A. La Camera

The study of an iterative method for the reconstruction of images corrupted by Poisson and Gaussian noise

In 1993, Snyder et al investigated the maximum-likelihood (ML) approach to the deconvolution of images acquired by a charge-coupled-device camera and proved that the iterative method proposed by Llacer and Nunez in 1990 can be derived from the expectation-maximization method of Dempster et al for the solution of ML problems. The utility of the approach was shown on the reconstruction of images of the Hubble space Telescope. This problem deserves further investigation because it can be important in the deconvolution of images of faint objects provided by next-generation ground-based telescopes that will be characterized by large collecting areas and advanced adaptive optics. In this paper, we first prove the existence of solutions of the ML problem by investigating the properties of the negative log of the likelihood function. Next, we show that the iterative method proposed by the above-mentioned authors is a scaled gradient method for the constrained minimization of this function in the closed and convex cone of the non-negative vectors and that, if it is convergent, the limit is a solution of the constrained ML problem. Moreover, by looking for the asymptotic behavior in the regime of high numbers of photons, we find an approximation that, as proved by numerical experiments, works well for any number of photons, thus providing an efficient implementation of the algorithm. In the case of image deconvolution, we also extend the method to take into account boundary effects and multiple images of the same object. The approximation proposed in this paper is tested on a few numerical examples.

A convergent blind deconvolution method for post-adaptive-optics astronomical imaging

In this paper, we propose a blind deconvolution method which applies to data perturbed by Poisson noise. The objective function is a generalized Kullback–Leibler (KL) divergence, depending on both the unknown object and unknown point spread function (PSF), without the addition of regularization terms; constrained minimization, with suitable convex constraints on both unknowns, is considered. The problem is non-convex and we propose to solve it by means of an inexact alternating minimization method, whose global convergence to stationary points of the objective function has been recently proved in a general setting. The method is iterative and each iteration, also called outer iteration, consists of alternating an update of the object and the PSF by means of a fixed number of iterations, also called inner iterations, of the scaled gradient projection (SGP) method. Therefore, the method is similar to other proposed methods based on the Richardson–Lucy (RL) algorithm, with SGP replacing RL. The use of SGP has two advantages: first, it allows one to prove global convergence of the blind method; secondly, it allows the introduction of different constraints on the object and the PSF. The specific constraint on the PSF, besides non-negativity and normalization, is an upper bound derived from the so-called Strehl ratio (SR), which is the ratio between the peak value of an aberrated versus a perfect wavefront. Therefore, a typical application, but not a unique one, is to the imaging of modern telescopes equipped with adaptive optics systems for the partial correction of the aberrations due to atmospheric turbulence. In the paper, we describe in detail the algorithm and we recall the results leading to its convergence. Moreover, we illustrate its effectiveness by means of numerical experiments whose results indicate that the method, pushed to convergence, is very promising in the reconstruction of non-dense stellar clusters. The case of more complex astronomical targets is also considered, but in this case regularization by early stopping of the outer iterations is required. However, the proposed method, based on SGP, allows generalization to the case of differentiable regularization terms added to the KL divergence, even if this generalization is outside the scope of this paper.

Imaging with LINC-NIRVANA, the Fizeau interferometer of the Large Binocular Telescope: state of the art and open problems

LINC-NIRVANA (LN) is the Fizeau interferometer of the Large Binocular Telescope which consists of two 8.4 m mirrors with a center-to-center distance of 14.4 m, hence providing a maximum path of 22.8 m in the direction of the baseline joining the two centers. LN is a true imager since interference occurs in the focal plane and not in the aperture plane as with essentially all the existing interferometers. However, an LN image is characterized by an anisotropic resolution: that of a 22.8 m mirror in the direction of the baseline and that of a 8.4 m mirror in the orthogonal direction. In order to obtain a unique image with a high and isotropic resolution, several images must be detected with different orientations of the baseline and suitably processed. Therefore, the instrument will routinely require the use of image reconstruction methods for providing astronomical images with unprecedented resolution, in principle ten times the resolution of the Hubble Space Telescope. This review concerns the image reconstruction problem for LN and is based essentially on our work. After a description of the main features of the telescope and of the interferometer, it contains a discussion of the problem and of the approximations introduced in its formulation. In short, it is reduced to multiple-image deconvolution with Poisson data. Similarity with the image reconstruction problem in emission tomography is stressed and utilized for introducing suitable iterative reconstruction methods. These methods are extended to regularized versions of the problem. Efficiency is another important issue because the size of LN images is of the order of 4.2 megapixels; therefore, acceleration methods are also discussed. All methods are tested on synthetic images because, even if the instrument is in an advanced stage of realization, it will be presumably operative in 2014. The algorithms of the proposed image reconstruction methods are implemented in the Software Package AIRY (astronomical image restoration in interferometry), which can be downloaded from http://www.airyproject.eu. AIRY is designed for simulation and subsequent reconstruction of LN images. A discussion of the several specific problems that must still be solved for obtaining accurate and efficient reconstructions is inserted at the end of this review.

