8,030 research outputs found
Landmark-Based Registration of Curves via the Continuous Wavelet Transform
This paper is concerned with the problem of the alignment of multiple sets of curves. We analyze two real examples arising from the biomedical area for which we need to test whether there are any statistically significant differences between two subsets of subjects. To synchronize a set of curves, we propose a new nonparametric landmark-based registration method based on the alignment of the structural intensity of the zero-crossings of a wavelet transform. The structural intensity is a multiscale technique recently proposed by Bigot (2003, 2005) which highlights the main features of a signal observed with noise. We conduct a simulation study to compare our landmark-based registration approach with some existing methods for curve alignment. For the two real examples, we compare the registered curves with FANOVA techniques, and a detailed analysis of the warping functions is provided
A scale-space approach with wavelets to singularity estimation
This paper is concerned with the problem of determining the typical features of a curve when it is observed with noise. It has been shown that one can characterize the Lipschitz singularities of a signal by following the propagation across scales of the modulus maxima of its continuous wavelet transform. A nonparametric approach, based on appropriate thresholding of the empirical wavelet coefficients, is proposed to estimate the wavelet maxima of a signal observed with noise at various scales. In order to identify the singularities of the unknown signal, we introduce a new tool, "the structural intensity", that computes the "density" of the location of the modulus maxima of a wavelet representation along various scales. This approach is shown to be an effective technique for detecting the significant singularities of a signal corrupted by noise and for removing spurious estimates. The asymptotic properties of the resulting estimators are studied and illustrated by simulations. An application to a real data set is also proposed
Poisson inverse problems
In this paper we focus on nonparametric estimators in inverse problems for
Poisson processes involving the use of wavelet decompositions. Adopting an
adaptive wavelet Galerkin discretization, we find that our method combines the
well-known theoretical advantages of wavelet--vaguelette decompositions for
inverse problems in terms of optimally adapting to the unknown smoothness of
the solution, together with the remarkably simple closed-form expressions of
Galerkin inversion methods. Adapting the results of Barron and Sheu [Ann.
Statist. 19 (1991) 1347--1369] to the context of log-intensity functions
approximated by wavelet series with the use of the Kullback--Leibler distance
between two point processes, we also present an asymptotic analysis of
convergence rates that justifies our approach. In order to shed some light on
the theoretical results obtained and to examine the accuracy of our estimates
in finite samples, we illustrate our method by the analysis of some simulated
examples.Comment: Published at http://dx.doi.org/10.1214/009053606000000687 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A deconvolution approach to estimation of a common shape in a shifted curves model
This paper considers the problem of adaptive estimation of a mean pattern in a randomly shifted curve model. We show that this problem can be transformed into a linear inverse problem, where the density of the random shifts plays the role of a convolution operator. An adaptive estimator of the mean pattern, based on wavelet thresholding is proposed. We study its consistency for the quadratic risk as the number of observed curves tends to infinity, and this estimator is shown to achieve a near-minimax rate of convergence over a large class of Besov balls. This rate depends both on the smoothness of the common shape of the curves and on the decay of the Fourier coefficients of the density of the random shifts. Hence, this paper makes a connection between mean pattern estimation and the statistical analysis of linear inverse problems, which is a new point of view on curve registration and image warping problems. We also provide a new method to estimate the unknown random shifts between curves. Some numerical experiments are given to illustrate the performances of our approach and to compare them with another algorithm existing in the literature
On the consistency of Fr\'echet means in deformable models for curve and image analysis
A new class of statistical deformable models is introduced to study
high-dimensional curves or images. In addition to the standard measurement
error term, these deformable models include an extra error term modeling the
individual variations in intensity around a mean pattern. It is shown that an
appropriate tool for statistical inference in such models is the notion of
sample Fr\'echet means, which leads to estimators of the deformation parameters
and the mean pattern. The main contribution of this paper is to study how the
behavior of these estimators depends on the number n of design points and the
number J of observed curves (or images). Numerical experiments are given to
illustrate the finite sample performances of the procedure
Stellar granulation and interferometry
Stars are not smooth. Their photosphere is covered by a granulation pattern
associated with the heat transport by convection. The convection-related
surface structures have different size, depth, and temporal variations with
respect to the stellar type. The related activity (in addition to other
phenomena such as magnetic spots, rotation, dust, etc.) potentially causes bias
in stellar parameters determination, radial velocity, chemical abundances
determinations, and exoplanet transit detections.
The role of long-baseline interferometric observations in this astrophysical
context is crucial to characterize the stellar surface dynamics and correct the
potential biases. In this Chapter, we present how the granulation pattern is
expected for different kind of stellar types ranging from main sequence to
extremely evolved stars of different masses and how interferometric techniques
help to study their photospheric dynamics.Comment: To appear in the Book of the VLTI School 2013, held 9-21 Sep 2013
Barcelonnette (France), "What the highest angular resolution can bring to
stellar astrophysics?", Ed. Millour, Chiavassa, Bigot, Chesneau, Meilland,
Stee, EAS Publications Series (2015
Atomic Energy Levels with QED and Contribution of the Screened Self-Energy
We present an introduction to the principles behind atomic energy level
calculations with Quantum Electrodynamics (QED) and the two-time Green's
function method; this method allows one to calculate an effective Hamiltonian
that contains all QED effects and that can be used to predict QED Lamb shifts
of degenerate, quasidegenerate and isolated atomic levels.Comment: 4 pages, 6 figures, summary of a talk given at the QED2000 Conference
held in Trieste, Italy in Oct. 200
- …