Robust spectral unmixing for anomaly detection

Newstadt, Gregory E.; Hero, Alfred O.; Simmons, Jeff

doi:10.1109/ssp.2014.6884587

Cited by 12 publications

(15 citation statements)

References 6 publications

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“…3) Anomaly model: As in [13], [14], the outliers are assumed to be spatially and spectrally sparse, i.e., for most of the pixels and spectral bands there are no outliers. To model outlier sparsity, we factor each outlier vector as…”

Section: June 14 2017 Draftmentioning

confidence: 99%

“…Different spectral and spatial neighbourhoods can be used in (13). In this paper, we consider a 4-neighbour 2D structure to account for the spatial correlation and a 2-neighbour 1D structure for the spectral dimension.…”

Section: June 14 2017 Draftmentioning

confidence: 99%

“…, a i,j,R ] T contains the abundances of the R endmembers in the pixel (i, j) and r i,j ∈ R L + is a sparse vector that captures anomalies that do not fit the LMM λ i,j = Ma i,j . As explained in [13], [14], these anomalies in the resulting robust LMM can be due to actual outliers/corrupted data, nonlinear spectral mixtures or intrinsic endmember variability over the spectral bands. Note that due to physical considerations the unknown abundance vectors {a i,j } i,j can be assumed to have positive entries.…”

Section: Introductionmentioning

confidence: 99%

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Robust Spectral Unmixing of Sparse Multispectral Lidar Waveforms Using Gamma Markov Random Fields

Altmann

Maccarone

McCarthy

et al. 2017

IEEE Trans. Comput. Imaging

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This paper presents a new Bayesian spectral unmixing algorithm to analyse remote scenes sensed via sparse multispectral Lidar measurements. To a first approximation, in the presence of a target, each Lidar waveform consists of a main peak, whose position depends on the target distance and whose amplitude depends on the wavelength of the laser source considered (i.e, on the target reflectivity). Besides, these temporal responses are usually assumed to be corrupted by Poisson noise in the low photon count regime. When considering multiple wavelengths, it becomes possible to use spectral information in order to identify and quantify the main materials in the scene, in addition to estimation of the Lidar-based range profiles. Due to its anomaly detection capability, the proposed hierarchical Bayesian model, coupled with an efficient Markov chain Monte Carlo algorithm, allows robust estimation of depth images together with abundance and outlier maps associated with the observed 3D scene. The proposed methodology is illustrated via experiments conducted with real multispectral Lidar data acquired in a controlled environment. The results demonstrate the possibility to unmix spectral responses constructed from extremely sparse photon counts (less than 10 photons per pixel and band). 2 Multispectral Lidar, Depth imaging, Robust spectral unmixing, Anomaly detection, Markov Chain Monte Carlo.

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Section: June 14 2017 Draftmentioning

confidence: 99%

Section: June 14 2017 Draftmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust Spectral Unmixing of Sparse Multispectral Lidar Waveforms Using Gamma Markov Random Fields

Altmann

Maccarone

McCarthy

et al. 2017

IEEE Trans. Comput. Imaging

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“…The Bayesian hierarchical linear model (BHLM) with hierarchical noise prior is used in a wide range of applications, including fusion This work was supported by the following projects: MAGELLAN (ANR-14-CE23-0004-01) and ICode blanc. [13], anomaly detection of hyperspectral images [5], channel estimation [14], blind deconvolution [15], segmentation of astronomical times series [16], etc.…”

Section: Introductionmentioning

confidence: 99%

Bayesian lower bounds for dense or sparse (Outlier) noise in the RMT framework

Ollier

Boyer

Korso

et al. 2016

2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM)

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Abstract-Robust estimation is an important and timely research subject. In this paper, we investigate performance lower bounds on the mean-square-error (MSE) of any estimator for the Bayesian linear model, corrupted by a noise distributed according to an i.i.d. Student's t-distribution. This class of prior parametrized by its degree of freedom is relevant to modelize either dense or sparse (accounting for outliers) noise. Using the hierarchical Normal-Gamma representation of the Student's t-distribution, the Van Trees' Bayesian Cramér-Rao bound (BCRB) on the amplitude parameters is derived. Furthermore, the random matrix theory (RMT) framework is assumed, i.e., the number of measurements and the number of unknown parameters grow jointly to infinity with an asymptotic finite ratio. Using some powerful results from the RMT, closed-form expressions of the BCRB are derived and studied. Finally, we propose a framework to fairly compare two models corrupted by noises with different degrees of freedom for a fixed common target signal-to-noise ratio (SNR). In particular, we focus our effort on the comparison of the BCRBs associated with two models corrupted by a sparse noise promoting outliers and a dense (Gaussian) noise, respectively.Index Terms-Bayesian hierarchical linear model, Bayesian Cramér-Rao bound, sparse outlier noise, dense noise, random matrix theory

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“…This class of models for robust linear SU allows for general deviations from the LMM to be handled in blind source separation methods, i.e., nonlinear effects, outliers or possible endmember variability [13]. In [12], spatial and spectral sparsity structures were considered for the additional term since deviations from the LMM can occur in specific regions or spectral bands of the HSI. This is typically the case when outliers are present, but also when nonlinear effects (relief) occurs and when the reflectance of materials present has significant variations in particular spectral ranges (e.g.…”

Section: Introductionmentioning

confidence: 99%

Robust Linear Spectral Unmixing Using Anomaly Detection

Altmann

McLaughlin

Hero

2015

IEEE Trans. Comput. Imaging

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This paper presents a Bayesian algorithm for linear spectral unmixing of hyperspectral images that accounts for anomalies present in the data. The model proposed assumes that the pixel reflectances are linear mixtures of unknown endmembers, corrupted by an additional nonlinear term modelling anomalies and additive Gaussian noise. A Markov random field is used for anomaly detection based on the spatial and spectral structures of the anomalies. This allows outliers to be identified in particular regions and wavelengths of the data cube. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding a joint linear unmixing and anomaly detection algorithm. Simulations conducted with synthetic and real hyperspectral images demonstrate the accuracy of the proposed unmixing and outlier detection strategy for the analysis of hyperspectral images.

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Robust spectral unmixing for anomaly detection

Cited by 12 publications

References 6 publications

Robust Spectral Unmixing of Sparse Multispectral Lidar Waveforms Using Gamma Markov Random Fields

Robust Spectral Unmixing of Sparse Multispectral Lidar Waveforms Using Gamma Markov Random Fields

Bayesian lower bounds for dense or sparse (Outlier) noise in the RMT framework

Robust Linear Spectral Unmixing Using Anomaly Detection

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