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19
Hyperspectral unmixing overview: Geometrical, statistical, and sparse regressionbased approaches
 IEEE J. SEL. TOPICS APPL. EARTH OBSERV. REMOTE SENS
, 2012
"... Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher sp ..."
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Cited by 103 (34 self)
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Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, illposed
Total Variation Spatial Regularization for Sparse Hyperspectral Unmixing
 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
, 2012
"... Spectral unmixing aims at estimating the fractional abundances of pure spectral signatures (also called endmembers) in each mixed pixel collected by a remote sensing hyperspectral imaging instrument. In recent work, the linear spectral unmixing problem has been approached in semisupervised fashion a ..."
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Cited by 19 (5 self)
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Spectral unmixing aims at estimating the fractional abundances of pure spectral signatures (also called endmembers) in each mixed pixel collected by a remote sensing hyperspectral imaging instrument. In recent work, the linear spectral unmixing problem has been approached in semisupervised fashion as a sparse regression one, under the assumption that the observed image signatures can be expressed as linear combinations of pure spectra, known aprioriand available in a library. It happens, however, that sparse unmixing focuses on analyzing the hyperspectral data without incorporating spatial information. In this paper, we include the total variation (TV) regularization to the classical sparse regression formulation, thus exploiting the spatial– contextual information present in the hyperspectral images and developing a new algorithm called sparse unmixing via variable splitting augmented Lagrangian and TV. Our experimental results, conducted with both simulated and real hyperspectral data sets, indicate the potential of including spatial information (through the TV term) on sparse unmixing formulations for improved characterization of mixed pixels in hyperspectral imagery.
Dictionary Learning for Noisy and Incomplete Hyperspectral Images
, 2011
"... We consider analysis of noisy and incomplete hyperspectral imagery, with the objective of removing the noise and inferring the missing data. The noise statistics may be wavelengthdependent, and the fraction of data missing (at random) may be substantial, including potentially entire bands, offering ..."
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Cited by 14 (4 self)
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We consider analysis of noisy and incomplete hyperspectral imagery, with the objective of removing the noise and inferring the missing data. The noise statistics may be wavelengthdependent, and the fraction of data missing (at random) may be substantial, including potentially entire bands, offering the potential to significantly reduce the quantity of data that need be measured. To achieve this objective, the imagery is divided into contiguous threedimensional (3D) spatiospectral blocks, of spatial dimension much less than the image dimension. It is assumed that each such 3D block may be represented as a linear combination of dictionary elements of the same dimension, plus noise, and the dictionary elements are learned in situ based on the observed data (no a priori training). The number of dictionary elements needed for representation of any particular block is typically small relative to the block dimensions, and all the image blocks are processed jointly (“collaboratively”) to infer the underlying dictionary. We address dictionary learning from a Bayesian perspective, considering two distinct means of imposing sparse dictionary usage. These models allow inference of the number of dictionary elements needed as well as the underlying wavelengthdependent noise statistics. It is demonstrated that drawing the dictionary elements from a Gaussian process prior, imposing structure on the wavelength dependence of the dictionary elements, yields significant advantages, relative to the moreconventional approach of using an i.i.d. Gaussian prior for the dictionary elements; this advantage is particularly evident in the presence of noise. The framework is demonstrated by processing hyperspectral imagery with a significant number of voxels missing uniformly at random, with imagery at specific wavelengths missing entirely, and in the presence of substantial additive noise.
A signal processing perspective on hyperspectral unmixing: Insights from remote sensing
 IEEE Signal Processing Magazine
, 2014
"... Blind hyperspectral unmixing (HU), also known as unsupervised HU, is one of the most prominent research topics in signal processing for hyperspectral remote sensing [1, 2]. Blind HU aims at identifying materials present in a captured scene, ..."
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Cited by 14 (7 self)
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Blind hyperspectral unmixing (HU), also known as unsupervised HU, is one of the most prominent research topics in signal processing for hyperspectral remote sensing [1, 2]. Blind HU aims at identifying materials present in a captured scene,
Interferometric Phase Image Estimation via Sparse Coding in the Complex Domain
, 2013
"... The paper addresses interferometric phase image estimation – that is, the estimation of phase modulo2π images from sinusoidal 2πperiodic and noisy observations. These degradation mechanisms make interferometric phase image estimation a quite challenging problem. We tackle this challenge by reform ..."
