15,388 research outputs found
Quantum computation and analysis of Wigner and Husimi functions: toward a quantum image treatment
We study the efficiency of quantum algorithms which aim at obtaining phase
space distribution functions of quantum systems. Wigner and Husimi functions
are considered. Different quantum algorithms are envisioned to build these
functions, and compared with the classical computation. Different procedures to
extract more efficiently information from the final wave function of these
algorithms are studied, including coarse-grained measurements, amplitude
amplification and measure of wavelet-transformed wave function. The algorithms
are analyzed and numerically tested on a complex quantum system showing
different behavior depending on parameters, namely the kicked rotator. The
results for the Wigner function show in particular that the use of the quantum
wavelet transform gives a polynomial gain over classical computation. For the
Husimi distribution, the gain is much larger than for the Wigner function, and
is bigger with the help of amplitude amplification and wavelet transforms. We
also apply the same set of techniques to the analysis of real images. The
results show that the use of the quantum wavelet transform allows to lower
dramatically the number of measurements needed, but at the cost of a large loss
of information.Comment: Revtex, 13 pages, 16 figure
Wavelet signatures of -splitting of the Isoscalar Giant Quadrupole Resonance in deformed nuclei from high-resolution (p,p) scattering off Nd
The phenomenon of fine structure of the Isoscalar Giant Quadrupole Resonance
(ISGQR) has been studied with high energy-resolution proton inelastic
scattering at iThemba LABS in the chain of stable even-mass Nd isotopes
covering the transition from spherical to deformed ground states. A wavelet
analysis of the background-subtracted spectra in the deformed 146,148,150Nd
isotopes reveals characteristic scales in correspondence with scales obtained
from a Skyrme RPA calculation using the SVmas10 parameterization. A semblance
analysis shows that these scales arise from the energy shift between the main
fragments of the K = 0, 1 and K = 2 components.Comment: 7 pages, 6 figure
Wavelet domain Bayesian denoising of string signal in the cosmic microwave background
An algorithm is proposed for denoising the signal induced by cosmic strings
in the cosmic microwave background (CMB). A Bayesian approach is taken, based
on modeling the string signal in the wavelet domain with generalized Gaussian
distributions. Good performance of the algorithm is demonstrated by simulated
experiments at arcminute resolution under noise conditions including primary
and secondary CMB anisotropies, as well as instrumental noise.Comment: 16 pages, 11 figures. Version 2 matches version accepted for
publication in MNRAS. Changes include substantial clarifications on our
approach and a significant reduction of manuscript lengt
Long-range particle correlations and wavelets
The problem of long-range correlations of particles produced in high- energy
collisions is discussed. Long-range correlations involve large groups of
particles. Among them are, e.g., those correlations which lead to ring-like and
elliptic flow shapes of individual high-multiplicity events in the
polar+azimuthal angles plane. The \w method of \an which allows to disentangle
various patterns has been proposed and applied to some central lead-lead
collisions at energy 158 GeV per nucleon. Previous attempts to find out the
ring-like correlations and recent results on \w \an of high- energy nuclei
interactions are reviewed.Comment: 21 pages, 5 Figs, Latex, to be published in Physics- Uspekhi,
Nov.200
Two-dimensional discrete wavelet analysis of multiparticle event topology in heavy ion collisions
The event-by-event analysis of multiparticle production in high energy hadron
and nuclei collisions can be performed using the discrete wavelet
transformation. The ring-like and jet-like structures in two-dimensional
angular histograms are well extracted by wavelet analysis. For the first time
the method is applied to the jet-like events with background simulated by event
generators, which are developed to describe nucleus-nucleus collisions at LHC
energies. The jet positions are located quite well by the discrete wavelet
transformation of angular particle distribution even in presence of strong
background.Comment: 6 pages, 6 figure
Seismic Ray Impedance Inversion
This thesis investigates a prestack seismic inversion scheme implemented in the ray
parameter domain. Conventionally, most prestack seismic inversion methods are
performed in the incidence angle domain. However, inversion using the concept of
ray impedance, as it honours ray path variation following the elastic parameter
variation according to Snell’s law, shows the capacity to discriminate different
lithologies if compared to conventional elastic impedance inversion.
