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103
ALTERNATING DIRECTION ALGORITHMS FOR CONSTRAINED SPARSE REGRESSION: APPLICATION TO HYPERSPECTRAL UNMIXING
"... Convex optimization problems are common in hyperspectral unmixing. Examples are the constrained least squares (CLS) problem used to compute the fractional abundances in a linear mixture of known spectra, the constrained basis pursuit (CBP) to find sparse (i.e., with a small number of terms) linear m ..."
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Cited by 33 (11 self)
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Convex optimization problems are common in hyperspectral unmixing. Examples are the constrained least squares (CLS) problem used to compute the fractional abundances in a linear mixture of known spectra, the constrained basis pursuit (CBP) to find sparse (i.e., with a small number of terms) linear mixtures of spectra, selected from large libraries, and the constrained basis pursuit denoising (CBPDN), which is a generalization of BP to admit modeling errors. In this paper, we introduce two new algorithms to efficiently solve these optimization problems, based on the alternating direction method of multipliers, a method from the augmented Lagrangian family. The algorithms are termed SUnSAL (sparse unmixing by variable splitting and augmented Lagrangian) and CSUnSAL (constrained SUnSAL). CSUnSAL solves the CBP and CBPDN problems, while SUnSAL solves CLS as well as a more general version thereof, called constrained sparse regression (CSR). CSUnSAL and SUnSAL are shown to outperform offtheshelf methods in terms of speed and accuracy. 1.
Fast and robust recursive algorithms for separable nonnegative matrix factorization. arXiv preprint arXiv:1208.1237
, 2012
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Hyperspectral Remote Sensing Data Analysis and Future Challenges
"... Abstract—Hyperspectral remote sensing ..."
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Nonlinear Unmixing of Hyperspectral Data Based on a LinearMixture/NonlinearFluctuation Model
"... Abstract—Spectral unmixing is an important issue to analyze remotely sensed hyperspectral data. Although the linear mixture model has obvious practical advantages, there are many situations in which it may not be appropriate and could be advantageously replaced by a nonlinear one. In this paper, we ..."
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Cited by 15 (6 self)
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Abstract—Spectral unmixing is an important issue to analyze remotely sensed hyperspectral data. Although the linear mixture model has obvious practical advantages, there are many situations in which it may not be appropriate and could be advantageously replaced by a nonlinear one. In this paper, we formulate a new kernelbased paradigm that relies on the assumption that the mixing mechanism can be described by a linear mixture of endmember spectra, with additive nonlinear fluctuations defined in a reproducing kernel Hilbert space. This family of models has clear interpretation, and allows to take complex interactions of endmembers into account. Extensive experiment results, with both synthetic and real images, illustrate the generality and effectiveness of this scheme compared with stateoftheart methods. Index Terms — Hyperspectral imaging, multikernel learning, nonlinear spectral unmixing, support vector regression.
A signal processing perspective on hyperspectral unmixing: Insights from remote sensing
 IEEE Signal Processing Magazine
, 2014
"... Blind hyperspectral unmixing (HU), also known as unsupervised HU, is one of the most prominent research topics in signal processing for hyperspectral remote sensing [1, 2]. Blind HU aims at identifying materials present in a captured scene, ..."
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Cited by 14 (7 self)
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Blind hyperspectral unmixing (HU), also known as unsupervised HU, is one of the most prominent research topics in signal processing for hyperspectral remote sensing [1, 2]. Blind HU aims at identifying materials present in a captured scene,
R.: Robust nearseparable nonnegative matrix factorization using linear optimization
 Journal of Machine Learning Research
, 2014
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Nonlinear Unmixing of Hyperspectral Images: Models and Algorithms
"... When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid and other nonlinear models need to be considered, for instance, when there are mul ..."
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Cited by 13 (4 self)
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When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid and other nonlinear models need to be considered, for instance, when there are multiscattering effects or intimate interactions. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM. In this paper, we present an overview of recent advances in nonlinear unmixing modeling.
Collaborative Sparse Regression For Hyperspectral Unmixing
 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
, 2013
"... Sparse unmixing has been recently introduced in hyperspectral imaging as a framework to characterize mixed pixels. It assumes that the observed image signatures can be expressed in the form of linear combinations of a number of pure spectral signatures known in advance (e.g., spectra collected on th ..."
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Cited by 11 (4 self)
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Sparse unmixing has been recently introduced in hyperspectral imaging as a framework to characterize mixed pixels. It assumes that the observed image signatures can be expressed in the form of linear combinations of a number of pure spectral signatures known in advance (e.g., spectra collected on the ground by a field spectroradiometer). Unmixing then amounts to finding the optimal subset of signatures in a (potentially very large) spectral library that can best model each mixed pixel in the scene. In this paper, we present a refinement of the sparse unmixing methodology recently introduced which exploits the usual very low number of endmembers present in real images, out of a very large library. Specifically, we adopt the collaborative (also called “multitask” or “simultaneous”) sparse regression framework that improves the unmixing results by solving a joint sparse regression problem, where the sparsity is simultaneously imposed to all pixels in the data set. Our experimental results with both synthetic and real hyperspectral data sets show clearly the advantages obtained using the new joint sparse regression strategy, compared with the pixelwise independent approach.
An empiricalBayes approach to recovering linearly constrained nonnegative sparse signals,”
, 2013
"... AbstractWe consider the recovery of an (approximately) sparse signal from noisy linear measurements, in the case that the signal is apriori known to be nonnegative and obeys certain linear equality constraints. For this, we propose a novel empiricalBayes approach that combines the Generalized App ..."
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Cited by 9 (5 self)
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AbstractWe consider the recovery of an (approximately) sparse signal from noisy linear measurements, in the case that the signal is apriori known to be nonnegative and obeys certain linear equality constraints. For this, we propose a novel empiricalBayes approach that combines the Generalized Approximate Message Passing (GAMP) algorithm with the expectation maximization (EM) algorithm. To enforce both sparsity and nonnegativity, we employ an i.i.d Bernoulli nonnegative Gaussian mixture (NNGM) prior and perform approximate minimum meansquared error (MMSE) recovery of the signal using sumproduct GAMP. To learn the NNGM parameters, we use the EM algorithm with a suitable initialization. Meanwhile, the linear equality constraints are enforced by augmenting GAMP's linear observation model with noiseless pseudomeasurements. Numerical experiments demonstrate the stateofthe art meansquarederror and runtime of our approach.
Nonlinear Spectral Unmixing of Hyperspectral Images Using Gaussian Processes
, 2013
"... This paper presents an unsupervised algorithm for nonlinear unmixing of hyperspectral images. The proposed model assumes that the pixel reflectances result from a nonlinear function of the abundance vectors associated with the pure spectral components. We assume that the spectral signatures of the ..."
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Cited by 7 (5 self)
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This paper presents an unsupervised algorithm for nonlinear unmixing of hyperspectral images. The proposed model assumes that the pixel reflectances result from a nonlinear function of the abundance vectors associated with the pure spectral components. We assume that the spectral signatures of the pure components and the nonlinear function are unknown. The first step of the proposed method estimates the abundance vectors for all the image pixels using a Bayesian approach an a Gaussian process latent variable model for the nonlinear function (relating the abundance vectors to the observations). The end members are subsequently estimated using Gaussian process regression. The performance of the unmixing strategy is first evaluated on synthetic data. The proposed method provides accurate abundance and endmember estimations when compared to other linear and nonlinear unmixing strategies. An interesting property is its robustness to the absence of pure pixels in the image. The analysis of a real hyperspectral image shows results that are in good agreement with state of the art unmixing strategies and with a recent classification method.