Advances in the reconstruction of LBT LINC-NIRVANA images

Context. LINC-NIRVANA, the Fizeau interferometer of the Large Binocular Telescope (LBT), will require routine use of image reconstruction methods for data reduction. To this purpose our group has already developed the software package AIRY (Astronomical Image Restoration in interferometrY). Aims. Observations of a target, with different orientations of the baseline of LINC-NIRVANA, will provide images with different orientations with respect to the CCD camera. This rotation effect was not taken into account in our previous work. Therefore in this paper we propose a method able to compensate for the rotation of the field of view. Moreover we investigate acceleration techniques for reducing the computational burden of multiple image deconvolution. Methods. The basic method is a suitable modification of the Richardson-Lucy algorithm, also implementing an approach we proposed for reducing boundary effects. Acceleration techniques, proposed by Biggs & Andrews, are extended and applied to this new algorithm. Finally a method for estimating the unknown point spread function (PSF) by extracting and extrapolating the image of a reference star is developed and implemented. Results. The method introduced for compensating object rotation and reducing boundary effects, as well as its accelerated versions, are tested on simulated LINC-NIRVANA images, using the VLT image of the Crab Nebula as test object. The results are very promising. Moreover the method for PSFs extraction is tested on simulated images, derived from the LBT image of the galaxy NGC 6946 and obtained by convolving this image with PSFs computed by means of the numerical code LOST (Layer Oriented Simulation Tool).

Sub-0.1′′ optical imaging of the Z CMa jets with SPHERE/ZIMPOL

Crucial information on the mass accretion-ejection in young stars can be obtained from high spatial resolution images of jets in sources with recurrent accretion outbursts. Using the SPHERE/ZIMPOL instrument, we observed the young binary Z CMa that is composed of a Herbig Be star and a FUor object, both driving a jet. We analyse the structure of the two jets in relation with previous accretion events observed in this target. We obtained optical images in the Halpha and OI 6300A lines at the unprecedented angular resolution of ~0.03 arcsec, on which we have performed both continuum subtraction and deconvolution, thereby deriving results that are consistent with each other. Our images reveal extended emission from both sources: a fairly compact and poorly collimated emission SW of the Herbig component and an extended collimated and precessing jet from the FUor component. The compact emission from the Herbig star is compatible with a wide-angle wind and is possibly connected to the recent outburst events shown by this component. The FUor jet is traced down to 70 mas (80 AU) from the source and is highly collimated with a width of 26-48 AU at distances 100-200 AU, which is similar to the width of jets from T Tauri stars. This strongly suggests that the same magneto-centrifugal jet-launching mechanism also operates in FUors. The observed jet wiggle can be modelled as originating from an orbital motion with a period of 4.2 yr around an unseen companion with mass between 0.48 and 1 Msun. The jet mass loss rate Mloss was derived from the OI luminosity and is in the range 1E-8 and 1E-6 Msun/yr. This is the first direct Mloss measurement from a jet in a FUor. If we assume previous Macc estimates obtained through modelling of the accretion disk, the derived range of Mloss would imply a very low mass-ejection efficiency (Mloss/Macc < 0.02), which is lower than that typical of T Tauri stars.

A blind deconvolution method for ground based telescopes and Fizeau interferometers

Abstract In the case of ground-based telescopes equipped with adaptive optics systems, the point spread function (PSF) is only poorly known or completely unknown. Moreover, an accurate modeling of the PSF is in general not available. Therefore in several imaging situations the so-called blind deconvolution methods, aiming at estimating both the scientific target and the PSF from the detected image, can be useful. A blind deconvolution problem is severely ill-posed and, in order to reduce the extremely large number of possible solutions, it is necessary to introduce sensible constraints on both the scientific target and the PSF. In a previous paper we proposed a sound mathematical approach based on a suitable inexact alternating minimization strategy for minimizing the generalized Kullback–Leibler divergence, assuring global convergence. In the framework of this method we showed that an important constraint on the PSF is the upper bound which can be derived from the knowledge of its Strehl ratio. The efficacy of the approach was demonstrated by means of numerical simulations. In this paper, besides improving the previous approach by the use of a further constraint on the unknown scientific target, we extend it to the case of multiple images of the same target obtained with different PSFs. The main application we have in mind is to Fizeau interferometry. As it is known this is a special feature of the Large Binocular Telescope (LBT). Of the two expected interferometers for LBT, one, LINC-NIRVANA, is forthcoming while the other, LBTI, is already operating and has provided the first Fizeau images, demonstrating the possibility of reaching the resolution of a 22.8xa0m telescope. Therefore the extension of our blind method to this imaging modality seems to be timely. The method is applied to realistic simulations of imaging both by single mirrors and Fizeau interferometers. Successes and failures of the method in the imaging of stellar fields are demonstrated in simple cases. These preliminary results look promising at least in specific situations. The IDL code of the proposed method is available on request and will be included in the forthcoming version of the Software Package AIRY (v.6.1).