The procedure starts with data transformation into the ray-parameter domain and then
implements the ray impedance inversion along constant ray-parameter profiles. With
different constant-ray-parameter profiles, mixed-phase wavelets are initially estimated
based on the high-order statistics of the data and further refined after a proper well-to-seismic
tie. With the estimated wavelets ready, a Cauchy inversion method is used to
invert for seismic reflectivity sequences, aiming at recovering seismic reflectivity
sequences for blocky impedance inversion. The impedance inversion from reflectivity
sequences adopts a standard generalised linear inversion scheme, whose results are
utilised to identify rock properties and facilitate quantitative interpretation. It has also
been demonstrated that we can further invert elastic parameters from ray impedance
values, without eliminating an extra density term or introducing a Gardner’s relation
to absorb this term.
Ray impedance inversion is extended to P-S converted waves by introducing the
definition of converted-wave ray impedance. This quantity shows some advantages in
connecting prestack converted wave data with well logs, if compared with the shearwave
elastic impedance derived from the Aki and Richards approximation to the
Zoeppritz equations. An analysis of P-P and P-S wave data under the framework of
ray impedance is conducted through a real multicomponent dataset, which can reduce
the uncertainty in lithology identification.Inversion is the key method in generating those examples throughout the entire thesis
as we believe it can render robust solutions to geophysical problems. Apart from the
reflectivity sequence, ray impedance and elastic parameter inversion mentioned above,
inversion methods are also adopted in transforming the prestack data from the offset
domain to the ray-parameter domain, mixed-phase wavelet estimation, as well as the
registration of P-P and P-S waves for the joint analysis.
The ray impedance inversion methods are successfully applied to different types of
datasets. In each individual step to achieving the ray impedance inversion, advantages,
disadvantages as well as limitations of the algorithms adopted are detailed. As a
conclusion, the ray impedance related analyses demonstrated in this thesis are highly
competent compared with the classical elastic impedance methods and the author
would like to recommend it for a wider application
A power-law distribution of phase-locking intervals does not imply critical interaction
Neural synchronisation plays a critical role in information processing,
storage and transmission. Characterising the pattern of synchronisation is
therefore of great interest. It has recently been suggested that the brain
displays broadband criticality based on two measures of synchronisation - phase
locking intervals and global lability of synchronisation - showing power law
statistics at the critical threshold in a classical model of synchronisation.
In this paper, we provide evidence that, within the limits of the model
selection approach used to ascertain the presence of power law statistics, the
pooling of pairwise phase-locking intervals from a non-critically interacting
system can produce a distribution that is similarly assessed as being power
law. In contrast, the global lability of synchronisation measure is shown to
better discriminate critical from non critical interaction.Comment: (v3) Fixed error in Figure 1; (v2) Added references. Minor edits
throughout. Clarified relationship between theoretical critical coupling for
infinite size system and 'effective' critical coupling system for finite size
system. Improved presentation and discussion of results; results unchanged.
Revised Figure 1 to include error bars on r and N; results unchanged; (v1) 11
pages, 7 figure
Watermarking for multimedia security using complex wavelets
This paper investigates the application of complex wavelet transforms to the field of digital data hiding. Complex wavelets offer improved directional selectivity and shift invariance over their discretely sampled counterparts allowing for better adaptation of watermark distortions to the host media. Two methods of deriving visual models for the watermarking system are adapted to the complex wavelet transforms and their performances are compared. To produce improved capacity a spread transform embedding algorithm is devised, this combines the robustness of spread spectrum methods with the high capacity of quantization based methods. Using established information theoretic methods, limits of watermark capacity are derived that demonstrate the superiority of complex wavelets over discretely sampled wavelets. Finally results for the algorithm against commonly used attacks demonstrate its robustness and the improved performance offered by complex wavelet transforms
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