5,127 research outputs found
ADAM: a general method for using various data types in asteroid reconstruction
We introduce ADAM, the All-Data Asteroid Modelling algorithm. ADAM is simple
and universal since it handles all disk-resolved data types (adaptive optics or
other images, interferometry, and range-Doppler radar data) in a uniform manner
via the 2D Fourier transform, enabling fast convergence in model optimization.
The resolved data can be combined with disk-integrated data (photometry). In
the reconstruction process, the difference between each data type is only a few
code lines defining the particular generalized projection from 3D onto a 2D
image plane. Occultation timings can be included as sparse silhouettes, and
thermal infrared data are efficiently handled with an approximate algorithm
that is sufficient in practice due to the dominance of the high-contrast
(boundary) pixels over the low-contrast (interior) ones. This is of particular
importance to the raw ALMA data that can be directly handled by ADAM without
having to construct the standard image. We study the reliability of the
inversion by using the independent shape supports of function series and
control-point surfaces. When other data are lacking, one can carry out fast
nonconvex lightcurve-only inversion, but any shape models resulting from it
should only be taken as illustrative global-scale ones.Comment: 11 pages, submitted to A&
STiC -- A multi-atom non-LTE PRD inversion code for full-Stokes solar observations
The inference of the underlying state of the plasma in the solar chromosphere
remains extremely challenging because of the nonlocal character of the observed
radiation and plasma conditions in this layer. Inversion methods allow us to
derive a model atmosphere that can reproduce the observed spectra by
undertaking several physical assumptions.
The most advanced approaches involve a depth-stratified model atmosphere
described by temperature, line-of-sight velocity, turbulent velocity, the three
components of the magnetic field vector, and gas and electron pressure. The
parameters of the radiative transfer equation are computed from a solid ground
of physical principles. To apply these techniques to spectral lines that sample
the chromosphere, NLTE effects must be included in the calculations.
We developed a new inversion code STiC to study spectral lines that sample
the upper chromosphere. The code is based the RH synthetis code, which we
modified to make the inversions faster and more stable. For the first time,
STiC facilitates the processing of lines from multiple atoms in non-LTE, also
including partial redistribution effects. Furthermore, we include a
regularization strategy that allows for model atmospheres with a complex
stratification, without introducing artifacts in the reconstructed physical
parameters, which are usually manifested in the form of oscillatory behavior.
This approach takes steps toward a node-less inversion, in which the value of
the physical parameters at each grid point can be considered a free parameter.
In this paper we discuss the implementation of the aforementioned techniques,
the description of the model atmosphere, and the optimizations that we applied
to the code. We carry out some numerical experiments to show the performance of
the code and the regularization techniques that we implemented. We made STiC
publicly available to the community.Comment: Accepted for publication in Astronomy & Astrophysic
Bayesian interpretation of periodograms
The usual nonparametric approach to spectral analysis is revisited within the
regularization framework. Both usual and windowed periodograms are obtained as
the squared modulus of the minimizer of regularized least squares criteria.
Then, particular attention is paid to their interpretation within the Bayesian
statistical framework. Finally, the question of unsupervised hyperparameter and
window selection is addressed. It is shown that maximum likelihood solution is
both formally achievable and practically useful
Local Behavior of Sparse Analysis Regularization: Applications to Risk Estimation
In this paper, we aim at recovering an unknown signal x0 from noisy
L1measurements y=Phi*x0+w, where Phi is an ill-conditioned or singular linear
operator and w accounts for some noise. To regularize such an ill-posed inverse
problem, we impose an analysis sparsity prior. More precisely, the recovery is
cast as a convex optimization program where the objective is the sum of a
quadratic data fidelity term and a regularization term formed of the L1-norm of
the correlations between the sought after signal and atoms in a given
(generally overcomplete) dictionary. The L1-sparsity analysis prior is weighted
by a regularization parameter lambda>0. In this paper, we prove that any
minimizers of this problem is a piecewise-affine function of the observations y
and the regularization parameter lambda. As a byproduct, we exploit these
properties to get an objectively guided choice of lambda. In particular, we
develop an extension of the Generalized Stein Unbiased Risk Estimator (GSURE)
and show that it is an unbiased and reliable estimator of an appropriately
defined risk. The latter encompasses special cases such as the prediction risk,
the projection risk and the estimation risk. We apply these risk estimators to
the special case of L1-sparsity analysis regularization. We also discuss
implementation issues and propose fast algorithms to solve the L1 analysis
minimization problem and to compute the associated GSURE. We finally illustrate
the applicability of our framework to parameter(s) selection on several imaging
problems
Confidence driven TGV fusion
We introduce a novel model for spatially varying variational data fusion,
driven by point-wise confidence values. The proposed model allows for the joint
estimation of the data and the confidence values based on the spatial coherence
of the data. We discuss the main properties of the introduced model as well as
suitable algorithms for estimating the solution of the corresponding biconvex
minimization problem and their convergence. The performance of the proposed
model is evaluated considering the problem of depth image fusion by using both
synthetic and real data from publicly available datasets
Problems of the Strategy of Regions
Problems that arise in the application of general prescriptions of the
so-called strategy of regions for asymptotic expansions of Feynman integrals in
various limits of momenta and masses are discussed with the help of
characteristic examples of two-loop diagrams. The strategy is also reformulated
in the language of alpha parameters.Comment: 12 pages, LaTeX with axodraw.st
Robust Estimation and Wavelet Thresholding in Partial Linear Models
This paper is concerned with a semiparametric partially linear regression
model with unknown regression coefficients, an unknown nonparametric function
for the non-linear component, and unobservable Gaussian distributed random
errors. We present a wavelet thresholding based estimation procedure to
estimate the components of the partial linear model by establishing a
connection between an -penalty based wavelet estimator of the
nonparametric component and Huber's M-estimation of a standard linear model
with outliers. Some general results on the large sample properties of the
estimates of both the parametric and the nonparametric part of the model are
established. Simulations and a real example are used to illustrate the general
results and to compare the proposed methodology with other methods available in
the recent literature
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