Minimum Volume Simplex Analysis Research Articles

Improved minimum volume simplex analysis algorithm for unmixing of hyperspectral data

Some of the robust and high-ability processing methods like the improved Minimum Simplex Volume Analysis (MVSA) algorithm are generally time-consuming in hyperspectral data dealing especially the ground resolution is higher. In this research, MVSA was conducted for spectral analysis of HyMap and Hyperion data after a proposed data reduction to overcome the mentioned problem. The data cloud was therefore clustered based on the spectral angle mapper and Multi-Attribute Decision Making (MADM) based methods were used to determine the best threshold angle. Consequently, four indicators were applied as evaluation attributes for selecting the appropriate alternative, and “Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)” and “ELimination Et Choice Translating REality (ELECTRE)” were employed to finalize the decision. The methods resulted in 0.8 and 1.3 degrees as optimal spectral angles for HyMap and Hyperion, respectively. In this case, the image processing computational burden and the noise effect were considerably alleviated and the procedure led to accurate endmember identification.

Quantitative analysis of mixed pigments for Chinese paintings using the improved method of ratio spectra derivative spectrophotometry based on mode

BackgroundMixed pigment analysis is an important and complex subject in preserving and restoring Chinese paintings since the colors observed by our naked eyes or instruments such as hyperspectral cameras are usually a mixture of several kinds of pigments. The purpose of this study was to explore a more effective method to confirm the type of every pure pigment and their proportion in pigment mixtures on the surface of paintings.MethodsTwo endmember extraction algorithms were adopted to identify the types of pigments and an improved method of ratio spectra derivative spectrophotometry was used to determine their proportion.Main works(1) Extracting the pure pigment components from mixed spectrum by adopting two blind source separation algorithms: Independent Component Analysis and Non-negative Matrix Factorization; (2) matching the separated pure spectrum with the pigment spectral library built in our laboratory to determine the pigment type; and (3) calculating the proportions of mixed pigments using the Ratio Spectra Derivative Spectrophotometry based on Mode, which is improved based on the original algorithm. Finally, a comparison was made with two abundance inversion algorithms: Least Squares Algorithm and Minimum Volume Simplex Analysis. The correlation coefficient and root mean square error were used to provide evidence for accuracy evaluation.Conclusions(1) Non-negative matrix factorization is more suitable for endmember extraction; and (2) Ratio spectra derivative spectrophotometry based on mode is more suitable for abundance inversion.

Endmember Extraction From Highly Mixed Data Using Linear Mixture Model Constrained Particle Swarm Optimization

Spectral unmixing is one of the most important techniques for analyzing hyperspectral images. Many of the hyperspectral unmixing algorithms developed in recent years have been developed under an assumption that pure pixels exist, and some algorithms, such as N-finder algorithm (N-FINDR) and vertex component analysis (VCA), can only search data points in this case. However, the pure-pixel assumption may be seriously violated for highly mixed data. Whether a pure pixel exists or not, the endmember extraction can be regarded as an optimization problem. In this paper, we incorporate the linear mixture model (LMM) and particle swarm optimization (PSO) to develop LMM constrained PSO (LMMC-PSO) for endmember extraction from highly mixed data. The main contribution of the proposed method is that we redefine the particle motion rules. Each particle in LMMC-PSO moves in the search space according to the LMM, rather than with a velocity. The LMM is one kind of relationship between endmembers and mixed pixels, which can help guide efforts to build a path from mixed pixels to endmembers in PSO. The proposed algorithm was tested and evaluated with both synthetic and real hyperspectral data sets. The experimental results indicated that the proposed method obtains better results with highly mixed data than the algorithms of VCA, minimum volume constrained nonnegative matrix factorization, minimum volume simplex analysis (MVSA), robust MVSA, the convex analysis-based minimum volume enclosing simplex, and simplex identification via variable splitting and augmented Lagrangian.

Robust Minimum Volume Simplex Analysis for Hyperspectral Unmixing

Most blind hyperspectral unmixing methods exploit convex geometry properties of hyperspectral data. The minimum volume simplex analysis (MVSA) is one of such methods, which, as many others, estimates the minimum volume (MV) simplex where the measured vectors live. MVSA was conceived to circumvent the matrix factorization step often implemented by MV-based algorithms and also to cope with outliers, which compromise the results produced by MV algorithms. Inspired by the recently proposed robust MV enclosing simplex (RMVES) algorithm, we herein introduce the robust MVSA (RMVSA), which is a version of MVSA robust to noise. As in RMVES, the robustness is achieved by employing chance constraints, which control the volume of the resulting simplex. RMVSA differs, however, substantially from RMVES in the way optimization is carried out. In this paper, we develop a linearization relaxation of the nonlinear chance constraints, which can greatly lighten the computational complex of chance constraint problems. The effectiveness of RMVSA is illustrated by comparing its performance with the state of the art.

