmembers) in each pixel of a hyperspectral image. The wide availability of large spectral libraries has fostered the role of sparse regression techniques in the task of characterizing mixed pixels in remotely sensed hyperspectral images. A general solution for sparse unmixing methods consists of using the $\ell _{1}$ regularizer to control the sparsity, resulting in a very promising performance but also suffering from sensitivity to large and small sparse coefficients. A recent trend to address this issue is to introduce weighting factors to penalize the nonzero coefficients in the unmixing solution. While most methods for this purpose focus on analyzing the hyperspectral data by considering the pixels as independent entities, it is known that there exists a strong spatial correlation among features in hyperspectral images. This information can be naturally exploited in order to improve the representation of pixels in the scene. In order to take advantage of the spatial information for hyperspectral unmixing, in this paper, we develop a new spectral–spatial weighted sparse unmixing (S2WSU) framework, which uses both spectral and spatial weighting factors, further imposing sparsity on the solution. Our experimental results, conducted using both simulated and real hyperspectral data sets, illustrate the good potential of the proposed S2WSU, which can greatly improve the abundance estimation results when compared with other advanced spectral unmixing methods.

Spatially adaptive hyperspectral unmixing through endmembers analytical localization based on sums of anisotropic 2D Gaussians

Spectral unmixing provides, for each pixel in the image, an estimated vector of fractional abundances that correspond to pure signatures, known as endmembers (EMs). Standard unmixing techniques rely only on spectral information and each pixel is solved as an individual entity. Recent studies show that incorporating the image's spatial information enhances accuracy of the unmixing results. Spatial information may allow better selection of relevant EMs, for each pixel, rather than utilizing all potential EMs in solving the spectral mixing problem. To implement this approach, we developed a new method for spatially adaptive spectral unmixing called Gaussian-based spatially adaptive unmixing (GBSAU). GBSAU fits for each EM, a surface by a series of spatial anisotropic 2D Gaussians whose sum represents the EM's fraction distribution over the whole image. These analytical surfaces facilitate a sparse solution for the unmixing process by spatial localization of EMs, which is then used to determine an adaptive subset of actual EMs for each pixel. The performance of our novel method was compared with that of the state-of-art spatially adaptive unimximg method, sparse unmixing via variable splitting augmented Lagrangian and total variation (SUnSAL-TV) as well as with two ordinary non-spatial methods, sparse unmixing by variable splitting and augmented Lagrangian (SUnSAL) and vectorized code projected gradient descent unmixing (VPGDU). The comparison was carried out on both simulated and real hyperspectral images. The results obtained with GBSAU indicated a significant improvement in the overall accuracy of the unmixing process compared with both spatially adaptive and ordinary methods. Quantitatively, GBSAU reduces the average mean absolute error (MAE) of the results by ∼15%, for cases with SNR = 30 db and 20 db, and by ∼30% for cases with SNR = 10 db and 5 db.

TARGET TRANSFORMATION CONSTRAINED SPARSE UNMIXING (TTCSU) ALGORITHM FOR RETRIEVING HYDROUS MINERALS ON MARS: APPLICATION TO SOUTHWEST MELAS CHASMA

Abstract. Quantitative analysis of hydrated minerals from hyperspectral remote sensing data is fundamental for understanding Martian geologic process. Because of the difficulties for selecting endmembers from hyperspectral images, a sparse unmixing algorithm has been proposed to be applied to CRISM data on Mars. However, it's challenge when the endmember library increases dramatically. Here, we proposed a new methodology termed Target Transformation Constrained Sparse Unmixing (TTCSU) to accurately detect hydrous minerals on Mars. A new version of target transformation technique proposed in our recent work was used to obtain the potential detections from CRISM data. Sparse unmixing constrained with these detections as prior information was applied to CRISM single-scattering albedo images, which were calculated using a Hapke radiative transfer model. This methodology increases success rate of the automatic endmember selection of sparse unmixing and could get more accurate abundances. CRISM images with well analyzed in Southwest Melas Chasma was used to validate our methodology in this study. The sulfates jarosite was detected from Southwest Melas Chasma, the distribution is consistent with previous work and the abundance is comparable. More validations will be done in our future work.

