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15
Supervised nonlinear spectral unmixing using a postnonlinear mixing model for hyperspectral imagery
, 2012
"... This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial func ..."
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Cited by 24 (13 self)
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This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial functions leading to a polynomial postnonlinear mixing model. A Bayesian algorithm and optimization methods are proposed to estimate the parameters involved in the model.The performance of the unmixing strategies is evaluated by simulations conducted on synthetic and real data.
Nonlinearity Detection in Hyperspectral Images Using a Polynomial PostNonlinear Mixing Model
, 2013
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Residual component analysis of hyperspectral images  Application to joint nonlinear unmixing and nonlinearity detection
, 2014
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Nonnegative blind source separation by sparse component analysis based on determinant measure
 IEEE Trans. Neural Netw. Learn. Syst
, 2012
"... Abstract — The problem of nonnegative blind source separation (NBSS) is addressed in this paper, where both the sources and the mixing matrix are nonnegative. Because many realworld signals are sparse, we deal with NBSS by sparse component analysis. First, a determinantbased sparseness measure, na ..."
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Cited by 3 (2 self)
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Abstract — The problem of nonnegative blind source separation (NBSS) is addressed in this paper, where both the sources and the mixing matrix are nonnegative. Because many realworld signals are sparse, we deal with NBSS by sparse component analysis. First, a determinantbased sparseness measure, named Dmeasure, is introduced to gauge the temporal and spatial sparseness of signals. Based on this measure, a new NBSS model is derived, and an iterative sparseness maximization (ISM) approach is proposed to solve this model. In the ISM approach, the NBSS problem can be cast into rowtorow optimizations with respect to the unmixing matrix, and then the quadratic programming (QP) technique is used to optimize each row. Furthermore, we analyze the source identifiability and the computational complexity of the proposed ISMQP method. The new method requires relatively weak conditions on the sources and the mixing matrix, has high computational efficiency, and is easy to implement. Simulation results demonstrate the effectiveness of our method. Index Terms — Blind source separation (BSS), determinantbased sparseness measure, nonnegative sources, sparse component analysis. I.
Unsupervised PostNonlinear Unmixing of Hyperspectral Images Using a Hamiltonian Monte Carlo Algorithm
, 2014
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ProjectionPursuitBased Method for Blind Separation of Nonnegative Sources
"... Abstract — This paper presents a projection pursuit (PP) based method for blind separation of nonnegative sources. First, the available observation matrix is mapped to construct a new mixing model, in which the inaccessible source matrix is normalized to be columnsumto1. Then, the PP method is pr ..."
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Abstract — This paper presents a projection pursuit (PP) based method for blind separation of nonnegative sources. First, the available observation matrix is mapped to construct a new mixing model, in which the inaccessible source matrix is normalized to be columnsumto1. Then, the PP method is proposed to solve this new model, where the mixing matrix is estimated column by column through tracing the projections to the mapped observations in specified directions, which leads to the recovery of the sources. The proposed method is much faster than Chan’s method, which has similar assumptions to ours, due to the usage of optimal projection. It is also more advantageous in separating crosscorrelated sources than the independenceand uncorrelationbased methods, as it does not employ any statistical information of the sources. Furthermore, the new method does not require the mixing matrix to be nonnegative. Simulation results demonstrate the superior performance of our method. Index Terms — Blind source separation, linear programming (LP), nonnegative sources, projection pursuit (PP). x, xi NOTATIONS Column vector, the ith element of x. X, x j, xij Matrix, the jth column of X, the(i, j)th entry of X. Xt Matrix with t columns. X(i: j, b: t) A submatrix of X with rows from i to j and columns from b to t. X � A submatrix of X with column index set �. X ⊥ The basis of a subspace orthogonal to X. ℜ Real number set.
BAYESIAN ALGORITHM FOR UNSUPERVISED UNMIXING OF HYPERSPECTRAL IMAGES USING A POSTNONLINEAR MODEL
"... This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are postnonlinear functions of unknown pure spectral components contaminated by an additive white Gaussian noise. The nonlinear effects are approximated by a polynom ..."
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Cited by 1 (1 self)
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This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are postnonlinear functions of unknown pure spectral components contaminated by an additive white Gaussian noise. The nonlinear effects are approximated by a polynomial leading to a polynomial postnonlinear mixing model. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding an unsupervised nonlinear unmixing algorithm. Due to the large number of parameters to be estimated, an efficient constrained Hamiltonian Monte Carlo algorithm is investigated. The performance of the unmixing strategy is finally evaluated on synthetic data. Index Terms — Hyperspectral imagery, unsupervised spectral unmixing, Hamiltonian Monte Carlo, postnonlinear model.
1A Convex Geometry Based Blind Source Separation Method for Separating Nonnegative Sources
"... Abstract—This paper presents a convex geometry (CG) based method for blind separation of nonnegative sources. First, the unaccessible source matrix is normalized to be columnsumtoone by mapping the available observation matrix. Then, its zerosamples are found by searching the facets of the conve ..."
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Abstract—This paper presents a convex geometry (CG) based method for blind separation of nonnegative sources. First, the unaccessible source matrix is normalized to be columnsumtoone by mapping the available observation matrix. Then, its zerosamples are found by searching the facets of the convex hull spanned by the mapped observations. By taken these zerosamples into account, a quadratic cost function with respect to each row of the unmixing matrix, together with a linear constraint in relation to the involved variables, is proposed. Upon which, an algorithm is presented to estimate the unmixing matrix by solving a classical convex optimization problem. Unlike the traditional blind source separation (BSS) methods, the CGbased method does not require the independence assumption, nor the uncorrelation assumption. Compared with the BSS methods that are specifically designed to distinguish between nonnegative sources, the proposed method requires a weaker sparsity condition. Provided simulation results illustrate the performance of our method. Index Terms—Blind source separation, convex geometry, correlated sources, nonnegative sources. I.
ADAPTIVE SPECTRAL UNMIXING FOR HISTOPATHOLOGY FLUORESCENT IMAGES
"... Accurate spectral unmixing of fluorescent images is clinically important because it is one of the key steps in multiplex histopathology image analysis. The narrowband reference spectra for quantum dot biomarkers are often precisely known apriori, while the broadband DAPI (nuclear biomarker) and t ..."
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Accurate spectral unmixing of fluorescent images is clinically important because it is one of the key steps in multiplex histopathology image analysis. The narrowband reference spectra for quantum dot biomarkers are often precisely known apriori, while the broadband DAPI (nuclear biomarker) and tissue autofluorescence reference spectra are tissue dependent and vary from image to image. This paper presents a novel spectral unmixing algorithm based on data adaptive broadband reference spectrum refinement for accurate reference spectra estimation of each image. The algorithm detects nuclear and tissue regions from the DAPI channel in the unmixed images, and estimates the new reference spectra for the biomarkers. A nuclear ranking algorithm is proposed for nuclear region segmentation to achieve more robust and accurate reference spectra estimations for the given image. The proposed framework iteratively updates the broadband reference spectra and unmixes the fluorescent image till convergence. The algorithm was tested on a clinical data set containing a large number of multiplex fluorescent slides and demonstrates better unmixing results than the existing spectral unmixing strategies. Index Terms — fluorescent images, multiplex, quantum dot, DAPI, spectral unmixing, adaptive unmixing 1.
unknown title
, 2014
"... 1Collaborative sparse regression using spatially correlated supports – Application to hyperspectral unmixing ..."
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1Collaborative sparse regression using spatially correlated supports – Application to hyperspectral unmixing