Fizeau interferometric imaging of Io volcanism with LBTI/LMIRcam

The Large Binocular Telescope (LBT) houses two 8.4-meter mirrors separated by 14.4 meters on a common mount. Coherent combination of these two AO-corrected apertures via the LBT Interferometer (LBTI) produces Fizeau interferometric images with a spatial resolution equivalent to that of a 22.8-meter telescope and the light- gathering power of single 11.8-meter mirror. Capitalizing on these unique capabilities, we used LBTI/LMIRcam to image thermal radiation from volcanic activity on the surface of Io at M-Band (4.8 μm) over a range of parallactic angles. At the distance of Io, the M-Band resolution of the interferometric baseline corresponds to a physical distance of ~135 km, enabling high-resolution monitoring of Io volcanism such as ares and outbursts inaccessible from other ground-based telescopes operating in this wavelength regime. Two deconvolution routines are used to recover the full spatial resolution of the combined images, resolving at least sixteen known volcanic hot spots. Coupling these observations with advanced image reconstruction algorithms demonstrates the versatility of Fizeau interferometry and realizes the LBT as the first in a series of extremely large telescopes.

The HH34 outflow as seen in [Fe ii] 1.64 μm by LBT-LUCI

Dense atomic jets from young stars copiously emit in [FeII] IR lines, which can, therefore, be used to trace the immediate environments of embedded protostars. We want to investigate the morphology of the bright [FeII] 1.64um line in the jet of the source HH34 IRS and compare it with the most commonly used optical tracer [SII]. We analyse a 1.64um narrow-band filter image obtained with the Large Binocular Telescope (LBT) LUCI instrument, which covers the HH34 jet and counterjet. A Point Spread Function (PSF) deconvolution algorithm was applied to enhance spatial resolution and make the IR image directly comparable to a [SII] HST image of the same source. The [FeII] emission is detected from both the jet, the (weak) counter-jet, and from the HH34-S and HH34-N bow shocks. The deconvolved image allows us to resolve jet knots close to about 1arcsec from the central source. The morphology of the [FeII] emission is remarkably similar to that of the [SII] emission, and the relative positions of [FeII] and [SII] peaks are shifted according to proper motion measurements, which were previously derived from HST images. An analysis of the [FeII]/[SII] emission ratio shows that Fe gas abundance is much lower than the solar value with up to 90% of Fe depletion in the inner jet knots. This confirms previous findings on dusty jets, where shocks are not efficient enough to remove refractory species from grains.

A method for space-variant deblurring with application to adaptive optics imaging in astronomy

Context. Images from adaptive optics systems are generally affected by significant distortions of the point spread functio n (PSF) across the field of view, depending on the position of natural and artificial guide stars. Image reduction techniques circ umventing or mitigating these effects are important tools to take full advantage of the scient ific information encoded in AO images. Aims. The aim of this paper is to propose a method for the deblurring of the astronomical image, given a set of samples of the space-variant PSF. Methods. The method is based on a partitioning of the image domain into regions of isoplanatism and on applying suitable deconvolution methods with boundary effects correction to each region. Results. The effectiveness of the boundary effects correction is proved. Moreover, the criterion for exte nding the disjoint sections to partially overlapping sections is validated. The method is applied to simulated images of a stellar system characterized by a spatially variable PSF. We obtain good photometric quality, and therefore good science quality, by performing aperture photometry on the deblurred images. The proposed method is implemented in IDL in the Software Package “Patch”, which is available on http://www.airyproject.eu.

Imaging with LINC-NIRVANA

The basic problem of LINC-NIRVANA (LN) imaging is to combine the different images for getting a single image, possibly with a resolution close to that of a 22.8 m mirror in all directions. This result can be hardly reached in practice because it depends on the level and uniformity of the adaptive optics (AO) correction and on the declination of the scientific target, controlling the orientations of the baseline that can be used during its observation. In this article, we give a brief introduction to this problem. It can be solved by iterative methods related to the well-known Richardson-Lucy (RL) algorithm. Since RL is a particular case of the maximum likelihood method introduced by Shepp and Vardi in emission tomography and denoted expectation maximization (EM), improvements of EM, proposed in the field of medical imaging can be applied to LN.