Formula omitted]-based sparse hyperspectral unmixing using spectral information and a multi-objectives formulation

Sparse unmixing aims at recovering pure materials from hyperpspectral images and estimating their abundance fractions. Sparse unmixing is actually ℓ0 problem which is NP-h ard, and a relaxation is often used. In this paper, we attempt to deal with ℓ0 problem directly via a multi-objective based method, which is a non-convex manner. The characteristics of hyperspectral images are integrated into the proposed method, which leads to a new spectra and multi-objective based sparse unmixing method (SMoSU). In order to solve the ℓ0 norm optimization problem, the spectral library is encoded in a binary vector, and a bit-wise flipping strategy is used to generate new individuals in the evolution process. However, a multi-objective method usually produces a number of non-dominated solutions, while sparse unmixing requires a single solution. How to make the final decision for sparse unmixing is challenging. To handle this problem, we integrate the spectral characteristic of hyperspectral images into SMoSU. By considering the spectral correlation in hyperspectral data, we improve the Tchebycheff decomposition function in SMoSU via a new regularization item. This regularization item is able to enforce the individual divergence in the evolution process of SMoSU. In this way, the diversity and convergence of population is further balanced, which is beneficial to the concentration of individuals. In the experiments part, three synthetic datasets and one real-world data are used to analyse the effectiveness of SMoSU, and several state-of-art sparse unmixing algorithms are compared.

Hyperspectral Image Resolution Enhancement Approach Based on Local Adaptive Sparse Unmixing and Subpixel Calibration

Unmixing based fusion aims at generating a high spectral-spatial resolution image (HSS) with the same surface features of the high spatial resolution multispectral image (MS) and low spatial resolution hyperspectral image (HS). In this paper, a new fusion method is proposed to improve the fusion performance by taking further advantage of the distribution characteristics of ground objects. First, we put forward a local adaptive sparse unmixing based fusion (LASUF) algorithm, in which the sparsity of the abundance matrices is appended as the constraint to the optimization fusion, considering the limited categories of ground objects in a specific range and the local correlation of their distribution. Then, to correct the possible original subpixel misregistrations or those introduced by the fusion procedures, a subpixel calibration method based on optimal matching adaptive morphology filtering (OM-AMF) is designed. Experiments on various datasets captured by different sensors demonstrate that the proposed fusion algorithm surpasses other typical fusion techniques in both spatial and spectral domains. The proposed method effectively preserves the spectral composition features of the isolated ground objects within a small area. In addition, the OM-AMF postprocessing is able to spatially correct the fusion results at a subpixel level and preserve the spectral features simultaneously.

Robust Sparse Unmixing for Hyperspectral Imagery

A linear sparse unmixing method based on spectral library has been widely used to tackle the hyperspectral unmixing problem, under the assumption that the spectrum of each pixel in the hyperspectral scene can be expressed as a linear combination of pure endmembers in the spectral library. However, because of the ion (atom) substitution in the geological process, there often exists spectral variability between the measured endmembers in the real environment and corresponding ones in the spectral library, which poses a significant challenge to linear sparse unmixing. Physically, the substitution leads to the variation of absorption peaks of endmembers, making the spectral variation of sparse property. To address the above problem, we introduce redundant spectrum to represent the spectral variation caused by ion (atom) substitution and develop a sparse redundant unmixing model by adding the redundant regularization into the classical sparse regression formulation. Based on the alternating direction method of multipliers, we develop a unified algorithm called sparse redundant unmixing to obtain the solution. Both simulation experiment and real data experiment demonstrate that the proposed method can effectively use the redundant spectrum to address the spectral variation problem caused by the ion (atom) substitution.

