7,366 research outputs found
Modulated Oscillations in Three Dimensions
The analysis of the fully three-dimensional and time-varying polarization
characteristics of a modulated trivariate, or three-component, oscillation is
addressed. The use of the analytic operator enables the instantaneous
three-dimensional polarization state of any square-integrable trivariate signal
to be uniquely defined. Straightforward expressions are given which permit the
ellipse parameters to be recovered from data. The notions of instantaneous
frequency and instantaneous bandwidth, generalized to the trivariate case, are
related to variations in the ellipse properties. Rates of change of the ellipse
parameters are found to be intimately linked to the first few moments of the
signal's spectrum, averaged over the three signal components. In particular,
the trivariate instantaneous bandwidth---a measure of the instantaneous
departure of the signal from a single pure sinusoidal oscillation---is found to
contain five contributions: three essentially two-dimensional effects due to
the motion of the ellipse within a fixed plane, and two effects due to the
motion of the plane containing the ellipse. The resulting analysis method is an
informative means of describing nonstationary trivariate signals, as is
illustrated with an application to a seismic record.Comment: IEEE Transactions on Signal Processing, 201
Intermittent process analysis with scattering moments
Scattering moments provide nonparametric models of random processes with
stationary increments. They are expected values of random variables computed
with a nonexpansive operator, obtained by iteratively applying wavelet
transforms and modulus nonlinearities, which preserves the variance. First- and
second-order scattering moments are shown to characterize intermittency and
self-similarity properties of multiscale processes. Scattering moments of
Poisson processes, fractional Brownian motions, L\'{e}vy processes and
multifractal random walks are shown to have characteristic decay. The
Generalized Method of Simulated Moments is applied to scattering moments to
estimate data generating models. Numerical applications are shown on financial
time-series and on energy dissipation of turbulent flows.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1276 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Assessing year to year variability of inertial oscillation in the Chukchi Sea using the wavelet transform
Master's Project (M.S.) University of Alaska Fairbanks, 2016Three years of ocean drifter data from the Chukchi Sea were examined using the wavelet transform to investigate inertial oscillation. There was an increasing trend in number, duration, and hence total proportion of time spent in inertial oscillation events. Additionally, the Chukchi Sea seems to facilitate inertial oscillation that is easier to discern using north-south velocity records rather than east-west velocity records. The data used in this analysis was transformed using wavelets, which are generally used as a qualitative statistical method. Because of this, in addition to measurement error and random ocean noise, there is an additional source of variability and correlation which makes concrete statistical results challenging to obtain. However, wavelets were an effective tool for isolating the specific period of inertial oscillation and examining how it changed over time
On The Continuous Steering of the Scale of Tight Wavelet Frames
In analogy with steerable wavelets, we present a general construction of
adaptable tight wavelet frames, with an emphasis on scaling operations. In
particular, the derived wavelets can be "dilated" by a procedure comparable to
the operation of steering steerable wavelets. The fundamental aspects of the
construction are the same: an admissible collection of Fourier multipliers is
used to extend a tight wavelet frame, and the "scale" of the wavelets is
adapted by scaling the multipliers. As an application, the proposed wavelets
can be used to improve the frequency localization. Importantly, the localized
frequency bands specified by this construction can be scaled efficiently using
matrix multiplication
Spatio-temporal wavelet regularization for parallel MRI reconstruction: application to functional MRI
Parallel MRI is a fast imaging technique that enables the acquisition of
highly resolved images in space or/and in time. The performance of parallel
imaging strongly depends on the reconstruction algorithm, which can proceed
either in the original k-space (GRAPPA, SMASH) or in the image domain
(SENSE-like methods). To improve the performance of the widely used SENSE
algorithm, 2D- or slice-specific regularization in the wavelet domain has been
deeply investigated. In this paper, we extend this approach using 3D-wavelet
representations in order to handle all slices together and address
reconstruction artifacts which propagate across adjacent slices. The gain
induced by such extension (3D-Unconstrained Wavelet Regularized -SENSE:
3D-UWR-SENSE) is validated on anatomical image reconstruction where no temporal
acquisition is considered. Another important extension accounts for temporal
correlations that exist between successive scans in functional MRI (fMRI). In
addition to the case of 2D+t acquisition schemes addressed by some other
methods like kt-FOCUSS, our approach allows us to deal with 3D+t acquisition
schemes which are widely used in neuroimaging. The resulting 3D-UWR-SENSE and
4D-UWR-SENSE reconstruction schemes are fully unsupervised in the sense that
all regularization parameters are estimated in the maximum likelihood sense on
a reference scan. The gain induced by such extensions is illustrated on both
anatomical and functional image reconstruction, and also measured in terms of
statistical sensitivity for the 4D-UWR-SENSE approach during a fast
event-related fMRI protocol. Our 4D-UWR-SENSE algorithm outperforms the SENSE
reconstruction at the subject and group levels (15 subjects) for different
contrasts of interest (eg, motor or computation tasks) and using different
parallel acceleration factors (R=2 and R=4) on 2x2x3mm3 EPI images.Comment: arXiv admin note: substantial text overlap with arXiv:1103.353
Motion magnification in coronal seismology
We introduce a new method for the investigation of low-amplitude transverse
oscillations of solar plasma non-uniformities, such as coronal loops,
individual strands in coronal arcades, jets, prominence fibrils, polar plumes,
and other contrast features, observed with imaging instruments. The method is
based on the two-dimensional dual tree complex wavelet transform
(DTWT). It allows us to magnify transverse, in the
plane-of-the-sky, quasi-periodic motions of contrast features in image
sequences. The tests performed on the artificial data cubes imitating
exponentially decaying, multi-periodic and frequency-modulated kink
oscillations of coronal loops showed the effectiveness, reliability and
robustness of this technique. The algorithm was found to give linear scaling of
the magnified amplitudes with the original amplitudes provided they are
sufficiently small. Also, the magnification is independent of the oscillation
period in a broad range of the periods. The application of this technique to
SDO/AIA EUV data cubes of a non-flaring active region allowed for the improved
detection of low-amplitude decay-less oscillations in the majority of loops.Comment: Accepted for publication in Solar Physic
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