4,914 research outputs found
Robust Linear Spectral Unmixing using Anomaly Detection
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
Distributed Gaussian Processes
To scale Gaussian processes (GPs) to large data sets we introduce the robust
Bayesian Committee Machine (rBCM), a practical and scalable product-of-experts
model for large-scale distributed GP regression. Unlike state-of-the-art sparse
GP approximations, the rBCM is conceptually simple and does not rely on
inducing or variational parameters. The key idea is to recursively distribute
computations to independent computational units and, subsequently, recombine
them to form an overall result. Efficient closed-form inference allows for
straightforward parallelisation and distributed computations with a small
memory footprint. The rBCM is independent of the computational graph and can be
used on heterogeneous computing infrastructures, ranging from laptops to
clusters. With sufficient computing resources our distributed GP model can
handle arbitrarily large data sets.Comment: 10 pages, 5 figures. Appears in Proceedings of ICML 201
PRISM: Sparse Recovery of the Primordial Power Spectrum
The primordial power spectrum describes the initial perturbations in the
Universe which eventually grew into the large-scale structure we observe today,
and thereby provides an indirect probe of inflation or other
structure-formation mechanisms. Here, we introduce a new method to estimate
this spectrum from the empirical power spectrum of cosmic microwave background
(CMB) maps.
A sparsity-based linear inversion method, coined \textbf{PRISM}, is
presented. This technique leverages a sparsity prior on features in the
primordial power spectrum in a wavelet basis to regularise the inverse problem.
This non-parametric approach does not assume a strong prior on the shape of the
primordial power spectrum, yet is able to correctly reconstruct its global
shape as well as localised features. These advantages make this method robust
for detecting deviations from the currently favoured scale-invariant spectrum.
We investigate the strength of this method on a set of WMAP 9-year simulated
data for three types of primordial power spectra: a nearly scale-invariant
spectrum, a spectrum with a small running of the spectral index, and a spectrum
with a localised feature. This technique proves to easily detect deviations
from a pure scale-invariant power spectrum and is suitable for distinguishing
between simple models of the inflation. We process the WMAP 9-year data and
find no significant departure from a nearly scale-invariant power spectrum with
the spectral index .
A high resolution primordial power spectrum can be reconstructed with this
technique, where any strong local deviations or small global deviations from a
pure scale-invariant spectrum can easily be detected
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