Image deblurring is an important topic in imaging science. In this review, we consider together fluorescence microscopy and optical/infrared astronomy because of two common features: in both cases the imaging system can be described, with a sufficiently good approximation, by a convolution operator, whose kernel is the so-called point-spread function (PSF); moreover, the data are affected by photon noise, described by a Poisson process. This statistical property of the noise, that is common also to emission tomography, is the basis of maximum likelihood and Bayesian approaches introduced in the mid eighties. From then on, a huge amount of literature has been produced on these topics. This review is a tutorial and a review of a relevant part of this literature, including some of our previous contributions. We discuss the mathematical modeling of the process of image formation and detection, and we introduce the so-called Bayesian paradigm that provides the basis of the statistical treatment of the problem. Next, we describe and discuss the most frequently used algorithms as well as other approaches based on a different description of the Poisson noise. We conclude with a review of other topics related to image deblurring such as boundary effect correction, space-variant PSFs, super-resolution, blind deconvolution and multiple-image deconvolution.
Context. The paper is about methods for multiple image deconvolution and their application to the reconstruction of the images acquired by the Fizeau interferometer, denoted LINC-NIRVANA, under development for the Large Binocular Telescope (LBT). The multiple images of the same target are obtained with different orientations of the baseline. Aims. To propose and develop a blind method for dealing with cases where no knowledge or very poor knowledge of the point spread functions (PSF) is available. Methods. The approach is an iterative one where object and PSFs are alternately updated using deconvolution methods related to the standard Richardson-Lucy method. It is basically an extension, to the multiple image case, of iterative blind deconvolution methods proposed in the case of a single image. Results. The method is applied to simulated LBT LINC-NIRVANA images and its limitations are investigated. The algorithm has been implemented in the module BLI of the software package AIRY (Astronomical Image Reconstruction in interferometrY), available under request. The preliminary results we have obtained are promising but an extensive simulation program is still necessary for a full understanding of the applicability of the method in the practice of the reconstruction of LINC-NIRVANA images.
Aims. We aim to improve blind deconvolution applied to post-adaptive-optics (AO) data by taking into account one of their basic characteristics, resulting from the necessarily partial AO correction: the Strehl ratio. Methods. We apply a Strehl constraint in the framework of iterative blind deconvolution (IBD) of post-AO near-infrared images simulated in a detailed end-to-end manner and considering a case that is as realistic as possible. Results. The results obtained clearly show the advantage of using such a constraint, from the point of view of both performance and stability, especially for poorly AO-corrected data. The proposed algorithm has been implemented in the freely-distributed and CAOS-based Software Package AIRY.
Context. The standard Richardson-Lucy method (RLM) does not work well in the deconvolution of astronomical images containing objects with very different angular scales and magnitudes. Therefore, modifications of RLM, applicable to this kind of objects, must be investigated. Aims. We recently proposed a regularization of RLM which provides satisfactory results in the case of particular test objects with high dynamic range. In this paper we extend this method to the case of multiple image deconvolution, having in mind application to the reconstruction of the images provided by Fizeau interferometers such as LINC-NIRVANA, the German-Italian beam combiner for the Large Binocular Telescope. Methods. RLM is an iterative method for the minimization of the Csiszár divergence, a problem equivalent to maximum likelihood estimation in the case of photon noise. In our approach, the problem is regularized by adding a suitable penalization term to the Csiszár divergence and an iterative method converging to the minimum of the resulting functional is derived from the so-called split gradient method (SGM).Results. The method is tested on a model of young binary star consisting of a core binary surrounded by a dusty circumbinary ring. The results are quite good in the case of exact knowledge of the point spread functions (PSF). However, in the case of approximate knowledge of the PSFs, the accuracy of the reconstruction depends on the difference of magnitude between the ring and the central binary.
LINC-NIRVANA (LN) is a Fizeau interferometer that will provide for the first time coherent images in the near-IR combining the beams from the two Large Binocular Telescope (LBT)arms, by adopting a Multi-Coniugate Adaptive Optics system (MCAO) that allows for atmospheric turbulence compensation. We applied a software for the simulation and the reconstruction of LN images (AIRY-LN, see Desiderá et al.1 this Conference) in two specific scientific cases: a relatively distant galaxy at redshift about 1 and a collimated jet from a Young Stellar Object (YSO). These two cases have been chosen to test the capability of LN in the observations of faint and small (1-2 arcsec) extragalactic objects and objects with diffuse emission and high dynamical range, respectively. A total of six images at different hour angles have been obtained for both cases. Using these simulated images, we obtained the final reconstructed images using the software package AIRY-LN. These images have been analyzed with the standard data reduction software (IRAF and IDL). Our analysis show that the reconstruction algorithm is fundamental to obtain a good reproduction of the original flux and morphology while the optimal number of iterations strongly depends on the scientific goal.
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