Hyperspectral Unmixing via Low-Rank Representation with Space Consistency Constraint and Spectral Library Pruning

Spectral unmixing is a popular technique for hyperspectral data interpretation. It focuses on estimating the abundance of pure spectral signature (called as endmembers) in each observed image signature. However, the identification of the endmembers in the original hyperspectral data becomes a challenge due to the lack of pure pixels in the scenes and the difficulty in estimating the number of endmembers in a given scene. To deal with these problems, the sparsity-based unmixing algorithms, which regard a large standard spectral library as endmembers, have recently been proposed. However, the high mutual coherence of spectral libraries always affects the performance of sparse unmixing. In addition, the hyperspectral image has the special characteristics of space. In this paper, a new unmixing algorithm via low-rank representation (LRR) based on space consistency constraint and spectral library pruning is proposed. The algorithm includes the spatial information on the LRR model by means of the spatial consistency regularizer which is based on the assumption that: it is very likely that two neighbouring pixels have similar fractional abundances for the same endmembers. The pruning strategy is based on the assumption that, if the abundance map of one material does not contain any large values, it is not a real endmember and will be removed from the spectral library. The algorithm not only can better capture the spatial structure of data but also can identify a subset of the spectral library. Thus, the algorithm can achieve a better unmixing result and improve the spectral unmixing accuracy significantly. Experimental results on both simulated and real hyperspectral datasets demonstrate the effectiveness of the proposed algorithm.

高光谱图像Pareto优化稀疏解混

高光谱图像Pareto优化稀疏解混

Joint Local Abundance Sparse Unmixing for Hyperspectral Images

Sparse unmixing is widely used for hyperspectral imagery to estimate the optimal fraction (abundance) of materials contained in mixed pixels (endmembers) of a hyperspectral scene, by considering the abundance sparsity. This abundance has a unique property, i.e., high spatial correlation in local regions. This is due to the fact that the endmembers existing in the region are highly correlated. This implies the low-rankness of the abundance in terms of the endmember. From this prior knowledge, it is expected that considering the low-rank local abundance to the sparse unmixing problem improves estimation performance. In this study, we propose an algorithm that exploits the low-rank local abundance by applying the nuclear norm to the abundance matrix for local regions of spatial and abundance domains. In our optimization problem, the local abundance regularizer is collaborated with the L 2 , 1 norm and the total variation for sparsity and spatial information, respectively. We conducted experiments for real and simulated hyperspectral data sets assuming with and without the presence of pure pixels. The experiments showed that our algorithm yields competitive results and performs better than the conventional algorithms.

Rolling Guidance Based Scale-Aware Spatial Sparse Unmixing for Hyperspectral Remote Sensing Imagery

Spatial regularization based sparse unmixing has attracted much attention in the hyperspectral remote sensing image processing field, which combines spatial information consideration with a sparse unmixing model, and has achieved improved fractional abundance results. However, the traditional spatial sparse unmixing approaches can suppress discrete wrong unmixing points and smooth an abundance map with low-contrast changes, and it has no concept of scale difference. In this paper, to better extract the different levels of spatial details, rolling guidance based scale-aware spatial sparse unmixing (namely, Rolling Guidance Sparse Unmixing (RGSU)) is proposed to extract and recover the different levels of important structures and details in the hyperspectral remote sensing image unmixing procedure, as the different levels of structures and edges in remote sensing imagery have different meanings and importance. Differing from the existing spatial regularization based sparse unmixing approaches, the proposed method considers the different levels of edges by combining a Gaussian filter-like method to realize small-scale structure removal with a joint bilateral filtering process to account for the spatial domain and range domain correlations. The proposed method is based on rolling guidance spatial regularization in a traditional spatial regularization sparse unmixing framework, and it accomplishes scale-aware sparse unmixing. The experimental results obtained with both simulated and real hyperspectral images show that the proposed method achieves visual effects better and produces higher quantitative results (i.e., higher SRE values) when compared to the current state-of-the-art sparse unmixing algorithms, which illustrates the effectiveness of the rolling guidance based scale aware method. In the future work, adaptive scale-aware spatial sparse unmixing framework will be studied and developed to enhance the current idea.

Sparse Unmixing of Hyperspectral Data with Noise Level Estimation

Recently, sparse unmixing has received particular attention in the analysis of hyperspectral images (HSIs). However, traditional sparse unmixing ignores the different noise levels in different bands of HSIs, making such methods sensitive to different noise levels. To overcome this problem, the noise levels at different bands are assumed to be different in this paper, and a general sparse unmixing method based on noise level estimation (SU-NLE) under the sparse regression framework is proposed. First, the noise in each band is estimated on the basis of the multiple regression theory in hyperspectral applications, given that neighboring spectral bands are usually highly correlated. Second, the noise weighting matrix can be obtained from the estimated noise. Third, the noise weighting matrix is integrated into the sparse regression unmixing framework, which can alleviate the impact of different noise levels at different bands. Finally, the proposed SU-NLE is solved by the alternative direction method of multipliers. Experiments on synthetic datasets show that the signal-to-reconstruction error of the proposed SU-NLE is considerably higher than those of the corresponding traditional sparse regression unmixing methods without noise level estimation, which demonstrates the efficiency of integrating noise level estimation into the sparse regression unmixing framework. The proposed SU-NLE also shows promising results in real HSIs.