Analysis of electron energy loss spectroscopy data using geometric extraction methods

A set of geometric data decomposition methods is discussed. In particular, randomized vertex component analysis (RVCA), an extension of vertex component analysis (VCA) for the application to noisy data, is established. Minimum volume simplex analysis (MVSA), a recent technique for the extraction of endmembers in the absence of pure pixels, is presented. A comparison between MVSA and the previously presented technique of Bayesian Linear Unmixing (BLU) is drawn. Lastly, the efficiency of these methods for high-dimensional data is examined. Improvement on the extracted source components spectral signatures are achieved by establishing Gaussian mixture modeling as extraction technique.

COMPRESSIVE SAMPLING MULTISPECTRAL IMAGING AND UNMIXING METHOD FOR FLUORESCENT IMAGING

Multispectral imaging is an important tool for understanding composite materials in many disciplines. Spectral unmixing enables the determination of individual fluorophore distributions. Due to the dispersive nature of biomaterials the observed spectra of fluorescent dyes is unknown. Spectral unmixing can be accomplished for unknown endmember spectra using minimum volume simplex analysis (MVSA). Compressive sampling (CS) is a method to reduce the computational cost of operating on sparse data sets and can be performed efficiently using NESTA based on Nesterov’s algorithm. Here we demonstrate that NESTA and MVSA can be combined with a denoising threshold to create a compressive sampling and multispectral unmixing (CSMIU) method that enables efficient bioimaging and unmixing with high levels of accuracy (spectral angle distances (SADs) < 0.05). This CSMIU method may potentially enable broadband and in vivo bioimaging modalities. © 2016, Electromagnetics Academy. All rights reserved.

Minimum Volume Simplex Analysis: A Fast Algorithm for Linear Hyperspectral Unmixing

Linear spectral unmixing aims at estimating the number of pure spectral substances, also called endmembers , their spectral signatures, and their abundance fractions in remotely sensed hyperspectral images. This paper describes a method for unsupervised hyperspectral unmixing called minimum volume simplex analysis (MVSA) and introduces a new computationally efficient implementation. MVSA approaches hyperspectral unmixing by fitting a minimum volume simplex to the hyperspectral data, constraining the abundance fractions to belong to the probability simplex. The resulting optimization problem, which is computationally complex, is solved in this paper by implementing a sequence of quadratically constrained subproblems using the interior point method, which is particularly effective from the computational viewpoint. The proposed implementation (available online: www.lx.it.pt/%7ejun/DemoMVSA.zip) is shown to exhibit state-of-the-art performance not only in terms of unmixing accuracy, particularly in nonpure pixel scenarios, but also in terms of computational performance. Our experiments have been conducted using both synthetic and real data sets. An important assumption of MVSA is that pure pixels may not be present in the hyperspectral data, thus addressing a common situation in real scenarios which are often dominated by highly mixed pixels. In our experiments, we observe that MVSA yields competitive performance when compared with other available algorithms that work under the nonpure pixel regime. Our results also demonstrate that MVSA is well suited to problems involving a high number of endmembers (i.e., complex scenes) and also for problems involving a high number of pixels (i.e., large scenes).

Measuring and comparing the resolution performance and the extent of rotation ambiguities of some bilinear modeling methods

Bilinear models are often used in the analysis of datasets from spectroscopy and chromatography. Whenever bilinear soft modeling approaches are applied, rotation ambiguities are ubiquitously present and they should be considered. In this work, results obtained by the application of different methods like independent component analysis (ICA), principal component analysis (PCA), and minimum volume simplex analysis (MVSA) are compared with those obtained by multivariate curve resolution (MCR). In order to do this comparison, mutual information (MI), Amari index (AI), and lack-of-fit (lof) parameters are used for the evaluation of the different methods, and the corresponding areas or regions of feasible solutions (AFS) and their boundaries are investigated in each case. The results obtained by the MCR-BANDS method in the calculation of the extension of rotation ambiguities are discussed and compared with those obtained by the FAC-PACK method, which has been recently proposed for the estimation of the whole range of feasible solutions.

