Results 11  20
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100
An EmpiricalBayes Approach to Recovering Linearly Constrained NonNegative Sparse Signals
"... Abstract—We 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 (6 self)
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Abstract—We 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. 1 I.
A robust test for nonlinear mixture detection in hyperspectral images
 in Proc. IEEE Int. Conf. Acoust., Speech, and Signal Processing (ICASSP
, 2013
"... This paper studies a pixel by pixel nonlinearity detector for hyperspectral image analysis. The reflectances of linearly mixed pixels are assumed to be a linear combination of known pure spectral components (endmembers) contaminated by additive white Gaussian noise. Nonlinear mixing, however, is not ..."
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Cited by 7 (2 self)
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This paper studies a pixel by pixel nonlinearity detector for hyperspectral image analysis. The reflectances of linearly mixed pixels are assumed to be a linear combination of known pure spectral components (endmembers) contaminated by additive white Gaussian noise. Nonlinear mixing, however, is not restricted to any prescribed nonlinear mixing model. The mixing coefficients (abundances) satisfy the physically motivated sumtoone and positivity constraints. The proposed detection strategy considers the distance between an observed pixel and the hyperplane spanned by the endmembers to decide whether that pixel satisfies the linear mixing model (null hypothesis) or results from a more general nonlinear mixture (alternative hypothesis). The distribution of this distance is derived under the two hypotheses. Closedform expressions are then obtained for the probabilities of false alarm and detection as functions of the test threshold. The proposed detector is compared to another nonlinearity detector recently investigated in the literature through simulations using synthetic data. It is also applied to a real hyperspectral image. Index Terms — Nonlinearity detection, Hyperspectral images, Linear mixing model.
Greedy algorithms for pure pixels identification in hyperspectral unmixing: A multiplemeasurement vector viewpoint
 in Proc. EUSIPCO’13
"... This paper studies a multiplemeasurement vector (MMV)based sparse regression approach to blind hyperspectral unmixing. In general, sparse regression requires a dictionary. The considered approach uses the measured hyperspectral data as the dictionary, thereby intending to represent the whole meas ..."
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Cited by 6 (3 self)
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This paper studies a multiplemeasurement vector (MMV)based sparse regression approach to blind hyperspectral unmixing. In general, sparse regression requires a dictionary. The considered approach uses the measured hyperspectral data as the dictionary, thereby intending to represent the whole measured data using the fewest number of measured hyperspectral vectors. We tackle this selfdictionary MMV (SDMMV) approach using greedy pursuit. It is shown that the resulting greedy algorithms are identical or very similar to some representative pure pixels identification algorithms, such as vertex component analysis. Hence, our study provides a new dimension on understanding and interpreting pure pixels identification methods. We also prove that in the noiseless case, the greedy SDMMV algorithms guarantee perfect identification of pure pixels when the pure pixel assumption holds. 1.
Estimating abundance fractions of materials in hyperspectral images by fitting a postnonlinear mixing model
 in Proc. IEEE WHISPERS
, 2013
"... Within the area of hyperspectral data processing, nonlinear unmixing techniques have emerged as promising alternatives for overcoming the limitations of linear methods. In this paper, we consider the class of postnonlinear mixing models of the partially linear form. More precisely, these composite ..."
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Cited by 6 (3 self)
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Within the area of hyperspectral data processing, nonlinear unmixing techniques have emerged as promising alternatives for overcoming the limitations of linear methods. In this paper, we consider the class of postnonlinear mixing models of the partially linear form. More precisely, these composite models consist of a linear mixing part and a nonlinear fluctuation term defined in a reproducing kernel Hilbert space, both terms being parameterized by the endmember spectral signatures and their respective abundances. These models consider that the reproducing kernel may also depend advantageously on the fractional abundances. An iterative algorithm is then derived to jointly estimate the fractional abundances and to infer the nonlinear functional term. Index Terms — Nonlinear unmixing, postnonlinear mixing model, kernel methods, hyperspectral data processing
The why and how of nonnegative matrix factorization
 Regularization, Optimization, Kernels, and Support Vector Machines. Chapman & Hall/CRC
, 2014
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Hyperspectral image unmixing via bilinear generalized approximate message passing
 Proc. SPIE
, 2013
"... In hyperspectral unmixing, the objective is to decompose an electromagnetic spectral dataset measured over M spectral bands and T pixels, into N constituent material spectra (or “endmembers”) with corresponding spatial abundances. In this paper, we propose a novel approach to hyperspectral unmixing ..."
