4,672 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
Automatic Bayesian Density Analysis
Making sense of a dataset in an automatic and unsupervised fashion is a
challenging problem in statistics and AI. Classical approaches for {exploratory
data analysis} are usually not flexible enough to deal with the uncertainty
inherent to real-world data: they are often restricted to fixed latent
interaction models and homogeneous likelihoods; they are sensitive to missing,
corrupt and anomalous data; moreover, their expressiveness generally comes at
the price of intractable inference. As a result, supervision from statisticians
is usually needed to find the right model for the data. However, since domain
experts are not necessarily also experts in statistics, we propose Automatic
Bayesian Density Analysis (ABDA) to make exploratory data analysis accessible
at large. Specifically, ABDA allows for automatic and efficient missing value
estimation, statistical data type and likelihood discovery, anomaly detection
and dependency structure mining, on top of providing accurate density
estimation. Extensive empirical evidence shows that ABDA is a suitable tool for
automatic exploratory analysis of mixed continuous and discrete tabular data.Comment: In proceedings of the Thirty-Third AAAI Conference on Artificial
Intelligence (AAAI-19
Collaborative sparse regression using spatially correlated supports - Application to hyperspectral unmixing
This paper presents a new Bayesian collaborative sparse regression method for
linear unmixing of hyperspectral images. Our contribution is twofold; first, we
propose a new Bayesian model for structured sparse regression in which the
supports of the sparse abundance vectors are a priori spatially correlated
across pixels (i.e., materials are spatially organised rather than randomly
distributed at a pixel level). This prior information is encoded in the model
through a truncated multivariate Ising Markov random field, which also takes
into consideration the facts that pixels cannot be empty (i.e, there is at
least one material present in each pixel), and that different materials may
exhibit different degrees of spatial regularity. Secondly, we propose an
advanced Markov chain Monte Carlo algorithm to estimate the posterior
probabilities that materials are present or absent in each pixel, and,
conditionally to the maximum marginal a posteriori configuration of the
support, compute the MMSE estimates of the abundance vectors. A remarkable
property of this algorithm is that it self-adjusts the values of the parameters
of the Markov random field, thus relieving practitioners from setting
regularisation parameters by cross-validation. The performance of the proposed
methodology is finally demonstrated through a series of experiments with
synthetic and real data and comparisons with other algorithms from the
literature
Acoustic Space Learning for Sound Source Separation and Localization on Binaural Manifolds
In this paper we address the problems of modeling the acoustic space
generated by a full-spectrum sound source and of using the learned model for
the localization and separation of multiple sources that simultaneously emit
sparse-spectrum sounds. We lay theoretical and methodological grounds in order
to introduce the binaural manifold paradigm. We perform an in-depth study of
the latent low-dimensional structure of the high-dimensional interaural
spectral data, based on a corpus recorded with a human-like audiomotor robot
head. A non-linear dimensionality reduction technique is used to show that
these data lie on a two-dimensional (2D) smooth manifold parameterized by the
motor states of the listener, or equivalently, the sound source directions. We
propose a probabilistic piecewise affine mapping model (PPAM) specifically
designed to deal with high-dimensional data exhibiting an intrinsic piecewise
linear structure. We derive a closed-form expectation-maximization (EM)
procedure for estimating the model parameters, followed by Bayes inversion for
obtaining the full posterior density function of a sound source direction. We
extend this solution to deal with missing data and redundancy in real world
spectrograms, and hence for 2D localization of natural sound sources such as
speech. We further generalize the model to the challenging case of multiple
sound sources and we propose a variational EM framework. The associated
algorithm, referred to as variational EM for source separation and localization
(VESSL) yields a Bayesian estimation of the 2D locations and time-frequency
masks of all the sources. Comparisons of the proposed approach with several
existing methods reveal that the combination of acoustic-space learning with
Bayesian inference enables our method to outperform state-of-the-art methods.Comment: 19 pages, 9 figures, 3 table
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