Thomas Rodet

Exact and approximate algorithms for helical cone-beam CT.

This paper concerns image reconstruction for helical x-ray transmission tomography (CT) with multi-row detectors. We introduce two approximate cone-beam (CB) filtered-backprojection (FBP) algorithms of the Feldkamp type, obtained by extending to three dimensions (3D) two recently proposed exact FBP algorithms for 2D fan-beam reconstruction. The new algorithms are similar to the standard Feldkamp-type FBP for helical CT. In particular, they can reconstruct each transaxial slice from data acquired along an arbitrary segment of helix, thereby efficiently exploiting the available data. In contrast to the standard Feldkamp-type algorithm, however, the redundancy weight is applied after filtering, allowing a more efficient numerical implementation. To partially alleviate the CB artefacts, which increase with increasing values of the helical pitch, a frequency-mixing method is proposed. This method reconstructs the high frequency components of the image using the longest possible segment of helix, whereas the low frequencies are reconstructed using a minimal, short-scan, segment of helix to minimize CB artefacts. The performance of the algorithms is illustrated using simulated data.

Bayesian estimation of regularization and point spread function parameters for Wiener–Hunt deconvolution

This paper tackles the problem of image deconvolution with joint estimation of point spread function (PSF) parameters and hyperparameters. Within a Bayesian framework, the solution is inferred via a global a posteriori law for unknown parameters and object. The estimate is chosen as the posterior mean, numerically calculated by means of a Monte Carlo Markov chain algorithm. The estimates are efficiently computed in the Fourier domain, and the effectiveness of the method is shown on simulated examples. Results show precise estimates for PSF parameters and hyperparameters as well as precise image estimates including restoration of high frequencies and spatial details, within a global and coherent approach.

The cone-beam algorithm of Feldkamp, Davis and Kress preserves oblique line integrals

The algorithm of Feldkamp, Davis, and Kress [J. Opt. Soc. Am. A 1, 612-619 (1984)] is a widely used filtered-backprojection algorithm for three-dimensional image reconstruction from cone-beam (CB) projections measured with a circular orbit of the x-ray source. A well-known property of this approximate algorithm is that the integral of the reconstructed image along any axial line orthogonal to the plane of the orbit is exact when the cone-beam projections are not truncated. We generalize this result to oblique line integrals, thus providing an efficient method to compute synthetic radiographs from cone-beam projections. Our generalized result is obtained by showing that the FDK algorithm is invariant under transformations that map oblique lines onto axial lines.

Physical properties of the Sh2-104 HII region as seen by Herschel

Context: Sh2-104 is a Galactic H ii region with a bubble morphology, detected at optical and radio wavelengths. It is considered the first observational confirmation of the collect-and-collapse model of triggered star-formation. Aims: We aim to analyze the dust and gas properties of the Sh2-104 region to better constrain its effect on local future generations of stars. In addition, we investigate the relationship between the dust emissivity index {\beta} and the dust temperature, T_dust. Methods: Using Herschel PACS and SPIRE images at 100, 160, 250, 350 and 500 {\mu}m we determine T_dust and {\beta} throughout Sh2-104, fitting the spectral energy distributions (SEDs) obtained from aperture photometry. With the SPIRE Fourier transform spectrometer (FTS) we obtained spectra at different positions in the Sh2-104 region. We detect J-ladders of CO and 13CO, with which we derive the gas temperature and column density. We also detect proxies of ionizing flux as the [NII] 3P1-3P0 and [CI] 3P2-3P1 transitions. Results: We find an average value of {\beta} ~ 1.5 throughout Sh2-104, as well as a T dust difference between the photodissociation region (PDR, ~ 25 K) and the interior (~ 40 K) of the bubble. We recover the anti-correlation between {\beta} and dust temperature reported numerous times in the literature. The relative isotopologue abundances of CO appear to be enhanced above the standard ISM values, but the obtained value is very preliminary and is still affected by large uncertainties.

