298 research outputs found
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
Estimating hyperparameters and instrument parameters in regularized inversion. Illustration for SPIRE/Herschel map making
We describe regularized methods for image reconstruction and focus on the
question of hyperparameter and instrument parameter estimation, i.e.
unsupervised and myopic problems. We developed a Bayesian framework that is
based on the \post density for all unknown quantities, given the observations.
This density is explored by a Markov Chain Monte-Carlo sampling technique based
on a Gibbs loop and including a Metropolis-Hastings step. The numerical
evaluation relies on the SPIRE instrument of the Herschel observatory. Using
simulated and real observations, we show that the hyperparameters and
instrument parameters are correctly estimated, which opens up many perspectives
for imaging in astrophysics
Regularized adaptive long autoregressive spectral analysis
This paper is devoted to adaptive long autoregressive spectral analysis when
(i) very few data are available, (ii) information does exist beforehand
concerning the spectral smoothness and time continuity of the analyzed signals.
The contribution is founded on two papers by Kitagawa and Gersch. The first one
deals with spectral smoothness, in the regularization framework, while the
second one is devoted to time continuity, in the Kalman formalism. The present
paper proposes an original synthesis of the two contributions: a new
regularized criterion is introduced that takes both information into account.
The criterion is efficiently optimized by a Kalman smoother. One of the major
features of the method is that it is entirely unsupervised: the problem of
automatically adjusting the hyperparameters that balance data-based versus
prior-based information is solved by maximum likelihood. The improvement is
quantified in the field of meteorological radar
An Improved Observation Model for Super-Resolution under Affine Motion
Super-resolution (SR) techniques make use of subpixel shifts between frames
in an image sequence to yield higher-resolution images. We propose an original
observation model devoted to the case of non isometric inter-frame motion as
required, for instance, in the context of airborne imaging sensors. First, we
describe how the main observation models used in the SR literature deal with
motion, and we explain why they are not suited for non isometric motion. Then,
we propose an extension of the observation model by Elad and Feuer adapted to
affine motion. This model is based on a decomposition of affine transforms into
successive shear transforms, each one efficiently implemented by row-by-row or
column-by-column 1-D affine transforms.
We demonstrate on synthetic and real sequences that our observation model
incorporated in a SR reconstruction technique leads to better results in the
case of variable scale motions and it provides equivalent results in the case
of isometric motions
Unsupervised Frequency Tracking beyond the Nyquist Limit using Markov Chains
This paper deals with the estimation of a sequence of frequencies from a
corresponding sequence of signals. This problem arises in fields such as
Doppler imaging where its specificity is twofold. First, only short noisy data
records are available (typically four sample long) and experimental constraints
may cause spectral aliasing so that measurements provide unreliable, ambiguous
information. Second, the frequency sequence is smooth. Here, this information
is accounted for by a Markov model and application of the Bayes rule yields the
a posteriori density. The maximum a postariori is computed by a combination of
Viterbi and descent procedures. One of the major features of the method is that
it is entirely unsupervised. Adjusting the hyperparameters that balance
data-based and prior-based information is done automatically by ML using an
EM-based gradient algorithm. We compared the proposed estimate to a reference
one and found that it performed better: variance was greatly reduced and
tracking was correct, even beyond the Nyquist frequency
Recent Outbursts from the Transient X-Ray Pulsar Cep X-4 (GS 2138+56)
We report on X-ray observations of the 66 s period transient X-ray pulsar Cep
X-4 (GS 2138+56) with the Burst and Transient Source Experiment (BATSE) on the
Compton Gamma-Ray Observatory (CGRO) and with the Rossi X-ray Timing Explorer
(RXTE). Two outbursts from Cep X-4 were observed with BATSE in 1993 June-July
and 1997 July. Pulse frequencies of 15.0941 +/- 0.0002 mHz on 1993 June 25 (MJD
49,163) and 15.0882 +/- 0.0002 mHz on 1997 July 12 (MJD 50,641) were each
measured from 2 day spans of BATSE data near each outburst's peak. Cep X-4
showed an average spin down rate of (-4.14 +/- 0.08)*10^(-14) Hz/s between the
1993 and 1997 outbursts. After BATSE could no longer detect Cep X-4, public
observations were performed on 1997 July 18 & 25 with the Proportional Counter
Array (PCA) on RXTE. A pulse frequency of 15.088 +/- 0.004 mHz was measured
from observations on 1997 July 18 (MJD 50,647). Significant aperiodic noise,
with an rms variance of ~18% in the frequency range 0.01-1.0 Hz was observed on
both days. Energy and intensity dependent pulse shape variations were also seen
in these data. Recently published optical observations associate Cep X-4 with a
Be companion star. If all 4 outbursts observed from Cep X-4 are assumed to
occur at the same orbital phase, we find that the orbital period is between 23
days and 147.3 days.Comment: 19 pages (LaTeX) including 9 figures. Accepted for publication in the
Astrophysical Journa
Super-resolution in map-making based on a physical instrument model and regularized inversion. Application to SPIRE/Herschel
We investigate super-resolution methods for image reconstruction from data
provided by a family of scanning instruments like the Herschel observatory. To
do this, we constructed a model of the instrument that faithfully reflects the
physical reality, accurately taking the acquisition process into account to
explain the data in a reliable manner. The inversion, ie the image
reconstruction process, is based on a linear approach resulting from a
quadratic regularized criterion and numerical optimization tools. The
application concerns the reconstruction of maps for the SPIRE instrument of the
Herschel observatory. The numerical evaluation uses simulated and real data to
compare the standard tool (coaddition) and the proposed method. The inversion
approach is capable to restore spatial frequencies over a bandwidth four times
that possible with coaddition and thus to correctly show details invisible on
standard maps. The approach is also applied to real data with significant
improvement in spatial resolution.Comment: Astronomy & Astrophysic
DATA INVERSION FOR HYPERSPECTRAL OBJECTS IN ASTRONOMY
ABSTRACT We present an original method for reconstruction of hyperspectral objects (two spatial and one spectral dimensions) from data provided by the infrared slit spectrograph on board the Spitzer Space Telescope. The originality of the work lies in the fact that both measurement model and inversion method are tackled in continuous (spatial and spectral) variables. The method is built in a deterministic regularization framework and enable to achieve both deconvolution and over-resolution. Results show that the method is able to evidence spatial structures not detectable by means of conventional methods. The spatial resolution is shown to be improved by a factor 1.5. We discuss our data processing approach for the new generation of infrared to millimeter space observatories launched in 2009 (Herschel and Planck)
The broad-band X-ray spectrum of RE 0751+14 (PQ Gem)
RE 0751+14 is a member of the class of Soft Intermediate Polars. Unlike classical Intermediate Polars, they are characterized by the presence of a soft component in their X-ray spectra, in addition to the hard component typical of these systems. The broad-band coverage of the Narrow-Field instruments on board BeppoSAX is ideal for the study of such objects. Here we report the preliminary results of the analysis of a BeppoSAX pointing to RE 0751+14. Both components are clearly detected, and their temperature determined (~50 eV and ~40 keV), enabling the possibility of studying them simultaneously
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