43,894 research outputs found
Finite sample performance of linear least squares estimators under sub-Gaussian martingale difference noise
Linear Least Squares is a very well known technique for parameter estimation,
which is used even when sub-optimal, because of its very low computational
requirements and the fact that exact knowledge of the noise statistics is not
required. Surprisingly, bounding the probability of large errors with finitely
many samples has been left open, especially when dealing with correlated noise
with unknown covariance. In this paper we analyze the finite sample performance
of the linear least squares estimator under sub-Gaussian martingale difference
noise. In order to analyze this important question we used concentration of
measure bounds. When applying these bounds we obtained tight bounds on the tail
of the estimator's distribution. We show the fast exponential convergence of
the number of samples required to ensure a given accuracy with high
probability. We provide probability tail bounds on the estimation error's norm.
Our analysis method is simple and uses simple type bounds on the
estimation error. The tightness of the bounds is tested through simulation. The
proposed bounds make it possible to predict the number of samples required for
least squares estimation even when least squares is sub-optimal and used for
computational simplicity. The finite sample analysis of least squares models
with this general noise model is novel
Direct exoplanet detection and characterization using the ANDROMEDA method: Performance on VLT/NaCo data
Context. The direct detection of exoplanets with high-contrast imaging
requires advanced data processing methods to disentangle potential planetary
signals from bright quasi-static speckles. Among them, angular differential
imaging (ADI) permits potential planetary signals with a known rotation rate to
be separated from instrumental speckles that are either statics or slowly
variable. The method presented in this paper, called ANDROMEDA for ANgular
Differential OptiMal Exoplanet Detection Algorithm is based on a maximum
likelihood approach to ADI and is used to estimate the position and the flux of
any point source present in the field of view. Aims. In order to optimize and
experimentally validate this previously proposed method, we applied ANDROMEDA
to real VLT/NaCo data. In addition to its pure detection capability, we
investigated the possibility of defining simple and efficient criteria for
automatic point source extraction able to support the processing of large
surveys. Methods. To assess the performance of the method, we applied ANDROMEDA
on VLT/NaCo data of TYC-8979-1683-1 which is surrounded by numerous bright
stars and on which we added synthetic planets of known position and flux in the
field. In order to accommodate the real data properties, it was necessary to
develop additional pre-processing and post-processing steps to the initially
proposed algorithm. We then investigated its skill in the challenging case of a
well-known target, Pictoris, whose companion is close to the detection
limit and we compared our results to those obtained by another method based on
principal component analysis (PCA). Results. Application on VLT/NaCo data
demonstrates the ability of ANDROMEDA to automatically detect and characterize
point sources present in the image field. We end up with a robust method
bringing consistent results with a sensitivity similar to the recently
published algorithms, with only two parameters to be fine tuned. Moreover, the
companion flux estimates are not biased by the algorithm parameters and do not
require a posteriori corrections. Conclusions. ANDROMEDA is an attractive
alternative to current standard image processing methods that can be readily
applied to on-sky data
Distributed Adaptive Learning of Graph Signals
The aim of this paper is to propose distributed strategies for adaptive
learning of signals defined over graphs. Assuming the graph signal to be
bandlimited, the method enables distributed reconstruction, with guaranteed
performance in terms of mean-square error, and tracking from a limited number
of sampled observations taken from a subset of vertices. A detailed mean square
analysis is carried out and illustrates the role played by the sampling
strategy on the performance of the proposed method. Finally, some useful
strategies for distributed selection of the sampling set are provided. Several
numerical results validate our theoretical findings, and illustrate the
performance of the proposed method for distributed adaptive learning of signals
defined over graphs.Comment: To appear in IEEE Transactions on Signal Processing, 201
- …