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

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

Time delay between the optical and X-ray outbursts in the high mass X-ray transient A0535+26/HDE245770

The optical behaviour of the Be star in the high mass X-ray transient A0535+26/HDE245770 shows that at the periastron typically there is an enhancement in the luminosity of order 0.02 to few tenths mag, and the X-ray outburst happens about 8 days after the periastron. We construct a quantitative model of this event, basing on the a nonstationary accretion disk behavior, connected with a high ellipticity of the orbital motion. The ephemeris used in this paper -- JD$_{\rm opt-outb}$ = JD$_0$(2,444,944) $\pm$ n(111.0 $\pm$ 0.4) days are derived from the orbital period of the system P$_{\rm orb} = 111.0 \pm 0.4$ days, determined by Priedhorsky & Terrell (1983), and from the optical flare of December 5, 1981 (Giovannelli et al., 1985) (here after 811205-E; E stands for the Event occurred at that date) that triggered the subsequent X-ray outburst of December 13, 1981 (Nagase et al., 1982) (here after 811213-E). We explain the observed time delay between the peaks of the optical and X-ray outbursts in this system by the time of radial motion of the matter in the accretion disk, after an increase of the mass flux in the vicinity of a periastral point in the binary. This time is determined by the turbulent viscosity, with the parameter $\alpha=0.1-0.3$. The increase of the mass flux is a sort of flush that reaches the external part of the accretion disk around the neutron star, producing an enhancement in the optical luminosity. The consequent X-ray flare happens when the matter reaches the hot central parts of the accretion disk, and the neutron star surface.Comment: 30 pages, 15 figures, with correction in abstrac

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