11,295 research outputs found
Sparse Representation of Astronomical Images
Sparse representation of astronomical images is discussed. It is shown that a
significant gain in sparsity is achieved when particular mixed dictionaries are
used for approximating these types of images with greedy selection strategies.
Experiments are conducted to confirm: i)Effectiveness at producing sparse
representations. ii)Competitiveness, with respect to the time required to
process large images.The latter is a consequence of the suitability of the
proposed dictionaries for approximating images in partitions of small
blocks.This feature makes it possible to apply the effective greedy selection
technique Orthogonal Matching Pursuit, up to some block size. For blocks
exceeding that size a refinement of the original Matching Pursuit approach is
considered. The resulting method is termed Self Projected Matching Pursuit,
because is shown to be effective for implementing, via Matching Pursuit itself,
the optional back-projection intermediate steps in that approach.Comment: Software to implement the approach is available on
http://www.nonlinear-approx.info/examples/node1.htm
Compressive Network Analysis
Modern data acquisition routinely produces massive amounts of network data.
Though many methods and models have been proposed to analyze such data, the
research of network data is largely disconnected with the classical theory of
statistical learning and signal processing. In this paper, we present a new
framework for modeling network data, which connects two seemingly different
areas: network data analysis and compressed sensing. From a nonparametric
perspective, we model an observed network using a large dictionary. In
particular, we consider the network clique detection problem and show
connections between our formulation with a new algebraic tool, namely Randon
basis pursuit in homogeneous spaces. Such a connection allows us to identify
rigorous recovery conditions for clique detection problems. Though this paper
is mainly conceptual, we also develop practical approximation algorithms for
solving empirical problems and demonstrate their usefulness on real-world
datasets
Distributed Sparse Signal Recovery For Sensor Networks
We propose a distributed algorithm for sparse signal recovery in sensor
networks based on Iterative Hard Thresholding (IHT). Every agent has a set of
measurements of a signal x, and the objective is for the agents to recover x
from their collective measurements at a minimal communication cost and with low
computational complexity. A naive distributed implementation of IHT would
require global communication of every agent's full state in each iteration. We
find that we can dramatically reduce this communication cost by leveraging
solutions to the distributed top-K problem in the database literature.
Evaluations show that our algorithm requires up to three orders of magnitude
less total bandwidth than the best-known distributed basis pursuit method
Gossip Algorithms for Distributed Signal Processing
Gossip algorithms are attractive for in-network processing in sensor networks
because they do not require any specialized routing, there is no bottleneck or
single point of failure, and they are robust to unreliable wireless network
conditions. Recently, there has been a surge of activity in the computer
science, control, signal processing, and information theory communities,
developing faster and more robust gossip algorithms and deriving theoretical
performance guarantees. This article presents an overview of recent work in the
area. We describe convergence rate results, which are related to the number of
transmitted messages and thus the amount of energy consumed in the network for
gossiping. We discuss issues related to gossiping over wireless links,
including the effects of quantization and noise, and we illustrate the use of
gossip algorithms for canonical signal processing tasks including distributed
estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page
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