A Stepwise Analytical Projected Gradient Descent Search for Hyperspectral Unmixing and Its Code Vectorization

We present, in this paper, a new methodology for spectral unmixing, where a vector of fractions, corresponding to a set of endmembers (EMs), is estimated for each pixel in the image. The process first provides an initial estimate of the fraction vector, followed by an iterative procedure that converges to an optimal solution. Specifically, projected gradient descent (PGD) optimization is applied to (a variant of) the spectral angle mapper objective function, so as to significantly reduce the estimation error due to amplitude (i.e., magnitude) variations in EM spectra, caused by the illumination change effect. To improve the computational efficiency of our method over a commonly used gradient descent technique, we have analytically derived the objective function’s gradient and the optimal step size (used in each iteration). To gain further improvement, we have implemented our unmixing module via code vectorization, where the entire process is “folded” into a single loop, and the fractions for all of the pixels are solved simultaneously. We call this new parallel scheme vectorized code PGD unmixing (VPGDU). VPGDU has the advantage of solving (simultaneously) an independent optimization problem per image pixel, exactly as other pixelwise algorithms, but significantly faster. Its performance was compared with the commonly used fully constrained least squares unmixing (FCLSU), the generalized bilinear model (GBM) method for hyperspectral unmixng, and the fast state-of-the-art methods, sparse unmixing by variable splitting and augmented Lagrangian (SUnSAL) and collaborative SUnSAL (CLSUnSAL) based on the alternating direction method of multipliers. Considering all of the prospective EMs of a scene at each pixel (i.e., without a priori knowledge which/how many EMs are actually present in a given pixel), we demonstrate that the accuracy due to VPGDU is considerably higher than that obtained by FCLSU, GBM, SUnSAL, and CLSUnSAL under varying illumination, and is, otherwise, comparable with respect to these methods. However, while our method is significantly faster than FCLSU and GBM, it is slower than SUnSAL and CLSUnSAL by roughly an order of magnitude.

MINERAL ABUNDANCE AND PARTICLE SIZE DISTRIBUTION DERIVED FROM IN-SITU SPECTRA MEASUREMENTS OF YUTU ROVER OF CHANG’E-3

Abstract. From geologic perspective, understanding the types, abundance, and size distributions of minerals allows us to address what geologic processes have been active on the lunar and planetary surface. The imaging spectrometer which was carried by the Yutu Rover of Chinese Chang’E-3 mission collected the reflectance at four different sites at the height of ~ 1 m, providing a new insight to understand the lunar surface. The mineral composition and Particle Size Distribution (PSD) of these four sites were derived in this study using a Radiative Transfer Model (RTM) and Sparse Unmixing (SU) algorithm. The endmembers used were clinopyroxene, orthopyroxene, olivine, plagioclase and agglutinate collected from the lunar sample spectral dataset in RELAB. The results show that the agglutinate, clinopyroxene and olivine are the dominant minerals around the landing site. In location Node E, the abundance of agglutinate can reach up to 70 %, and the abundances of clinopyroxene and olivine are around 10 %. The mean particle sizes and the deviations of these endmembers were retrieved. PSDs of all these endmembers are close to normal distribution, and differences exist in the mean particle sizes, indicating the difference of space weathering rate of these endmembers.

