PCE: Piecewise Convex Endmember Detection

Zare, Alina; Gader, Paul D.

doi:10.1109/tgrs.2010.2041062

Cited by 81 publications

(27 citation statements)

References 23 publications

(40 reference statements)

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“…It leads to a fundamentally hard optimization problem, although practical solutions based on two-block AO usually offer good performance by experience. Also, we should highlight that the more exciting developments of NMF-based blind HU lie in extensions to scenarios such as nonlinear HU [77], EV [78], and multispectral and hyperspectral data fusion [79]. Such extensions may not be easily achieved in other approaches.…”

Section: Nonnegative Matrix Factorizationmentioning

confidence: 99%

A Signal Processing Perspective on Hyperspectral Unmixing: Insights from Remote Sensing

Bioucas-Dias

Chan

et al. 2014

IEEE Signal Process. Mag.

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410

322

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Blind hyperspectral unmixing (HU), also known as unsupervised HU, is one of the most prominent research topics in signal processing (SP) for hyperspectral remote sensing [1], [2]. Blind HU aims at identifying materials present in a captured scene, as well as their compositions, by using high spectral resolution of hyperspectral images. It is a blind source separation (BSS) problem from a SP viewpoint. Research on this topic started in the 1990s in geoscience and remote sensing [3]- [7], enabled by technological advances in hyperspectral sensing at the time. In recent years, blind HU has attracted much interest from other fields such as SP, machine learning, and optimization, and the subsequent cross-disciplinary research activities have made blind HU a vibrant topic. The resulting impact is not just on remote sensing-blind HU has provided a unique problem scenario that inspired researchers from different fields to devise novel blind SP methods. In fact, one may say that blind HU has established a new branch of BSS approaches not seen in classical BSS studies. In particular, the convex geometry concepts-discovered by early remote sensing researchers through empirical observations [3]- [7] and refined by later research-are elegant and very different from statistical independence-based BSS approaches established in

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Section: Nonnegative Matrix Factorizationmentioning

confidence: 99%

A Signal Processing Perspective on Hyperspectral Unmixing: Insights from Remote Sensing

Bioucas-Dias

Chan

et al. 2014

IEEE Signal Process. Mag.

Self Cite

410

322

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“…The proportion of this model has to satisfy two constraints in the following equations (Nascimento, 2005a), (Manolaskis, 2003a), (Zare, 2010a), , (Heinz, 2001a), (Huck, 2010a):…”

Section: Introductionmentioning

confidence: 99%

Improving Linear Spectral Unmixing Through Local Endmember Detection

Ramak¹,

Zouj²,

Mojaradi

2015

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:There are a considerable number of mixed pixels in remotely sensed images. Different sub-pixel analyses have been recently developed correspondingly. A well-known method is linear spectral unmixing which obtains an abundance of each endmember in a given pixel. This model assumes that each pixel is a linear combination of all endmembers in a scene. This assumption is not correct since each pixel can only be a composition of some surrounding endmembers. Even though, a fully mathematical technique is used for spectral analysis, the output of the model may not represent the physical nature of the objects over the pixel under test. In this regard, this paper proposes a Local Linear Spectral Unmixing which is based on neighbor pixels classes. Having classified the image, using a supervised classifier, it is scanned through a window of an appropriate size. For each pixel at the center of the window, the endmember matrix is formed only based on the majority classes existed in the window. Then the amount of each one is calculated. The LLSU method was evaluated on an AVIRIS data set collected from an agricultural area of northern Indiana. The results of the proposed method demonstrate a significant improvement in comparison with the LSU results. Moreover, due to the dimension reduction of the endmember matrix in this method, the computation time of the LLSU speeds up by three to eight times compared to the conventional Linear Spectral Unmixing method. As a result, the proposed method is efficient over the spectral unmixing tasks.

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“…However, NMF minimizes a nonconvex function with respect to factor matrices leading to local minima solutions. The Bayesian framework, where constraints can be incorporated directly in the problem formulation and any parameter involved modeled as a random variable, opens the door to highly flexible approaches to unmixing [35], [36], [47], [48].…”

Section: Introductionmentioning

confidence: 99%

“…Dirichlet processes have been used in the piecewise convex endmember detection (PCE) [48] algorithm to determine the number of convex regions needed to describe an input hyperspectral image. PCE estimates a set of endmember distributions for each context, rather than a single spectrum.…”

Section: Introductionmentioning

confidence: 99%

Hyperspectral Unmixing Based on Mixtures of Dirichlet Components

Nascimento

Bioucas-Dias

2012

IEEE Trans. Geosci. Remote Sensing

141

102

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Abstract-This paper introduces a new unsupervised hyperspectral unmixing method conceived to linear but highly mixed hyperspectral data sets, in which the simplex of minimum volume, usually estimated by the purely geometrically based algorithms, is far way from the true simplex associated with the endmembers. The proposed method, an extension of our previous studies, resorts to the statistical framework. The abundance fraction prior is a mixture of Dirichlet densities, thus automatically enforcing the constraints on the abundance fractions imposed by the acquisition process, namely, nonnegativity and sum-to-one. A cyclic minimization algorithm is developed where the following are observed: 1) The number of Dirichlet modes is inferred based on the minimum description length principle; 2) a generalized expectation maximization algorithm is derived to infer the model parameters; and 3) a sequence of augmented Lagrangian-based optimizations is used to compute the signatures of the endmembers. Experiments on simulated and real data are presented to show the effectiveness of the proposed algorithm in unmixing problems beyond the reach of the geometrically based state-of-the-art competitors.Index Terms-Augmented Lagrangian method of multipliers, blind hyperspectral unmixing, dependent components, generalized expectation maximization (GEM), minimum description length (MDL), mixtures of Dirichlet densities.

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PCE: Piecewise Convex Endmember Detection

Cited by 81 publications

References 23 publications

A Signal Processing Perspective on Hyperspectral Unmixing: Insights from Remote Sensing

A Signal Processing Perspective on Hyperspectral Unmixing: Insights from Remote Sensing

Improving Linear Spectral Unmixing Through Local Endmember Detection

Hyperspectral Unmixing Based on Mixtures of Dirichlet Components

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