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Cited by 4 (2 self)
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The paper addresses interferometric phase image estimation – that is, the estimation of phase modulo2π images from sinusoidal 2πperiodic and noisy observations. These degradation mechanisms make interferometric phase image estimation a quite challenging problem. We tackle this challenge by reformulating the true estimation problem as a sparse regression, often termed sparse coding, in the complex domain. Following the standard procedure in patchbased image restoration, the image is partitioned into small overlapping square patches and the vector corresponding to each patch is modeled as a sparse linear combination of vectors, termed atoms, taken from a set called dictionary. Aiming at optimal sparse representations, and thus at optimal noise removing capabilities, the dictionary is learned from the data it represents via matrix factorization with sparsity constraints on the code (i.e., the regression coefficients) enforced by the ℓ1 norm. The effectiveness of the new sparse coding based approach to interferometric phase estimation, termed SpInPHASE, is illustrated in a series of experiments with simulated and real data where it outperforms the stateoftheart.
Sparsity and structure in hyperspectral imaging
 Sensing, reconstruction, and target detection,” Signal Processing Magazine, IEEE
, 2014
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Spatialaware dictionary learning for hyperspectral image classication
 IEEE Transactions on Medical Imaging
, 2015
"... Abstract—This paper presents a structured dictionarybased model for hyperspectral data that incorporates both spectral and contextual characteristics of a spectral sample, with the goal of hyperspectral image classification. The idea is to partition the pixels of a hyperspectral image into a number ..."
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Cited by 3 (0 self)
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Abstract—This paper presents a structured dictionarybased model for hyperspectral data that incorporates both spectral and contextual characteristics of a spectral sample, with the goal of hyperspectral image classification. The idea is to partition the pixels of a hyperspectral image into a number of spatial neighborhoods called contextual groups and to model each pixel with a linear combination of a few dictionary elements learned from the data. Since pixels inside a contextual group are often made up of the same materials, their linear combinations are constrained to use common elements from the dictionary. To this end, dictionary learning is carried out with a joint sparse regularizer to induce a common sparsity pattern in the sparse coefficients of each contextual group. The sparse coefficients are then used for classification using a linear SVM. Experimental results on a number of real hyperspectral images confirm the effectiveness of the proposed representation for hyperspectral image classification. Moreover, experiments with simulated multispectral data show that the proposed model is capable of finding representations that may effectively be used for classification of multispectralresolution samples. Index Terms—Classification, hyperspectral imagery, dictionary learning, probabilistic joint sparse model, linear support vector machines. I.
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 ..."
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Cited by 1 (1 self)
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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
Title of Document: DETECTION AND CLASSIFICATION OF NONSTATIONARY SIGNALS USING SPARSE REPRESENTATIONS IN ADAPTIVE DICTIONARIES
"... Automatic classification of nonstationary radio frequency (RF) signals is of particular interest in persistent surveillance and remote sensing applications. Such signals are often acquired in noisy, cluttered environments, and may be characterized by complex or unknown analytical models, making fea ..."
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Automatic classification of nonstationary radio frequency (RF) signals is of particular interest in persistent surveillance and remote sensing applications. Such signals are often acquired in noisy, cluttered environments, and may be characterized by complex or unknown analytical models, making feature extraction and classification difficult. This thesis proposes an adaptive classification approach for poorly characterized targets and backgrounds based on sparse representations in nonanalytical dictionaries learned from data. Conventional analytical orthogonal dictionaries, e.g., Short Time Fourier and Wavelet Transforms, can be suboptimal for classification of nonstationary signals, as they provide a rigid tiling of the timefrequency space, and are not specifically designed for a particular signal class. They generally do not lead to sparse decompositions (i.e., with very few nonzero coefficients), and use in classification requires separate feature selection algorithms. Pursuittype decompositions in analytical overcomplete (nonorthogonal) dictionaries yield sparse representations, by design, and work well for signals that are similar to the dictionary elements. The pursuit search, however, has a high computational cost,