Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin

Hyperspectral Endmember Extraction Techniques

Hyperspectral data processing and analysis mainly plays a vital role in detection, identification, discrimination and estimation of earth surface materials. It involves atmospheric correction, dimensionality reduction, endmember extraction, spectral unmixing and classification phases. One of the ultimate aims of hyperspectral data processing and analysis is to achieve high classification accuracy. The classification accuracy of hyperspectral data most probably depends upon image-derived endmembers. Ideally, an endmember is defined as a spectrally unique, idealized and pure signature of a surface material. Extraction of consistent and desired endmember is one of the important criteria to achieve the high accuracy of hyperspectral data classification and spectral unmixing. Several methods, strategies and algorithms are proposed by various researchers to extract the endmembers from hyperspectral imagery. Most of these techniques and algorithms are significantly dependent on user-defined input parameters, and this issue is subjective because there is no standard specificity about these input parameters. This leads to inconsistencies in overall endmember extraction. To resolve the aforementioned problems, systematic, generic, robust and automated mechanism of endmember extraction is required. This chapter gives and highlights the generic approach of endmember extraction with popular algorithm limitations and challenges

Real-time N-finder processing algorithms for hyperspectral imagery

N-finder algorithm (N-FINDR) is probably one of most popular and widely used algorithms for endmember extraction in hyperspectral imagery. When it comes to practical implementation, four major obstacles need to be overcome. One is the number of endmembers which must be known a priori. A second one is the use of random initial endmembers to initialize N-FINDR, which generally results in different sets of final extracted endmembers. Consequently, the results are inconsistent and not reproducible. A third one is requirement of dimensionality reduction (DR) where different used DR techniques produce different results. Finally yet importantly, it is the very expensive computational cost caused by an exhaustive search for endmembers all together simultaneously. This paper re-designs N-FINDR in a real time processing fashion to cope with these issues. Four versions of Real Time (RT) N-FINDR are developed, RT Iterative N-FINDR (RT IN-FINDR), RT SeQuential N-FINDR (RT SQ N-FINDR), RT Circular N-FINDR, RT SuCcessive N-FINDR (RT SC N-FINDR), each of which has its own merit for implementation. Experimental results demonstrate that real time processing algorithms perform as well as their counterparts with no real-time processing

Manifold learning based spectral unmixing of hyperspectral remote sensing data

Nonlinear mixing effects inherent in hyperspectral data are not properly represented in linear spectral unmixing models. Although direct nonlinear unmixing models provide capability to capture nonlinear phenomena, they are difficult to formulate and the results are not always generalizable. Manifold learning based spectral unmixing accommodates nonlinearity in the data in the feature extraction stage followed by linear mixing, thereby incorporating some characteristics of nonlinearity while retaining advantages of linear unmixing approaches. Since endmember selection is critical to successful spectral unmixing, it is important to select proper endmembers from the manifold space. However, excessive computational burden hinders development of manifolds for large-scale remote sensing datasets. This dissertation addresses issues related to high computational overhead requirements of manifold learning for developing representative manifolds for the spectral unmixing task. Manifold approximations using landmarks are popular for mitigating the computational complexity of manifold learning. A new computationally effective landmark selection method that exploits spatial redundancy in the imagery is proposed. A robust, less costly landmark set with low spectral and spatial redundancy is successfully incorporated with a hybrid manifold which shares properties of both global and local manifolds. While landmark methods reduce computational demand, the resulting manifolds may not represent subtle features of the manifold adequately. Active learning heuristics are introduced to increase the number of landmarks, with the goal of developing more representative manifolds for spectral unmixing. By communicating between the landmark set and the query criteria relative to spectral unmixing, more representative and stable manifolds with less spectrally and spatially redundant landmarks are developed. A new ranking method based on the pixels with locally high spectral variability within image subsets and convex-geometry finds a solution more quickly and precisely. Experiments were conducted to evaluate the proposed methods using the AVIRIS Cuprite hyperspectral reference dataset. A case study of manifold learning based spectral unmixing in agricultural areas is included in the dissertation.Remotely sensed data collected by airborne or spaceborne sensors are utilized to quantify crop residue cover over an extensive area. Although remote sensing indices are popular for characterizing residue amounts, they are not effective with noisy Hyperion data because the effect of residual striping artifacts is amplified in ratios involving band differences. In this case study, spectral unmixing techniques are investigated for estimating crop residue as an alternative approach to empirical models developed using band based indices. The spectral unmixing techniques, and especially the manifold learning approaches, provide more robust, lower RMSE estimates for crop residue cover than the hyperspectral index based method for Hyperion data