A Time-Evolving 3D Method Dedicated to the Reconstruction of Solar Plumes and Results Using Extreme Ultraviolet Data

An important issue in the tomographic reconstruction of the solar poles is the relatively rapid evolution of the polar plumes. We demonstrate that it is possible to take into account this temporal evolution in the reconstruction. The difficulty of this problem comes from the fact that we want a four-dimensional reconstruction (three spatial dimensions plus time) whereas we only have three-dimensional data (two-dimensional images plus time). To overcome this difficulty, we introduce a model that describes polar plumes as stationary objects whose intensity varies homogeneously with time. This assumption can be physically justified if one accepts the stability of the magnetic structure. This model leads to a bilinear inverse problem. We describe how to extend linear inversion methods to these kinds of problems. Studies of simulations show the reliability of our method. Results for SOHO/EIT data show that we can estimate the temporal evolution of polar plumes to improve the reconstruction of the solar poles from only one point of view. We expect further improvements from STEREO/EUVI data when the two probes will be separated by about 60°.

A Measure-Theoretic Variational Bayesian Algorithm for Large Dimensional Problems

In this paper we provide an algorithm adapted to variational Bayesian approximation. The main contribution is to transpose a classical iterative algorithm of optimization in the metric space of measures involved in Bayesian methodology. Once given the convergence properties of this algorithm, we consider its application to large dimensional inverse problems, especially for unsupervised reconstruction. The interest of our method is enhanced by its application to large dimensional linear inverse problems involving sparse objects. Finally, we provide simulation results. First we show the good numerical performances of our method compared to classical ones on a small example. Then we deal with a large dimensional dictionary learning problem.

Data Inversion for Over-Resolved Spectral Imaging in Astronomy

We present an original method for reconstructing a 3-D object having two spatial dimensions and one spectral dimension from data provided by the infrared slit spectrograph on board the Spitzer Space Telescope. During acquisition, the light flux is deformed by a complex process comprising four main elements (the telescope aperture, the slit, the diffraction grating, and optical distortion) before it reaches the 2-D sensor. The originality of this work lies in the physical modeling, in integral form, of this process of data formation in continuous variables. The inversion is also approached with continuous variables in a semi-parametric format decomposing the object into a family of Gaussian functions. The estimate is built in a deterministic regularization framework as the minimizer of a quadratic criterion. These specificities give our method the power to over-resolve. Its performance is illustrated using real and simulated data. We also present a study of the resolution showing a 1.5-fold improvement relative to conventional methods.

A gradient-like variational Bayesian algorithm

In this paper we provide a new algorithm allowing to solve a variational Bayesian issue which can be seen as a functional optimization problem. The main contribution of this paper is to transpose a classical iterative algorithm of optimization in the metric space of probability densities involved in the Bayesian methodology. Another important part is the application of our algorithm to a class of linear inverse problems where estimated quantities are assumed to be sparse. Finally, we compare performances of our method with classical ones on a tomographic problem. Preliminary results on a small dimensional example show that our new algorithm is faster than the classical approaches for the same quality of reconstruction.

Efficient Variational Bayesian Approximation Method Based on Subspace Optimization

Variational Bayesian approximations have been widely used in fully Bayesian inference for approximating an intractable posterior distribution by a separable one. Nevertheless, the classical variational Bayesian approximation (VBA) method suffers from slow convergence to the approximate solution when tackling large dimensional problems. To address this problem, we propose in this paper a more efficient VBA method. Actually, variational Bayesian issue can be seen as a functional optimization problem. The proposed method is based on the adaptation of subspace optimization methods in Hilbert spaces to the involved function space, in order to solve this optimization problem in an iterative way. The aim is to determine an optimal direction at each iteration in order to get a more efficient method. We highlight the efficiency of our new VBA method and demonstrate its application to image processing by considering an ill-posed linear inverse problem using a total variation prior. Comparisons with state of the art variational Bayesian methods through a numerical example show a notable improvement in computation time.

Herschel-SPIRE spectroscopy of the DR21 molecular cloud core

We present far-infrared spectra and maps of the DR21 molecular cloud core between 196 and 671 μm, using the Herschel-SPIRE spectrometer. Nineteen molecular lines originating from CO, 13 CO, HCO + and H2O, plus lines of [N ii] and [CI] were recorded, including several transitions not previously detected. The CO lines are excited in warm gas with Tkin ∼ 125 K and nH2 ∼ 7 × 10 4 cm −3 , CO column density N(CO) ∼ 3.5 × 10 18 cm −2 and a filling factor of ∼12%, and appear to trace gas associated with an outflow. The rotational temperature analysis incorporating observations from ground-based telescopes reveals an additional lower excitation CO compoment which has a temperature ∼78 K and N(CO) ∼ 4.5×10 21 cm −2 .