Multi-GPU Implementation of the Minimum Volume Simplex Analysis Algorithm for Hyperspectral Unmixing

Spectral unmixing is an important task in remotely sensed hyperspectral data exploitation. The linear mixture model has been widely used to unmix hyperspectral images by identifying a set of pure spectral signatures, called endmembers, and estimating their respective abundances in each pixel of the scene. Several algorithms have been proposed in the recent literature to automatically identify endmembers, even if the original hyperspectral scene does not contain any pure signatures. A popular strategy for endmember identification in highly mixed hyperspectral scenes has been the minimum volume simplex analysis (MVSA), known to be a computationally very expensive algorithm. This algorithm calculates the minimum volume enclosing simplex, as opposed to other algorithms that perform maximum simplex volume analysis (MSVA). The high computational complexity of MVSA, together with its very high memory requirements, has limited its adoption in the hyperspectral imaging community. In this paper, we develop several optimizations to the MVSA algorithm. The main computational task of MVSA is the solution of a quadratic optimization problem with equality and inequality constraints, with the inequality constraints being in the order of the number of pixels multiplied by the number of endmembers. As a result, storing and computing the inequality constraint matrix is highly inefficient. The first optimization presented in this paper uses algebra operations in order to reduce the memory requirements of the algorithm. In the second optimization, we use graphics processing units (GPUs) to effectively solve (in parallel) the quadratic optimization problem involved in the computation of MVSA. In the third optimization, we extend the single GPU implementation to a multi-GPU one, developing a hybrid strategy that distributes the computation while taking advantage of GPU accelerators at each node. The presented optimizations are tested in different analysis scenarios (using both synthetic and real hyperspectral data) and shown to provide state-of-the-art results from the viewpoint of unmixing accuracy and computational performance. The speedup achieved using the full GPU cluster compared to the CPU implementation in tenfold in a real hyperspectral image.

Uniqueness and rotation ambiguities in Multivariate Curve Resolution methods

The presence of rotation ambiguities and unique solutions in Multivariate Curve Resolution (MCR) chemometric methods is discussed in detail. Using recently proposed graphical approaches to display the bands and areas of feasible solutions in a subspace of reduced dimensions, the results obtained by different MCR methods are compared. These results show that in the presence of rotation ambiguities and under a particular set of constraints, the solutions obtained by the different MCR methods can differ among them and also from the true solution depending on initial estimates and on the applied algorithm. In absence of rotational ambiguities, all MCR methods should give the same unique solution which should be equal to the true one. Many of the MCR methods proposed in the literature like MCR-ALS, RFA, MCR-FMIN, or MCR-BANDS are confirmed to give a valid solution within the band or area of feasible solutions. On the contrary, and according to the results of this study, in its present implementation, the minimum volume simplex analysis, MVSA method can give unfeasible solutions when resolving bilinear data systems with more than two components, because it only applies non-negativity constraints to concentration profiles and not to spectral profiles.

Near-Infrared Hyperspectral Unmixing Based on a Minimum Volume Criterion for Fast and Accurate Chemometric Characterization of Counterfeit Tablets

A rapid detection of the nonauthenticity of suspect tablets is a key first step in the fight against pharmaceutical counterfeiting. The chemical characterization of these tablets is the logical next step to evaluate their impact on patient health and help authorities in tracking their source. Hyperspectral unmixing of near-infrared (NIR) image data is an emerging effective technology to infer the number of compounds, their spectral signatures, and the mixing fractions in a given tablet, with a resolution of a few tens of micrometers. In a linear mixing scenario, hyperspectral vectors belong to a simplex whose vertices correspond to the spectra of the compounds present in the sample. SISAL (simplex identification via split augmented Lagrangian), MVSA (minimum volume simplex analysis), and MVES (minimum-volume enclosing simplex) are recent algorithms designed to identify the vertices of the minimum volume simplex containing the spectral vectors and the mixing fractions at each pixel (vector). This work demonstrates the usefulness of these techniques, based on minimum volume criteria, for unmixing NIR hyperspectral data of tablets. The experiments herein reported show that SISAL/MVSA and MVES largely outperform MCR-ALS (multivariate curve resolution-alternating least-squares), which is considered the state-of-the-art in spectral unmixing for analytical chemistry. These experiments are based on synthetic data (studying the effect of noise and the presence/absence of pure pixels) and on a real data set composed of NIR images of counterfeit tablets.