9,281 research outputs found
Astronomical Data Analysis and Sparsity: from Wavelets to Compressed Sensing
Wavelets have been used extensively for several years now in astronomy for
many purposes, ranging from data filtering and deconvolution, to star and
galaxy detection or cosmic ray removal. More recent sparse representations such
ridgelets or curvelets have also been proposed for the detection of anisotropic
features such cosmic strings in the cosmic microwave background.
We review in this paper a range of methods based on sparsity that have been
proposed for astronomical data analysis. We also discuss what is the impact of
Compressed Sensing, the new sampling theory, in astronomy for collecting the
data, transferring them to the earth or reconstructing an image from incomplete
measurements.Comment: Submitted. Full paper will figures available at
http://jstarck.free.fr/IEEE09_SparseAstro.pd
The application of compressive sampling to radio astronomy I: Deconvolution
Compressive sampling is a new paradigm for sampling, based on sparseness of
signals or signal representations. It is much less restrictive than
Nyquist-Shannon sampling theory and thus explains and systematises the
widespread experience that methods such as the H\"ogbom CLEAN can violate the
Nyquist-Shannon sampling requirements. In this paper, a CS-based deconvolution
method for extended sources is introduced. This method can reconstruct both
point sources and extended sources (using the isotropic undecimated wavelet
transform as a basis function for the reconstruction step). We compare this
CS-based deconvolution method with two CLEAN-based deconvolution methods: the
H\"ogbom CLEAN and the multiscale CLEAN. This new method shows the best
performance in deconvolving extended sources for both uniform and natural
weighting of the sampled visibilities. Both visual and numerical results of the
comparison are provided.Comment: Published by A&A, Matlab code can be found:
http://code.google.com/p/csra/download
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
Encoding dynamics for multiscale community detection: Markov time sweeping for the Map equation
The detection of community structure in networks is intimately related to
finding a concise description of the network in terms of its modules. This
notion has been recently exploited by the Map equation formalism (M. Rosvall
and C.T. Bergstrom, PNAS, 105(4), pp.1118--1123, 2008) through an
information-theoretic description of the process of coding inter- and
intra-community transitions of a random walker in the network at stationarity.
However, a thorough study of the relationship between the full Markov dynamics
and the coding mechanism is still lacking. We show here that the original Map
coding scheme, which is both block-averaged and one-step, neglects the internal
structure of the communities and introduces an upper scale, the `field-of-view'
limit, in the communities it can detect. As a consequence, Map is well tuned to
detect clique-like communities but can lead to undesirable overpartitioning
when communities are far from clique-like. We show that a signature of this
behavior is a large compression gap: the Map description length is far from its
ideal limit. To address this issue, we propose a simple dynamic approach that
introduces time explicitly into the Map coding through the analysis of the
weighted adjacency matrix of the time-dependent multistep transition matrix of
the Markov process. The resulting Markov time sweeping induces a dynamical
zooming across scales that can reveal (potentially multiscale) community
structure above the field-of-view limit, with the relevant partitions indicated
by a small compression gap.Comment: 10 pages, 6 figure
Multiscale Markov Decision Problems: Compression, Solution, and Transfer Learning
Many problems in sequential decision making and stochastic control often have
natural multiscale structure: sub-tasks are assembled together to accomplish
complex goals. Systematically inferring and leveraging hierarchical structure,
particularly beyond a single level of abstraction, has remained a longstanding
challenge. We describe a fast multiscale procedure for repeatedly compressing,
or homogenizing, Markov decision processes (MDPs), wherein a hierarchy of
sub-problems at different scales is automatically determined. Coarsened MDPs
are themselves independent, deterministic MDPs, and may be solved using
existing algorithms. The multiscale representation delivered by this procedure
decouples sub-tasks from each other and can lead to substantial improvements in
convergence rates both locally within sub-problems and globally across
sub-problems, yielding significant computational savings. A second fundamental
aspect of this work is that these multiscale decompositions yield new transfer
opportunities across different problems, where solutions of sub-tasks at
different levels of the hierarchy may be amenable to transfer to new problems.
Localized transfer of policies and potential operators at arbitrary scales is
emphasized. Finally, we demonstrate compression and transfer in a collection of
illustrative domains, including examples involving discrete and continuous
statespaces.Comment: 86 pages, 15 figure
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