Hyperspectral Image Unmixing via Alternating Projected Subgradients

Zymnis, A.; Kim, S.-J.; Skaf, Joëlle; Parente, M.; Boyd, Stephen

doi:10.1109/acssc.2007.4487406

Cited by 49 publications

(53 citation statements)

References 15 publications

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“…Moreover, every limit point of {( , )} A S ( ) ( ) k k k is a stationary point of (42) under some fairly mild assumptions [75], [76]. For practical reasons, most algorithms use cheap but inexact updates for (46a) and (46b), e.g., multiplicative update [71], one-step projected gradient or subgradient update [60], [69], [72], and one-step majorization minimization [74]. Convergence to a stationary point of these inexact AO methods has still to be thoroughly analyzed.…”

Section: Nonnegative Matrix Factorizationmentioning

confidence: 99%

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

Bioucas-Dias

Chan

et al. 2014

IEEE Signal Process. Mag.

411

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%

“…Following the same spirit, L / 1 2 -NMF [71] uses a nonconvex, but stronger sparsity-promoting regularizer based on the / 1 2 , quasinorm. Apart from sparsity, exploitation of spatial contextual information via TV regularization may also be used [72].…”

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.

411

322

View full text Add to dashboard Cite

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“…2, this now works well because the user-defined step is fixed and small. A simple and fast algorithm for projecting onto the probability simplex 52 was utilized. It is also necessary to project xðrÞ onto its own constraint (xðrÞ 2 ½0; 1) after each step.…”

mentioning

confidence: 99%

Modeling diffusion‐weighted MRI as a spatially variant Gaussian mixture: Application to image denoising

Iglesias¹,

Thompson²,

Zhao

et al. 2011

Medical Physics

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Purpose: This work describes a spatially variant mixture model constrained by a Markov random field to model high angular resolution diffusion imaging (HARDI) data. Mixture models suit HARDI well because the attenuation by diffusion is inherently a mixture. The goal is to create a general model that can be used in different applications. This study focuses on image denoising and segmentation (primarily the former). Methods: HARDI signal attenuation data are used to train a Gaussian mixture model in which the mean vectors and covariance matrices are assumed to be independent of spatial locations, whereas the mixture weights are allowed to vary at different lattice positions. Spatial smoothness of the data is ensured by imposing a Markov random field prior on the mixture weights. The model is trained in an unsupervised fashion using the expectation maximization algorithm. The number of mixture components is determined using the minimum message length criterion from information theory. Once the model has been trained, it can be fitted to a noisy diffusion MRI volume by maximizing the posterior probability of the underlying noiseless data in a Bayesian framework, recovering a denoised version of the image. Moreover, the fitted probability maps of the mixture components can be used as features for posterior image segmentation. Results: The model-based denoising algorithm proposed here was compared on real data with three other approaches that are commonly used in the literature: Gaussian filtering, anisotropic diffusion, and Rician-adapted nonlocal means. The comparison shows that, at low signal-to-noise ratio, when these methods falter, our algorithm considerably outperforms them. When tractography is performed on the model-fitted data rather than on the noisy measurements, the quality of the output improves substantially. Finally, ventricle and caudate nucleus segmentation experiments also show the potential usefulness of the mixture probability maps for classification tasks. Conclusions: The presented spatially variant mixture model for diffusion MRI provides excellent denoising results at low signal-to-noise ratios. This makes it possible to restore data acquired with a fast (i.e., noisy) pulse sequence to acceptable noise levels. This is the case in diffusion MRI, where a large number of diffusion-weighted volumes have to be acquired under clinical time constraints.

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“…At the level of underlying mathematics, a similar problem appears in material classification and recognition from hyperspectral images [5]. Some remarkable results on hyperspectral unmixing are the Alternating Projected Subgradients [6], the Non-negative Least-correlated Component Analysis (nLCA) [7], the Non-negative Matrix Factorization Minimum Volume Transform (NMF-MVT) [8], the Minimal Volume Simplex Analysis (MVSA) [9] and the Minimal Volume Enclosed Simplex (MVES) [10]. The MVSA algorithm is outstanding in terms of computational time and efficiency [10], [11].…”

Section: Introductionmentioning

confidence: 99%

Minimal Volume Simplex (MVS) approach for convex hull generation in TP Model Transformation

Kuti

Galambos

Bárányi

2014

IEEE 18th International Conference on Intelligent Engineering Systems INES 2014

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Abstract-To a large degree, systems and control applications of TP Model Transformation rely on convex hull manipulation of polytopic LPV/qLPV system models. In this respect, the creation of tight convex hulls is an especially challenging problem, as it requires complex nonlinear optimisation. By defining the Minimal Volume Simplex (MVS) type hull, the paper presents a novel approach for tight convex hull generation. The approach, which involves the so-called MVSA algorithm, leads to a radical reduction in computational time while showing improved numerical properties in terms of repeatability and reliability as compared to other hull generation methods. Furthermore, the proposed method allows for the taking into account of special design considerations regarding the alignment of the convex hull.

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Hyperspectral Image Unmixing via Alternating Projected Subgradients

Cited by 49 publications

References 15 publications

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

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

Modeling diffusion‐weighted MRI as a spatially variant Gaussian mixture: Application to image denoising

Minimal Volume Simplex (MVS) approach for convex hull generation in TP Model Transformation

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