Results 1  10
of
15
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 ..."
Abstract

Cited by 16 (5 self)
 Add to MetaCart
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. MOTIVATION FOR NONLINEAR MODELS Spectral unmixing (SU) is widely used for analyzing hyperspectral data arising in areas such as: remote sensing, planetary science chemometrics, materials science and other areas of microspectroscopy. SU provides a comprehensive
Blind Separation of QuasiStationary Sources: Exploiting Convex Geometry in Covariance Domain
"... Abstract—This paper revisits blind source separation of instantaneously mixed quasistationary sources (BSSQSS), motivated by the observation that in certain applications (e.g., speech) there exist time frames during which only one source is active, or locally dominant. Combined with nonnegativity ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
Abstract—This paper revisits blind source separation of instantaneously mixed quasistationary sources (BSSQSS), motivated by the observation that in certain applications (e.g., speech) there exist time frames during which only one source is active, or locally dominant. Combined with nonnegativity of source powers, this endows the problem with a nice convex geometry that enables elegant and efficient BSS solutions. Local dominance is tantamount to the socalled pure pixel/separability assumption in hyperspectral unmixing/nonnegative matrix factorization, respectively. Building on this link, a very simple algorithm called successive projection algorithm (SPA) is considered for estimating the mixing system in closed form. To complement SPA in the specific BSSQSS context, an algebraic preprocessing procedure is proposed to suppress shortterm source crosscorrelation interference. The proposed procedure is simple, effective, and supported by theoretical analysis. Solutions based on volume minimization (VolMin) are also considered. By theoretical analysis, it is shown that VolMin guarantees perfect mixing system identifiability under an assumption more relaxed than (exact) local dominance—which means wider applicability in practice. Exploiting the specific structure of BSSQSS, a fast VolMin algorithm is proposed for the overdetermined case. Careful simulations using real speech sources showcase the simplicity, efficiency, and accuracy of the proposed algorithms. Index Terms—Blind source separation, local dominance, purepixel, separability, volume minimization, identifiability, speech, audio. I.
A Vavasis, “Semidefinite programming based preconditioning for more robust nearseparable nonnegative matrix factorization,” arXiv preprint arXiv:1310.2273
, 2013
"... ar ..."
(Show Context)
Hierarchical Clustering of Hyperspectral Images Using RankTwo Nonnegative Matrix Factorization
 IEEE, Transactions on Geoscience and Remote Sensing
, 2015
"... In this paper, we design a hierarchical clustering algorithm for highresolution hyperspectral images. At the core of the algorithm, a new ranktwo nonnegative matrix factorizations (NMF) algorithm is used to split the clusters, which is motivated by convex geometry concepts. The method starts with ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
(Show Context)
In this paper, we design a hierarchical clustering algorithm for highresolution hyperspectral images. At the core of the algorithm, a new ranktwo nonnegative matrix factorizations (NMF) algorithm is used to split the clusters, which is motivated by convex geometry concepts. The method starts with a single cluster containing all pixels, and, at each step, (i) selects a cluster in such a way that the error at the next step is minimized, and (ii) splits the selected cluster into two disjoint clusters using ranktwo NMF in such a way that the clusters are well balanced and stable. The proposed method can also be used as an endmember extraction algorithm in the presence of pure pixels. The effectiveness of this approach is illustrated on several synthetic and realworld hyperspectral images, and shown to outperform standard clustering techniques such as kmeans, spherical kmeans and standard NMF.
SelfDictionary Sparse Regression for Hyperspectral Unmixing: Greedy Pursuit and Pure Pixel Search Are Related
"... Abstract—This paper considers a recently emerged hyperspectral unmixing formulation based on sparse regression of a selfdictionary multiple measurement vector (SDMMV) model, wherein the measured hyperspectral pixels are used as the dictionary. Operating under the pure pixel assumption, this SD ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract—This paper considers a recently emerged hyperspectral unmixing formulation based on sparse regression of a selfdictionary multiple measurement vector (SDMMV) model, wherein the measured hyperspectral pixels are used as the dictionary. Operating under the pure pixel assumption, this SDMMV formalism is special in that it allows simultaneous identification of the endmember spectral signatures and the number of endmembers. Previous SDMMV studies mainly focus on convex relaxations. In this study, we explore the alternative of greedy pursuit, which generally provides efficient and simple algorithms. In particular, we design a greedy SDMMV algorithm using simultaneous orthogonal matching pursuit. Intriguingly, the proposed greedy algorithm is shown to be closely related to some existing pure pixel search algorithms, especially, the successive projection algorithm (SPA). Thus, a link between SDMMV and pure pixel search is revealed. We then perform exact recovery analyses, and prove that the proposed greedy algorithm is robust to noiseincluding its identification of the (unknown) number of endmembersunder a sufficiently low noise level. The identification performance of the proposed greedy algorithm is demonstrated through both synthetic and realdata experiments. Index Terms—Greedy pursuit, hyperspectral unmixing, number of endmembers estimation, selfdictionary sparse regression.