A Variable Splitting Augmented Lagrangian Approach to Linear Spectral Unmixing

This paper presents a new linear hyperspectral unmixing method of the minimum volume class, termed \emph{simplex identification via split augmented Lagrangian} (SISAL). Following Craig's seminal ideas, hyperspectral linear unmixing amounts to finding the minimum volume simplex containing the hyperspectral vectors. This is a nonconvex optimization problem with convex constraints. In the proposed approach, the positivity constraints, forcing the spectral vectors to belong to the convex hull of the endmember signatures, are replaced by soft constraints. The obtained problem is solved by a sequence of augmented Lagrangian optimizations. The resulting algorithm is very fast and able so solve problems far beyond the reach of the current state-of-the art algorithms. The effectiveness of SISAL is illustrated with simulated data.Comment: 4 pages, 2 figures. Submitted to "First IEEE GRSS Workshop on Hyperspectral Image and Signal Processing, 2009

Spectral unmixing of 3D data from selective plane ilumination microscopy

The main contribution of this bachelor thesis is the development and implementation of spectral unmixing techniques for Selective plane illumination microscopy (SPIM) images, where the usage of several fluorescent dyes with different spectrums may lead into spectral mixing, complicating the labor of distinguishing each one. In the present work, most common techniques are reviewed and explained in detail, to select afterwards those that are more effective and simple for our purpose. First, an adequate background on spectral mixing is shown, reviewing how spectral images are obtained and how they represent information. Moreover, it is important to understand the mathematical model that represents the physical phenomenon of spectral mixing. The main approach for dealing with the mixture problem in the literature has been linear spectral unmixing, due to its advantages such as ease of implementation and flexibility in different applications. Nonlinear model was discarded in this study because of its high complexity, although nonlinear spectral unmixing may best characterize the resultant mixed spectra, especially endmember distributions where multiple scattering is present. The main goal in this study is the spectral unmixing process, which has been faced firstly understanding the traditional methodology and its phases, being principally: dimensional reduction of the data, endmember extraction and abundance estimation. Several well-known algorithms are described and analyzed for each aim, such as Pixel Purity Index, N-FINDR or Fully Constrained Least Squares (FCLS). On the other hand, a more simple and efficient method is proposed, based on the Linear Mixing Model and the usage of a weight matrix, representing the relationship among the fluorophores in the mixed image. Two manners were checked in order to obtain the weight matrix: one experimentally, extracting intensity values from previous images of each dye alone; and another theoretically, applying values from data sheets. For the development of the spectral unmixing tool, Matlab has been chosen due to its intrinsic advantages like the ease to understand and learn Matlab language or its predefined functions and instructions to work with matrices. Actually, Matlab is practically standard for engineering and science studies in every university.Ingeniería Biomédic

Improving Hyperspectral Subpixel Target Detection Using Hybrid Detection Space

A Hyper-Spectral Image (HSI) has high spectral and low spatial resolution. As a result, most targets exist as subpixels, which pose challenges in target detection. Moreover, limitation of target and background samples always hinders the target detection performance. In this thesis, a hybrid method for subpixel target detection of an HSI using minimal prior knowledge is developed. The Matched Filter (MF) and Adaptive Cosine Estimator (ACE) are two popular algorithms in HSI target detection. They have different advantages in differentiating target from background. In the proposed method, the scores of MF and ACE algorithms are used to construct a hybrid detection space. First, some high abundance target spectra are randomly picked from the scene to perform initial detection to determine the target and background subsets. Then, the reference target spectrum and background covariance matrix are improved iteratively, using the hybrid detection space. As the iterations continue, the reference target spectrum gets closer and closer to the central line that connects the centers of target and background and resulting in noticeable improvement in target detection. Two synthetic datasets and two real datasets are used in the experiments. The results are evaluated based on the mean detection rate, Receiver Operating Characteristic (ROC) curve and observation of the detection results. Compared to traditional MF and ACE algorithms with Reed-Xiaoli Detector (RXD) background covariance matrix estimation, the new method shows much better performance on all four datasets. This method can be applied in environmental monitoring, mineral detection, as well as oceanography and forestry reconnaissance to search for extremely small target distribution in a large scene