Search

Hyperspectral unmixing including endmember extraction and abundance estimation has been investigated successively in recent years due to increasingly hyperspectral processing requirements. As one type of decision after solution paradigm, the multiobjective endmember estimation (MoEE) method is able to obtain a set of Pareto optimal solutions, thus providing a wealth of information to determine the most representative endmembers. In addition, multiobjective optimization methods also have the characteristics of flexible modeling, excellent global convergence, commendable adaptability, and so on. However, the evolutionary algorithms designed for this kind of method generally use little spatial–spectral information of the hyperspectral image. In this article, we delve into the memetic strategy by exploiting the topological structure of hyperspectral data in the high-dimensional space to establish a vertex-directed MoEE method, termed VD-MoEE. According to the frequently used linear mixture model, endmembers of hyperspectral images are generally distributed at the vertices of the hyperspectral data manifold. Therefore, we design a vertex-directed local search operator to guide the search direction of the individuals in evolutionary algorithms. Experimental results on synthetic and real datasets demonstrated that the proposed VD-MOEE is able to achieve appealing performance in terms of solution selection and accuracy in comparison with several classic and state-of-the-art endmember estimation methods. [ABSTRACT FROM AUTHOR]

Independent component analysis (ICA) has been recently applied into hyperspectral unmixing as a result of its low computation time and its ability to perform without prior information. However, when applying ICA for hyperspectral unmixing, the independence assumption in the ICA model conflicts with the abundance sum-to-one constraint and the abundance nonnegative constraint in the linear mixture model, which affects the hyperspectral unmixing accuracy. In this paper, we consider an abundance matrix composed of Np-dimensional variables, and we propose a new hyperspectral unmixing approach with an abundance characteristic-based ICA model. Two characteristics of the abundance variables are explored, and the model is constructed by these characteristics. A corresponding gradient descent algorithm is also proposed to solve the proposed objective function. Both the synthetic and real experimental results demonstrate that the proposed method performs better than the other state-of-the-art methods in abundance and endmember extraction. [ABSTRACT FROM PUBLISHER]

The recently developed theory of compressive sensing (CS) exhibits enormous potentials in signal recovery. In this paper, we investigate its application on spectral unmixing, which appears in hyperspectral data analysis and is usually based on a linear mixture model (LMM) that assumes that a mixed pixel is a linear combination of a set of pure spectral signatures (called endmembers) weighted by their corresponding abundances. Unlike the classical LMM that is a compact representation, we first extend it to a sparse representation (SR) by using a redundant and known endmember set instead of the complete one. Then, the SR model is multiplied by a random Gaussian measurement matrix, so spectral unmixing is casted in the framework of CS. Finally, the ℓ1-minimization algorithms are used to recover the nonnegative abundances by solving the SR model and our proposed model named CS+SR, respectively. Experimental results on both simulated and real hyperspectral data demonstrate that the CS+SR model, formed by multiplying a random Gaussian matrix on the SR model, can improve, at least in the sense of probability, the ability of the ℓ1-minimization algorithms for recovering the nonnegative sparse abundances. [ABSTRACT FROM PUBLISHER]

Sparsity-based unmixing algorithms, exploiting the sparseness property of the abundances, have recently been proposed with promising performances. However, these algorithms are developed for the linear mixture model (LMM), which cannot effectively handle the nonlinear effects. In this paper, we extend the current sparse regression methods for the LMM to bilinear mixture models (BMMs), where the BMMs introduce additional bilinear terms in the LMM in order to model second-order photon scattering effects. To solve the abundance estimation problem for the BMMs, we propose to perform a sparsity-based abundance estimation by using two dictionaries: a linear dictionary containing all the pure endmembers and a bilinear dictionary consisting of all the possible second-order endmember interaction components. Then, the abundance values can be estimated from the sparse codes associated with the linear dictionary. Moreover, to exploit the spatial data structure where the adjacent pixels are usually homogeneous and are often mixtures of the same materials, we first employ the joint-sparsity (row-sparsity) model to enforce structured sparsity on the abundance coefficients. However, the joint-sparsity model is often a strict assumption, which might cause some aliasing artifacts for the pixels that lie on the boundaries of different materials. To deal with this problem, the low-rank-representation model, which seeks the lowest rank representation of the data, is further introduced to better capture the spatial data structure. Our simulation results demonstrate that the proposed algorithms provide much enhanced performance compared with state-of-the-art algorithms. [ABSTRACT FROM PUBLISHER]

In the linear unmixing of hyperspectral images, the observation pixels form a simplex whose vertices correspond to the endmembers, hence finding the endmembers is equivalent to extracting these vertices. A common technique for determining vertices is to analyze the simplex volume, but it usually has a high computational complexity, resulting from the exhaustive searching of volume in the large hyperspectral data. This problem limits the practicability and real-time application. In this paper, we utilize triangular factorization (TF) to calculate the volume, deducing a method named simplex volume analysis based on TF (SVATF). It requires just one comparison through the data to succeed in finding the global optimal solution for all the endmembers, thus improving the searching efficiency. Dimensionality reduction transformation is not necessary, which is another advantage of this method. Moreover, since TF is a broad conception including different methods, SVATF is a framework including various implementations. Based on TF, we also propose a fast learning algorithm named abundance quantification based on TF to estimate the abundances, which further saves the computation by utilizing the intermediate values involved in SVATF. The abundance estimation method can rectify possible errors in the given endmembers by utilizing two important constraints (abundance nonnegative constraint and abundance sum-to-one constraint) of the linear mixture model, so it is useful for the imagery without pure pixels. Experimental results on synthetic and real hyperspectral data demonstrate that the proposed methods can obtain accurate results with much lower computational complexity, with respect to other state-of-the-art methods. [ABSTRACT FROM AUTHOR]