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Cited by 5 (3 self)
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In hyperspectral unmixing, the objective is to decompose an electromagnetic spectral dataset measured over M spectral bands and T pixels, into N constituent material spectra (or “endmembers”) with corresponding spatial abundances. In this paper, we propose a novel approach to hyperspectral unmixing (i.e., joint estimation of endmembers and abundances) based on loopy belief propagation. In particular, we employ the bilinear generalized approximate message passing algorithm (BiGAMP), a recently proposed beliefpropagationbased approach to matrix factorization, in a “turbo ” framework that enables the exploitation of spectral coherence in the endmembers, as well as spatial coherence in the abundances. In conjunction, we propose an expectationmaximization (EM) technique that can be used to automatically tune the prior statistics assumed by turbo BiGAMP. Numerical experiments on synthetic and realworld data confirm the stateoftheart performance of our approach.
SUPERVISED NONLINEAR UNMIXING OF HYPERSPECTRAL IMAGES USING A PREIMAGE METHODS
"... Abstract. Spectral unmixing is an important issue to analyze remotely sensed hyperspectral data. This involves the decomposition of each mixed pixel into its pure endmember spectra, and the estimation of the abundance value for each endmember. Although linear mixture models are often considered beca ..."
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Cited by 5 (1 self)
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Abstract. Spectral unmixing is an important issue to analyze remotely sensed hyperspectral data. This involves the decomposition of each mixed pixel into its pure endmember spectra, and the estimation of the abundance value for each endmember. Although linear mixture models are often considered because of their simplicity, there are many situations in which they can be advantageously replaced by nonlinear mixture models. In this chapter, we derive a supervised kernelbased unmixing method that relies on a preimage problemsolving technique. The kernel selection problem is also briefly considered. We show that partiallylinear kernels can serve as an appropriate solution, and the nonlinear part of the kernel can be advantageously designed with manifoldlearningbased techniques. Finally, we incorporate spatial information into our method in order to improve unmixing performance. 1
Hyperspectral data geometrybased estimation of number of endmembers using pnormbased pure pixel identification algorithm
 IEEE Trans. Geosci. Remote Sens
, 2013
"... Abstract—Hyperspectral endmember extraction is a process to estimate endmember signatures from the hyperspectral observations, in an attempt to study the underlying mineral composition of a landscape. However, estimating the number of endmembers, which is usually assumed to be known a priori in mos ..."
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Cited by 4 (1 self)
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Abstract—Hyperspectral endmember extraction is a process to estimate endmember signatures from the hyperspectral observations, in an attempt to study the underlying mineral composition of a landscape. However, estimating the number of endmembers, which is usually assumed to be known a priori in most endmember estimation algorithms (EEAs), still remains a challenging task. In this paper, assuming hyperspectral linear mixing model, we propose a hyperspectral data geometrybased approach for estimating the number of endmembers by utilizing successive endmember estimation strategy of an EEA. The approach is fulfilled by two novel algorithms, namely geometrybased estimation of number of endmembers—convex hull (GENECH) algorithm and affine hull (GENEAH) algorithm. The GENECH and GENEAH algorithms are based on the fact that all the observed pixel vectors lie in the convex hull and affine hull of the endmember signatures,
A Method for Finding Structured Sparse Solutions to Nonnegative Least Squares Problems with Applications
 SIAM J. Imaging Sciences
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