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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]

We propose and analyze a new model for hyperspectral images (HSIs) based on the assumption that the whole signal is composed of a linear combination of few sources, each of which has a specific spectral signature, and that the spatial abundance maps of these sources are themselves piecewise smooth and therefore efficiently encoded via typical sparse models. We derive new sampling schemes exploiting this assumption and give theoretical lower bounds on the number of measurements required to reconstruct HSI data and recover their source model parameters. This allows us to segment HSIs into their source abundance maps directly from compressed measurements. We also propose efficient optimization algorithms and perform extensive experimentation on synthetic and real datasets, which reveals that our approach can be used to encode HSI with far less measurements and computational effort than traditional compressive sensing methods. [ABSTRACT FROM AUTHOR]

Determining the intrinsic dimension of a hyperspectral image is an important step in the spectral unmixing process and under- or overestimation of this number may lead to incorrect unmixing in unsupervised methods. In this paper, we discuss a new method for determining the intrinsic dimension using recent advances in random matrix theory. This method is entirely unsupervised, free from any user-determined parameters and allows spectrally correlated noise in the data. Robustness tests are run on synthetic data, to determine how the results were affected by noise levels, noise variability, noise approximation, and spectral characteristics of the endmembers. Success rates are determined for many different synthetic images, and the method is tested on two pairs of real images, namely a Cuprite scene taken from Airborne Visible InfraRed Imaging Spectrometer (AVIRIS) and SpecTIR sensors, and a Lunar Lakes scene taken from AVIRIS and Hyperion, with good results. [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]

Many methods have been proposed in the literature for estimating the number of materials/endmembers in a hyperspectral image. This is sometimes called the "intrinsic" dimension (ID) of the image. A number of recent papers have proposed ID estimation methods based on various aspects of random matrix theory (RMT), under the assumption that the errors are uncorrelated, but with possibly unequal variances. A recent paper, which reviewed a number of the better known methods (including one RMT-based method), has shown that they are all biased, especially when the true ID is greater than about 20 or 30, even when the error structure is known. I introduce two RMT-based estimators ( R M T G , which is new, and R M T K N , which is a modification of an existing estimator), which are approximately unbiased when the error variances are known. However, they are biased when the error variance is unknown and needs to be estimated. This bias increases as ID increases. I show how this bias can be reduced. The results use semi-realistic simulations based on three real hyperspectral scenes. Despite this, when applied to the real scenes, R M T G and R M T K N are larger than expected. Possible reasons for this are discussed, including the presence of errors which are either deterministic, spectrally and/or spatially correlated, or signal-dependent. Possible future research into ID estimation in the presence of such errors is outlined. [ABSTRACT FROM AUTHOR]