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