Urban Modelling: Algorithms
, 1976
"... OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.
Successive Nonnegative Projection Algorithm for Robust Nonnegative Blind Source Separation
"... ar ..."
(Show Context)
HYPERSPECTRAL SUPERRESOLUTION OF LOCALLY LOW RANK IMAGES FROM COMPLEMENTARY MULTISOURCE DATA
, 2014
"... Remote sensing hyperspectral images (HSI) are quite often locally low rank, in the sense that the spectral vectors acquired from a given spatial neighborhood belong to a low dimensional subspace/manifold. This has been recently exploited for the fusion of low spatial resolution HSI with high spatial ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Remote sensing hyperspectral images (HSI) are quite often locally low rank, in the sense that the spectral vectors acquired from a given spatial neighborhood belong to a low dimensional subspace/manifold. This has been recently exploited for the fusion of low spatial resolution HSI with high spatial resolution multispectral images (MSI) in order to obtain superresolution HSI. Most approaches adopt an unmixing or a matrix factorization perspective. The derived methods have led to stateoftheart results when the spectral information lies in a low dimensional subspace/manifold. However, if the subspace/manifold dimensionality spanned by the complete data set is large, the performance of these methods decrease mainly because the underlying sparse regression is severely illposed. In this paper, we propose a local approach to cope with this difficulty. Fundamentally, we exploit the fact that real world HSI are locally low rank, to partition the image into patches and solve the data fusion problem independently for each patch. This way, in each patch the subspace/manifold dimensionality is low enough to obtain useful superresolution. We explore two alternatives to define the local regions, using sliding windows and binary partition trees. The effectiveness of the proposed approach is illustrated with synthetic and semireal data. 1
IEEE SIGNAL PROCESSING MAGAZINE [82] JANUARY 2014 10535888/14/$31.00©2014IEEE Digital Object Identifier 10.1109/MSP.2013.2279274
, 2013
"... hen 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 ..."
Abstract
 Add to MetaCart
hen 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 article, we present an overview of recent advances in nonlinear unmixing modeling. MOTIVATION FOR NONLINEAR MODELS Spectral unmixing (SU) is widely used for analyzing hyperspectral data arising in areas such as remote sensing, planetary science chemometrics, materials science, and other areas of microspectroscopy. SU provides a comprehensive and quantitative mapping of the elementary materials that are present in the acquired data. More precisely, SU can identify the spectral signatures of these materials (usually called endmembers) and can estimate their relative contributions (known as abundances) to the measured spectra. Similar to other blind source separation tasks, the SU problem is naturally ill posed and admits a wide range of admissible solutions. As a consequence, SU is a challenging problem that has received considerable attention in the remote sensing, signal, and image processing communities [1]. Hyperspectral data analysis can be supervised, when the endmembers are known, or unsupervised, when they are unknown. Irrespective of the case, W
Principled NeuroFunctional Connectivity Discovery
"... How can we reverseengineer the brain connectivity, given the input stimulus, and the corresponding brainactivity measurements, for several experiments? We show how to solve the problem in a principled way, modeling the brain as a linear dynamical system (LDS), and solving the resulting “syste ..."
Abstract
 Add to MetaCart
(Show Context)
How can we reverseengineer the brain connectivity, given the input stimulus, and the corresponding brainactivity measurements, for several experiments? We show how to solve the problem in a principled way, modeling the brain as a linear dynamical system (LDS), and solving the resulting “system identification ” problem after imposing sparsity and nonnegativity constraints on the appropriate matrices. These are reasonable assumptions in some applications, including magnetoencephalography (MEG). There are three contributions: (a) Proof: We prove that this simple condition resolves the ambiguity of similarity transformation in the LDS identification problem; (b) Algorithm: we propose an effective algorithm which further induces sparse connectivity in a principled way; and (c) Validation: our experiments on semisynthetic (C. elegans), as well as real MEG data, show that our method recovers the neural connectivity, and it leads to interpretable results. 1