2,356 research outputs found
Wavelet analysis of magnetic turbulence in the Earth's plasma sheet
Recent studies provide evidence for the multi-scale nature of magnetic
turbulence in the plasma sheet. Wavelet methods represent modern time series
analysis techniques suitable for the description of statistical characteristics
of multi-scale turbulence. Cluster FGM (fluxgate magnetometer) magnetic field
high-resolution (~67 Hz) measurements are studied during an interval in which
the spacecraft are in the plasma sheet. As Cluster passes through different
plasma regions, physical processes exhibit non-steady properties on
magnetohydrodynamic (MHD) and small, possibly kinetic scales. As a consequence,
the implementation of wavelet-based techniques becomes complicated due to the
statistically transitory properties of magnetic fluctuations and finite size
effects. Using a supervised multi-scale technique which allows existence test
of moments, the robustness of higher-order statistics is investigated. On this
basis the properties of magnetic turbulence are investigated for changing
thickness of the plasma sheet.Comment: 17 pages, 5 figure
Self-Similar Anisotropic Texture Analysis: the Hyperbolic Wavelet Transform Contribution
Textures in images can often be well modeled using self-similar processes
while they may at the same time display anisotropy. The present contribution
thus aims at studying jointly selfsimilarity and anisotropy by focusing on a
specific classical class of Gaussian anisotropic selfsimilar processes. It will
first be shown that accurate joint estimates of the anisotropy and
selfsimilarity parameters are performed by replacing the standard 2D-discrete
wavelet transform by the hyperbolic wavelet transform, which permits the use of
different dilation factors along the horizontal and vertical axis. Defining
anisotropy requires a reference direction that needs not a priori match the
horizontal and vertical axes according to which the images are digitized, this
discrepancy defines a rotation angle. Second, we show that this rotation angle
can be jointly estimated. Third, a non parametric bootstrap based procedure is
described, that provides confidence interval in addition to the estimates
themselves and enables to construct an isotropy test procedure, that can be
applied to a single texture image. Fourth, the robustness and versatility of
the proposed analysis is illustrated by being applied to a large variety of
different isotropic and anisotropic self-similar fields. As an illustration, we
show that a true anisotropy built-in self-similarity can be disentangled from
an isotropic self-similarity to which an anisotropic trend has been
superimposed
Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity
A general framework for solving image inverse problems is introduced in this
paper. The approach is based on Gaussian mixture models, estimated via a
computationally efficient MAP-EM algorithm. A dual mathematical interpretation
of the proposed framework with structured sparse estimation is described, which
shows that the resulting piecewise linear estimate stabilizes the estimation
when compared to traditional sparse inverse problem techniques. This
interpretation also suggests an effective dictionary motivated initialization
for the MAP-EM algorithm. We demonstrate that in a number of image inverse
problems, including inpainting, zooming, and deblurring, the same algorithm
produces either equal, often significantly better, or very small margin worse
results than the best published ones, at a lower computational cost.Comment: 30 page
Nonparametric estimation of the stationary density and the transition density of a Markov chain
In this paper, we study first the problem of nonparametric estimation of the
stationary density of a discrete-time Markov chain . We consider a
collection of projection estimators on finite dimensional linear spaces. We
select an estimator among the collection by minimizing a penalized contrast.
The same technique enables to estimate the density of and
so to provide an adaptive estimator of the transition density . We
give bounds in norm for these estimators and we show that they are
adaptive in the minimax sense over a large class of Besov spaces. Some examples
and simulations are also provided
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