Hyperspectral Unmixing Using Double Reweighted Sparse Regression and Total Variation

Spectral unmixing is an important technique in hyperspectral image applications. Recently, sparse regression has been widely used in hyperspectral unmixing, but its performance is limited by the high mutual coherence of spectral libraries. To address this issue, a new sparse unmixing algorithm, called double reweighted sparse unmixing and total variation (TV), is proposed in this letter. Specifically, the proposed algorithm enhances the sparsity of fractional abundances in both spectral and spatial domains through the use of double weights, where one is used to enhance the sparsity of endmembers in spectral library, and the other is introduced to improve the sparsity of fractional abundances. Moreover, a TV-based regularization is further adopted to explore the spatial–contextual information. As such, the simultaneous utilization of both double reweighted $l_{1}$ minimization and TV regularizer can significantly improve the sparse unmixing performance. Experimental results on both synthetic and real hyperspectral data sets demonstrate the effectiveness of the proposed algorithm both visually and quantitatively.

Centralized Collaborative Sparse Unmixing for Hyperspectral Images

Spectral unmixing is very important in hyperspectral image analysis and processing, which aims at identifying the constituent spectra (i.e., endmembers) and estimating their fractional abundances from the mixed pixels. In recent years, sparse unmixing has received considerable interest. However, the acquired hyperspectral images are generally degraded by the noise, making sparse unmixing not faithful enough. To address this issue, this paper proposes a novel framework to couple sparse hyperspectral unmixing and abundance estimation error reduction together. Specifically, with the definition of abundance estimation error, a centralized constraint is incorporated into the collaborative sparse unmixing framework by exploiting the nonlocal redundancy of abundance map. This way we suppress the abundance estimation error, and improve the unmixing accuracy. Meanwhile, the alternating direction method of multipliers is introduced to solve the underlying constrained model. Experimental results on both synthetic and real hyperspectral data demonstrate the effectiveness of our proposed algorithm.

A Multiobjective Cooperative Coevolutionary Algorithm for Hyperspectral Sparse Unmixing

Sparse unmixing of hyperspectral data is an important technique aiming at estimating the fractional abundances of the endmembers. Traditional sparse unmixing is faced with the $\boldsymbol {l_{0}}$ -norm problem which is an NP-hard problem. Sparse unmixing is inherently a multiobjective optimization problem. Most of the recent works combine cost functions into single one to construct an aggregate objective function, which involves weighted parameters that are sensitive to different data sets and difficult to tune. In this paper, a novel multiobjective cooperative coevolutionary algorithm is proposed to optimize the reconstruction term, the sparsity term and the total variation regularization term simultaneously. A problem-dependent cooperative coevolutionary strategy is designed because sparse unmixing encounters a large scale optimization problem. The proposed approach optimizes the nonconvex $\boldsymbol {l_{0}}$ -norm problem directly and can find a better compromise between two or more competing cost function terms automatically. Experimental results on simulated and real hyperspectral data sets demonstrate the effectiveness of the proposed method.

Robust Sparse Hyperspectral Unmixing With $\ell_{2,1}$ Norm

Sparse unmixing (SU) of hyperspectral data have recently received particular attention for analyzing remote sensing images, which aims at finding the optimal subset of signatures to best model the mixed pixel in the scene. However, most SU methods are based on the commonly admitted linear mixing model, which ignores the possible nonlinear effects (i.e., nonlinearity), and the nonlinearity is merely treated as outlier. Besides, the traditional SU algorithms often adopt the $\ell _{2}$ norm loss function, which makes them sensitive to noises and outliers. In this paper, we propose a robust SU (RSU) method with $\ell _{2,1}$ norm loss function, which is robust for noises and outliers. Then, the RSU can be solved by the alternative direction method of multipliers. Finally, the experiments on both synthetic data sets and real hyperspectral images demonstrate that the proposed RSU is efficient for solving the hyperspectral SU problem compared with the state-of-the-art algorithms.

