90 research outputs found
Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches
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, ill-posed inverse problem because of
model inaccuracies, observation noise, environmental conditions, endmember
variability, and data set size. Researchers have devised and investigated many
models searching for robust, stable, tractable, and accurate unmixing
algorithms. This paper presents an overview of unmixing methods from the time
of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models
are first discussed. Signal-subspace, geometrical, statistical, sparsity-based,
and spatial-contextual unmixing algorithms are described. Mathematical problems
and potential solutions are described. Algorithm characteristics are
illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of
Selected Topics in Applied Earth Observations and Remote Sensin
A convex model for non-negative matrix factorization and dimensionality reduction on physical space
A collaborative convex framework for factoring a data matrix into a
non-negative product , with a sparse coefficient matrix , is proposed.
We restrict the columns of the dictionary matrix to coincide with certain
columns of the data matrix , thereby guaranteeing a physically meaningful
dictionary and dimensionality reduction. We use regularization
to select the dictionary from the data and show this leads to an exact convex
relaxation of in the case of distinct noise free data. We also show how
to relax the restriction-to- constraint by initializing an alternating
minimization approach with the solution of the convex model, obtaining a
dictionary close to but not necessarily in . We focus on applications of the
proposed framework to hyperspectral endmember and abundances identification and
also show an application to blind source separation of NMR data.Comment: 14 pages, 9 figures. EE and JX were supported by NSF grants
{DMS-0911277}, {PRISM-0948247}, MM by the German Academic Exchange Service
(DAAD), SO and MM by NSF grants {DMS-0835863}, {DMS-0914561}, {DMS-0914856}
and ONR grant {N00014-08-1119}, and GS was supported by NSF, NGA, ONR, ARO,
DARPA, and {NSSEFF.
A Method for Finding Structured Sparse Solutions to Non-negative Least Squares Problems with Applications
Demixing problems in many areas such as hyperspectral imaging and
differential optical absorption spectroscopy (DOAS) often require finding
sparse nonnegative linear combinations of dictionary elements that match
observed data. We show how aspects of these problems, such as misalignment of
DOAS references and uncertainty in hyperspectral endmembers, can be modeled by
expanding the dictionary with grouped elements and imposing a structured
sparsity assumption that the combinations within each group should be sparse or
even 1-sparse. If the dictionary is highly coherent, it is difficult to obtain
good solutions using convex or greedy methods, such as non-negative least
squares (NNLS) or orthogonal matching pursuit. We use penalties related to the
Hoyer measure, which is the ratio of the and norms, as sparsity
penalties to be added to the objective in NNLS-type models. For solving the
resulting nonconvex models, we propose a scaled gradient projection algorithm
that requires solving a sequence of strongly convex quadratic programs. We
discuss its close connections to convex splitting methods and difference of
convex programming. We also present promising numerical results for example
DOAS analysis and hyperspectral demixing problems.Comment: 38 pages, 14 figure
Subspace Structure Regularized Nonnegative Matrix Factorization for Hyperspectral Unmixing
Hyperspectral unmixing is a crucial task for hyperspectral images (HSI) processing, which estimates the proportions of constituent materials of a mixed pixel. Usually, the mixed pixels can be approximated using a linear mixing model. Since each material only occurs in a few pixels in real HSI, sparse nonnegative matrix factorization (NMF) and its extensions are widely used as solutions. Some recent works assume that materials are distributed in certain structures, which can be added as constraints to sparse NMF model. However, they only consider the spatial distribution within a local neighborhood and define the distribution structure manually, while ignoring the real distribution of materials that is diverse in different images. In this paper, we propose a new unmixing method that learns a subspace structure from the original image and incorporate it into the sparse NMF framework to promote unmixing performance. Based on the self-representation property of data points lying in the same subspace, the learned subspace structure can indicate the global similar graph of pixels that represents the real distribution of materials. Then the similar graph is used as a robust global spatial prior which is expected to be maintained in the decomposed abundance matrix. The experiments conducted on both simulated and real-world HSI datasets demonstrate the superior performance of our proposed method
Hyperspectral Image Analysis through Unsupervised Deep Learning
Hyperspectral image (HSI) analysis has become an active research area in computer vision field with a wide range of applications. However, in order to yield better recognition and analysis results, we need to address two challenging issues of HSI, i.e., the existence of mixed pixels and its significantly low spatial resolution (LR). In this dissertation, spectral unmixing (SU) and hyperspectral image super-resolution (HSI-SR) approaches are developed to address these two issues with advanced deep learning models in an unsupervised fashion. A specific application, anomaly detection, is also studied, to show the importance of SU.Although deep learning has achieved the state-of-the-art performance on supervised problems, its practice on unsupervised problems has not been fully developed. To address the problem of SU, an untied denoising autoencoder is proposed to decompose the HSI into endmembers and abundances with non-negative and abundance sum-to-one constraints. The denoising capacity is incorporated into the network with a sparsity constraint to boost the performance of endmember extraction and abundance estimation.Moreover, the first attempt is made to solve the problem of HSI-SR using an unsupervised encoder-decoder architecture by fusing the LR HSI with the high-resolution multispectral image (MSI). The architecture is composed of two encoder-decoder networks, coupled through a shared decoder, to preserve the rich spectral information from the HSI network. It encourages the representations from both modalities to follow a sparse Dirichlet distribution which naturally incorporates the two physical constraints of HSI and MSI. And the angular difference between representations are minimized to reduce the spectral distortion.Finally, a novel detection algorithm is proposed through spectral unmixing and dictionary based low-rank decomposition, where the dictionary is constructed with mean-shift clustering and the coefficients of the dictionary is encouraged to be low-rank. Experimental evaluations show significant improvement on the performance of anomaly detection conducted on the abundances (through SU).The effectiveness of the proposed approaches has been evaluated thoroughly by extensive experiments, to achieve the state-of-the-art results
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