246 research outputs found
A self-calibration approach for optical long baseline interferometry imaging
Current optical interferometers are affected by unknown turbulent phases on
each telescope. In the field of radio-interferometry, the self-calibration
technique is a powerful tool to process interferometric data with missing phase
information. This paper intends to revisit the application of self-calibration
to Optical Long Baseline Interferometry (OLBI). We cast rigorously the OLBI
data processing problem into the self-calibration framework and demonstrate the
efficiency of the method on real astronomical OLBI dataset
Period Analysis using the Least Absolute Shrinkage and Selection Operator (Lasso)
We introduced least absolute shrinkage and selection operator (lasso) in
obtaining periodic signals in unevenly spaced time-series data. A very simple
formulation with a combination of a large set of sine and cosine functions has
been shown to yield a very robust estimate, and the peaks in the resultant
power spectra were very sharp. We studied the response of lasso to low
signal-to-noise data, asymmetric signals and very closely separated multiple
signals. When the length of the observation is sufficiently long, all of them
were not serious obstacles to lasso. We analyzed the 100-year visual
observations of delta Cep, and obtained a very accurate period of 5.366326(16)
d. The error in period estimation was several times smaller than in Phase
Dispersion Minimization. We also modeled the historical data of R Sct, and
obtained a reasonable fit to the data. The model, however, lost its predictive
ability after the end of the interval used for modeling, which is probably a
result of chaotic nature of the pulsations of this star. We also provide a
sample R code for making this analysis.Comment: 9 pages, 13 figures, accepted for publication in PAS
Sparsity and adaptivity for the blind separation of partially correlated sources
Blind source separation (BSS) is a very popular technique to analyze
multichannel data. In this context, the data are modeled as the linear
combination of sources to be retrieved. For that purpose, standard BSS methods
all rely on some discrimination principle, whether it is statistical
independence or morphological diversity, to distinguish between the sources.
However, dealing with real-world data reveals that such assumptions are rarely
valid in practice: the signals of interest are more likely partially
correlated, which generally hampers the performances of standard BSS methods.
In this article, we introduce a novel sparsity-enforcing BSS method coined
Adaptive Morphological Component Analysis (AMCA), which is designed to retrieve
sparse and partially correlated sources. More precisely, it makes profit of an
adaptive re-weighting scheme to favor/penalize samples based on their level of
correlation. Extensive numerical experiments have been carried out which show
that the proposed method is robust to the partial correlation of sources while
standard BSS techniques fail. The AMCA algorithm is evaluated in the field of
astrophysics for the separation of physical components from microwave data.Comment: submitted to IEEE Transactions on signal processin
Approximate cross-validation formula for Bayesian linear regression
Cross-validation (CV) is a technique for evaluating the ability of
statistical models/learning systems based on a given data set. Despite its wide
applicability, the rather heavy computational cost can prevent its use as the
system size grows. To resolve this difficulty in the case of Bayesian linear
regression, we develop a formula for evaluating the leave-one-out CV error
approximately without actually performing CV. The usefulness of the developed
formula is tested by statistical mechanical analysis for a synthetic model.
This is confirmed by application to a real-world supernova data set as well.Comment: 5 pages, 2 figures, invited paper for Allerton2016 conferenc
Polca SARA - Full polarization, direction-dependent calibration and sparse imaging for radio interferometry
New generation of radio interferometers are envisaged to produce high
quality, high dynamic range Stokes images of the observed sky from the
corresponding under-sampled Fourier domain measurements. In practice, these
measurements are contaminated by the instrumental and atmospheric effects that
are well represented by Jones matrices, and are most often varying with
observation direction and time. These effects, usually unknown, act as a
limiting factor in achieving the required imaging performance and thus, their
calibration is crucial. To address this issue, we develop a global algorithm,
named Polca SARA, aiming to perform full polarization, direction-dependent
calibration and sparse imaging by employing a non-convex optimization
technique. In contrast with the existing approaches, the proposed method offers
global convergence guarantees and flexibility to incorporate sophisticated
priors to regularize the imaging as well as the calibration problem. Thus, we
adapt a polarimetric imaging specific method, enforcing the physical
polarization constraint along with a sparsity prior for the sought images. We
perform extensive simulation studies of the proposed algorithm. While
indicating the superior performance of polarization constraint based imaging,
the obtained results also highlight the importance of calibrating for
direction-dependent effects as well as for off-diagonal terms (denoting
polarization leakage) in the associated Jones matrices, without inclusion of
which the imaging quality deteriorates
Learning and inverse problems: from theory to solar physics applications
The problem of approximating a function from a set of discrete measurements has been extensively studied since the seventies. Our theoretical analysis proposes a formalization of the function approximation problem which allows dealing with inverse problems and supervised kernel learning as two sides of the same coin. The proposed formalization takes into account arbitrary noisy data (deterministically or statistically defined), arbitrary loss functions (possibly seen as a log-likelihood), handling both direct and indirect measurements. The core idea of this part relies on the analogy between statistical learning and inverse problems. One of the main evidences of the connection occurring across these two areas is that regularization methods, usually developed for ill-posed inverse problems, can be used for solving learning problems. Furthermore, spectral regularization convergence rate analyses provided in these two areas, share the same source conditions but are carried out with either increasing number of samples in learning theory or decreasing noise level in inverse problems. Even more in general, regularization via sparsity-enhancing methods is widely used in both areas and it is possible to apply well-known -penalized methods for solving both learning and inverse problems. In the first part of the Thesis, we analyze such a connection at three levels: (1) at an infinite dimensional level, we define an abstract function approximation problem from which the two problems can be derived; (2) at a discrete level, we provide a unified formulation according to a suitable definition of sampling; and (3) at a convergence rates level, we provide a comparison between convergence rates given in the two areas, by quantifying the relation between the noise level and the number of samples. In the second part of the Thesis, we focus on a specific class of problems where measurements are distributed according to a Poisson law. We provide a data-driven, asymptotically unbiased, and globally quadratic approximation of the Kullback-Leibler divergence and we propose Lasso-type methods for solving sparse Poisson regression problems, named PRiL for Poisson Reweighed Lasso and an adaptive version of this method, named APRiL for Adaptive Poisson Reweighted Lasso, proving consistency properties in estimation and variable selection, respectively. Finally we consider two problems in solar physics: 1) the problem of forecasting solar flares (learning application) and 2) the desaturation problem of solar flare images (inverse problem application). The first application concerns the prediction of solar storms using images of the magnetic field on the sun, in particular physics-based features extracted from active regions from data provided by Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). The second application concerns the reconstruction problem of Extreme Ultra-Violet (EUV) solar flare images recorded by a second instrument on board SDO, the Atmospheric Imaging Assembly (AIA). We propose a novel sparsity-enhancing method SE-DESAT to reconstruct images affected by saturation and diffraction, without using any a priori estimate of the background solar activity
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