766,965 research outputs found
A symbol-based algorithm for decoding bar codes
We investigate the problem of decoding a bar code from a signal measured with
a hand-held laser-based scanner. Rather than formulating the inverse problem as
one of binary image reconstruction, we instead incorporate the symbology of the
bar code into the reconstruction algorithm directly, and search for a sparse
representation of the UPC bar code with respect to this known dictionary. Our
approach significantly reduces the degrees of freedom in the problem, allowing
for accurate reconstruction that is robust to noise and unknown parameters in
the scanning device. We propose a greedy reconstruction algorithm and provide
robust reconstruction guarantees. Numerical examples illustrate the
insensitivity of our symbology-based reconstruction to both imprecise model
parameters and noise on the scanned measurements.Comment: 24 pages, 12 figure
Reconstruction on trees and spin glass transition
Consider an information source generating a symbol at the root of a tree
network whose links correspond to noisy communication channels, and
broadcasting it through the network. We study the problem of reconstructing the
transmitted symbol from the information received at the leaves. In the large
system limit, reconstruction is possible when the channel noise is smaller than
a threshold.
We show that this threshold coincides with the dynamical (replica symmetry
breaking) glass transition for an associated statistical physics problem.
Motivated by this correspondence, we derive a variational principle which
implies new rigorous bounds on the reconstruction threshold. Finally, we apply
a standard numerical procedure used in statistical physics, to predict the
reconstruction thresholds in various channels. In particular, we prove a bound
on the reconstruction problem for the antiferromagnetic ``Potts'' channels,
which implies, in the noiseless limit, new results on random proper colorings
of infinite regular trees.
This relation to the reconstruction problem also offers interesting
perspective for putting on a clean mathematical basis the theory of glasses on
random graphs.Comment: 34 pages, 16 eps figure
Computing Bounds on Network Capacity Regions as a Polytope Reconstruction Problem
We define a notion of network capacity region of networks that generalizes
the notion of network capacity defined by Cannons et al. and prove its notable
properties such as closedness, boundedness and convexity when the finite field
is fixed. We show that the network routing capacity region is a computable
rational polytope and provide exact algorithms and approximation heuristics for
computing the region. We define the semi-network linear coding capacity region,
with respect to a fixed finite field, that inner bounds the corresponding
network linear coding capacity region, show that it is a computable rational
polytope, and provide exact algorithms and approximation heuristics. We show
connections between computing these regions and a polytope reconstruction
problem and some combinatorial optimization problems, such as the minimum cost
directed Steiner tree problem. We provide an example to illustrate our results.
The algorithms are not necessarily polynomial-time.Comment: Appeared in the 2011 IEEE International Symposium on Information
Theory, 5 pages, 1 figur
On a Reconstruction Problem for Sequences
AbstractIt is shown that any word of lengthnis uniquely determined by all its[formula]subwords of lengthk, providedk⩾⌊167n⌋+5. This improves the boundk⩾⌊n/2⌋ given in B. Manvelet al.(Discrete Math.94(1991), 209–219)
Reconstruction of the primordial Universe by a Monge--Ampere--Kantorovich optimisation scheme
A method for the reconstruction of the primordial density fluctuation field
is presented. Various previous approaches to this problem rendered {\it
non-unique} solutions. Here, it is demonstrated that the initial positions of
dark matter fluid elements, under the hypothesis that their displacement is the
gradient of a convex potential, can be reconstructed uniquely. In our approach,
the cosmological reconstruction problem is reformulated as an assignment
problem in optimisation theory. When tested against numerical simulations, our
scheme yields excellent reconstruction on scales larger than a few megaparsecs.Comment: 14 pages, 10 figure
Grid-free compressive beamforming
The direction-of-arrival (DOA) estimation problem involves the localization
of a few sources from a limited number of observations on an array of sensors,
thus it can be formulated as a sparse signal reconstruction problem and solved
efficiently with compressive sensing (CS) to achieve high-resolution imaging.
On a discrete angular grid, the CS reconstruction degrades due to basis
mismatch when the DOAs do not coincide with the angular directions on the grid.
To overcome this limitation, a continuous formulation of the DOA problem is
employed and an optimization procedure is introduced, which promotes sparsity
on a continuous optimization variable. The DOA estimation problem with
infinitely many unknowns, i.e., source locations and amplitudes, is solved over
a few optimization variables with semidefinite programming. The grid-free CS
reconstruction provides high-resolution imaging even with non-uniform arrays,
single-snapshot data and under noisy conditions as demonstrated on experimental
towed array data.Comment: 14 pages, 8 figures, journal pape
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