76,669 research outputs found
Spectral X-ray CT for fast NDT using discrete tomography
We present progress in fast, high-resolution imaging, material classification, and fault detection using
hyperspectral X-ray measurements. Classical X-ray CT approaches rely on data from many projection
angles, resulting in long acquisition and reconstruction times. Additionally, conventional CT cannot
distinguish between materials with similar densities. However, in additive manufacturing, the majority of
materials used are known a priori. This knowledge allows to vastly reduce the data collected and increase
the accuracy of fault detection. In this context, we propose an imaging method for non-destructive testing
of materials based on the combination of spectral X-ray CT and discrete tomography. We explore the
use of spectral X-ray attenuation models and measurements to recover the characteristic functions of
materials in heterogeneous media with piece-wise uniform composition. We show by means of numerical
simulation that using spectral measurements from a small number of angles, our approach can alleviate
the typical deterioration of spatial resolution and the appearance of streaking artifacts.Mechanical Engineerin
Compressive Source Separation: Theory and Methods for Hyperspectral Imaging
With the development of numbers of high resolution data acquisition systems
and the global requirement to lower the energy consumption, the development of
efficient sensing techniques becomes critical. Recently, Compressed Sampling
(CS) techniques, which exploit the sparsity of signals, have allowed to
reconstruct signal and images with less measurements than the traditional
Nyquist sensing approach. However, multichannel signals like Hyperspectral
images (HSI) have additional structures, like inter-channel correlations, that
are not taken into account in the classical CS scheme. In this paper we exploit
the linear mixture of sources model, that is the assumption that the
multichannel signal is composed of a linear combination of sources, each of
them having its own spectral signature, and propose new sampling schemes
exploiting this model to considerably decrease the number of measurements
needed for the acquisition and source separation. Moreover, we give theoretical
lower bounds on the number of measurements required to perform reconstruction
of both the multichannel signal and its sources. We also proposed optimization
algorithms and extensive experimentation on our target application which is
HSI, and show that our approach recovers HSI with far less measurements and
computational effort than traditional CS approaches.Comment: 32 page
Imaging the dynamical atmosphere of the red supergiant Betelgeuse in the CO first overtone lines with VLTI/AMBER
We present the first 1-D aperture synthesis imaging of the red supergiant
Betelgeuse in the individual CO first overtone lines with VLTI/AMBER. The
reconstructed 1-D projection images reveal that the star appears differently in
the blue wing, line center, and red wing of the individual CO lines. The 1-D
projection images in the blue wing and line center show a pronounced,
asymmetrically extended component up to ~1.3 stellar radii, while those in the
red wing do not show such a component. The observed 1-D projection images in
the lines can be reasonably explained by a model in which the CO gas within a
region more than half as large as the stellar size is moving slightly outward
with 0--5 km s^-1, while the gas in the remaining region is infalling fast with
20--30 km s^-1. A comparison between the CO line AMBER data taken in 2008 and
2009 shows a significant time variation in the dynamics of the CO line-forming
region in the photosphere and the outer atmosphere. In contrast to the line
data, the reconstructed 1-D projection images in the continuum show only a
slight deviation from a uniform disk or limb-darkened disk. We derive a
uniform-disk diameter of 42.05 +/- 0.05 mas and a power-law-type limb-darkened
disk diameter of 42.49 +/- 0.06 mas and a limb-darkening parameter of (9.7 +/-
0.5) x 10^{-2}. This latter angular diameter leads to an effective temperature
of 3690 +/- 54 K for the continuum-forming layer. These diameters confirm that
the near-IR size of Betelgeuse was nearly constant over the last 18 years, in
marked contrast to the recently reported noticeable decrease in the mid-IR
size. The continuum data taken in 2008 and 2009 reveal no or only marginal time
variations, much smaller than the maximum variation predicted by the current
3-D convection simulations.Comment: 21 pages, 12 figures, accepted for publication in Astronomy and
Astrophysic
Revisiting the Nystrom Method for Improved Large-Scale Machine Learning
We reconsider randomized algorithms for the low-rank approximation of
symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel
matrices that arise in data analysis and machine learning applications. Our
main results consist of an empirical evaluation of the performance quality and
running time of sampling and projection methods on a diverse suite of SPSD
matrices. Our results highlight complementary aspects of sampling versus
projection methods; they characterize the effects of common data preprocessing
steps on the performance of these algorithms; and they point to important
differences between uniform sampling and nonuniform sampling methods based on
leverage scores. In addition, our empirical results illustrate that existing
theory is so weak that it does not provide even a qualitative guide to
practice. Thus, we complement our empirical results with a suite of worst-case
theoretical bounds for both random sampling and random projection methods.
These bounds are qualitatively superior to existing bounds---e.g. improved
additive-error bounds for spectral and Frobenius norm error and relative-error
bounds for trace norm error---and they point to future directions to make these
algorithms useful in even larger-scale machine learning applications.Comment: 60 pages, 15 color figures; updated proof of Frobenius norm bounds,
added comparison to projection-based low-rank approximations, and an analysis
of the power method applied to SPSD sketche
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
Frame Theory for Signal Processing in Psychoacoustics
This review chapter aims to strengthen the link between frame theory and
signal processing tasks in psychoacoustics. On the one side, the basic concepts
of frame theory are presented and some proofs are provided to explain those
concepts in some detail. The goal is to reveal to hearing scientists how this
mathematical theory could be relevant for their research. In particular, we
focus on frame theory in a filter bank approach, which is probably the most
relevant view-point for audio signal processing. On the other side, basic
psychoacoustic concepts are presented to stimulate mathematicians to apply
their knowledge in this field
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