1,036 research outputs found
Matched Filtering of Numerical Relativity Templates of Spinning Binary Black Holes
Tremendous progress has been made towards the solution of the
binary-black-hole problem in numerical relativity. The waveforms produced by
numerical relativity will play a role in gravitational wave detection as either
test-beds for analytic template banks or as template banks themselves. As the
parameter space explored by numerical relativity expands, the importance of
quantifying the effect that each parameter has on first the detection of
gravitational waves and then the parameter estimation of their sources
increases. In light of this, we present a study of equal-mass, spinning
binary-black-hole evolutions through matched filtering techniques commonly used
in data analysis. We study how the match between two numerical waveforms varies
with numerical resolution, initial angular momentum of the black holes and the
inclination angle between the source and the detector. This study is limited by
the fact that the spinning black-hole-binaries are oriented axially and the
waveforms only contain approximately two and a half orbits before merger. We
find that for detection purposes, spinning black holes require the inclusion of
the higher harmonics in addition to the dominant mode, a condition that becomes
more important as the black-hole-spins increase. In addition, we conduct a
preliminary investigation of how well a template of fixed spin and inclination
angle can detect target templates of arbitrary spin and inclination for the
axial case considered here
Atomic norm denoising with applications to line spectral estimation
Motivated by recent work on atomic norms in inverse problems, we propose a
new approach to line spectral estimation that provides theoretical guarantees
for the mean-squared-error (MSE) performance in the presence of noise and
without knowledge of the model order. We propose an abstract theory of
denoising with atomic norms and specialize this theory to provide a convex
optimization problem for estimating the frequencies and phases of a mixture of
complex exponentials. We show that the associated convex optimization problem
can be solved in polynomial time via semidefinite programming (SDP). We also
show that the SDP can be approximated by an l1-regularized least-squares
problem that achieves nearly the same error rate as the SDP but can scale to
much larger problems. We compare both SDP and l1-based approaches with
classical line spectral analysis methods and demonstrate that the SDP
outperforms the l1 optimization which outperforms MUSIC, Cadzow's, and Matrix
Pencil approaches in terms of MSE over a wide range of signal-to-noise ratios.Comment: 27 pages, 10 figures. A preliminary version of this work appeared in
the Proceedings of the 49th Annual Allerton Conference in September 2011.
Numerous numerical experiments added to this version in accordance with
suggestions by anonymous reviewer
Transfer learning for piecewise-constant mean estimation: Optimality, - and -penalisation
We study transfer learning for estimating piecewise-constant signals when
source data, which may be relevant but disparate, are available in addition to
the target data. We first investigate transfer learning estimators that
respectively employ - and -penalties for unisource data
scenarios and then generalise these estimators to accommodate multisources. To
further reduce estimation errors, especially when some sources significantly
differ from the target, we introduce an informative source selection algorithm.
We then examine these estimators with multisource selection and establish their
minimax optimality. Unlike the common narrative in the transfer learning
literature that the performance is enhanced through large source sample sizes,
our approaches leverage higher observation frequencies and accommodate diverse
frequencies across multiple sources. Our theoretical findings are supported by
extensive numerical experiments, with the code available online, see
https://github.com/chrisfanwang/transferlearnin
A New Template Family For The Detection Of Gravitational Waves From Comparable Mass Black Hole Binaries
In order to improve the phasing of the comparable-mass waveform as we
approach the last stable orbit for a system, various re-summation methods have
been used to improve the standard post-Newtonian waveforms. In this work we
present a new family of templates for the detection of gravitational waves from
the inspiral of two comparable-mass black hole binaries. These new adiabatic
templates are based on re-expressing the derivative of the binding energy and
the gravitational wave flux functions in terms of shifted Chebyshev
polynomials. The Chebyshev polynomials are a useful tool in numerical methods
as they display the fastest convergence of any of the orthogonal polynomials.
In this case they are also particularly useful as they eliminate one of the
features that plagues the post-Newtonian expansion. The Chebyshev binding
energy now has information at all post-Newtonian orders, compared to the
post-Newtonian templates which only have information at full integer orders. In
this work, we compare both the post-Newtonian and Chebyshev templates against a
fiducially exact waveform. This waveform is constructed from a hybrid method of
using the test-mass results combined with the mass dependent parts of the
post-Newtonian expansions for the binding energy and flux functions. Our
results show that the Chebyshev templates achieve extremely high fitting
factors at all PN orders and provide excellent parameter extraction. We also
show that this new template family has a faster Cauchy convergence, gives a
better prediction of the position of the Last Stable Orbit and in general
recovers higher Signal-to-Noise ratios than the post-Newtonian templates.Comment: Final published version. Accepted for publication in Phys. Rev.
Adaptive Denoising of Signals with Shift-Invariant Structure
We study the problem of discrete-time signal denoising, following the line of
research initiated by [Nem91] and further developed in [JN09, JN10, HJNO15,
OHJN16]. Previous papers considered the following setup: the signal is assumed
to admit a convolution-type linear oracle -- an unknown linear estimator in the
form of the convolution of the observations with an unknown time-invariant
filter with small -norm. It was shown that such an oracle can be
"mimicked" by an efficiently computable non-linear convolution-type estimator,
in which the filter minimizes the Fourier-domain -norm of the
residual, regularized by the Fourier-domain -norm of the filter.
Following [OHJN16], here we study an alternative family of estimators,
replacing the -norm of the residual with the -norm. Such
estimators are found to have better statistical properties, in particular, we
prove sharp oracle inequalities for their -loss. Our guarantees require
an extra assumption of approximate shift-invariance: the signal must be
-close, in -metric, to some shift-invariant linear subspace
with bounded dimension . However, this subspace can be completely unknown,
and the remainder terms in the oracle inequalities scale at most polynomially
with and . In conclusion, we show that the new assumption
implies the previously considered one, providing explicit constructions of the
convolution-type linear oracles with -norm bounded in terms of
parameters and
Statistical Analysis of Audio Signals using Time-Frequency Analysis
In this thesis, we provide nonparametric estimation of signals corrupted by stationary noise in the white noise model. We derive adaptive and rate-optimal estimators of signals in modulation spaces by thresholding the coefficients obtained from the Gabor expansion. The rates obtained using the classical oracle inequalities of Donoho and Johnstone (1994) exhibit new features that reflect the inclusion of both time and frequency. The scope of our results is extended to alpha-modulation spaces in the one-dimensional setting, allowing a comparison with Sobolev and Besov spaces. To confirm the practical applicability of our methods, we perform extensive simulations. These simulations evaluate the performance of our methods in comparison to state-of-the-art methods over a range of scenarios
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