Retrieving the hydrous minerals on Mars by sparse unmixing and the Hapke model using MRO/CRISM data

The hydrous minerals on Mars preserve records of potential past aqueous activity. Quantitative information regarding mineralogical composition would enable a better understanding of the formation processes of these hydrous minerals, and provide unique insights into ancient habitable environments and the geological evolution of Mars. The Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) has the advantage of both a high spatial and spectral resolution, which makes it suitable for the quantitative analysis of minerals on Mars. However, few studies have attempted to quantitatively retrieve the mineralogical composition of hydrous minerals on Mars using visible-infrared (VISIR) hyperspectral data due to their distribution characteristics (relatively low concentrations, located primarily in Noachian terrain, and unclear or unknown background minerals) and limitations of the spectral unmixing algorithms. In this study, we developed a modified sparse unmixing (MSU) method, combining the Hapke model with sparse unmixing. The MSU method considers the nonlinear mixed effects of minerals and avoids the difficulty of determining the spectra and number of endmembers from the image. The proposed method was tested successfully using laboratory mixture spectra and an Airborne Visible Infrared Imaging Spectrometer (AVIRIS) image of the Cuprite site (Nevada, USA). Then it was applied to CRISM hyperspectral images over Gale crater. Areas of hydrous mineral distribution were first identified by spectral features of water and hydroxyl absorption. The MSU method was performed on these areas, and the abundances were retrieved. The results indicated that the hydrous minerals consisted mostly of hydrous silicates, with abundances of up to 35%, as well as hydrous sulfates, with abundances ≤10%. Several main subclasses of hydrous minerals (e.g., Fe/Mg phyllosilicate, prehnite, and kieserite) were retrieved. Among these, Fe/Mg- phyllosilicate was the most abundant, with abundances ranging up to almost 30%, followed by prehnite and kieserite, with abundances lower than 15%. Our results are consistent with related research and in situ analyses of data from the rover Curiosity; thus, our method has the potential to be widely used for quantitative mineralogical mapping at the global scale of the surface of Mars.

A comparative study of signal transformation techniques in automated spectral unmixing of infrared spectra for remote sensing applications

ABSTRACTFrom geological and planetary exploration perspectives, automated sub-pixel classification of hyperspectral data is the most difficult task as it involves blind unmixing with library spectra of minerals. In this study, we demonstrate a procedure involving spectral transformation and linear unmixing to achieve the above task. For this purpose, infrared spectra of rocks from the spectral library, field, and remotely sensed hyperspectral image cube were used. Potential spectra of minerals for unmixing rock spectra were drawn from the library based on similarity of absorption features measured using Pearson correlation coefficient. Eight transformation techniques namely, first derivative, fast Fourier transform, discrete wavelet transform, Hilbert–Huang transform, crude low pass filter, S-transform, binary encoding, spectral effective peak matching, and two sparsity-based techniques (orthogonal matching pursuit, sparse unmixing via variable splitting, and augmented Lagrangian) were evaluated. Subsequently, minerals identified by above techniques were unmixed by linear mixture model (LMM) to decipher mineralogical composition and abundance. Results of LMM achieved using fully constrained least-square-estimation-based quadratic programming optimization approach were evaluated by conventional procedures such as X-ray diffraction and microscopy. In the case of image cube, endmembers derived using minimum noise fraction and pixel purity index were subjected to above procedure. It is evident that the discrete-wavelet-transformation-based approach produced excellent and meaningful results due to its flexibility in scaling the data and capability to handle noisy spectra. It is interesting to note that the adopted procedure could perform sub-pixel classification of image cube automatically and identify predominance of dolomite in limestone and sodium in alunite based on subtle differences in absorption positions.

Sparse Unmixing With Dictionary Pruning for Hyperspectral Change Detection

The localization of changes that occur between the images in a multitemporal series is crucial for many applications, ranging from environmental monitoring to military surveillance. In contrast to traditional change detection methods, unmixing-based change detection has been shown to have the important added benefit of providing subpixel-level information on the nature of the changes, instead of only providing the location of the changes. Recently, sparse unmixing has also been introduced to hyperspectral change detection, resulting in a method that circumvents the drawbacks of regular spectral unmixing approaches. Sparse unmixing-based change detection reveals the changes that occur in a multitemporal series, at subpixel level, and in terms of the library spectra and their sparse abundances, and provides enhanced change detection performance, especially when subpixel-level changes have occurred. However, sparse unmixing is generally an ill-conditioned and time-consuming process, especially as the size of the utilized spectral library increases. In this paper, dictionary pruning is exploited for the first time for hyperspectral change detection using sparse unmixing, in order to alleviate the ill-conditioning of the problem and achieve decreased computation times and enhanced change detection performance. Experimental results on both realistic synthetic and real datasets are used to validate the proposed approach.