Many blind deconvolution algorithms have been proposed for image deblurring when the instrumental point spread function (PSF) is unknown. Blind deconvolution can be stated as an inverse problem whose unknowns are the object of interest and the PSF. In that case, the direct model is bilinear and has an intrinsic scaling degeneracy: scaling one of the components can be compensated by inversely scaling the other one. Provided that homogeneous regularization functions are chosen for the object and for the PSF, the scaling degeneracy of the direct model can be exploited to reduce the number of hyper-parameters in the problem. Using this property, we propose an instance of a blind deconvolution algorithm that amounts to alternately estimating and scaling the two components of the bilinear model. Our algorithm is insensitive to the scaling of the initial estimate of the component (PSF or object) used to start the iterations. We show that this yields much faster convergence and, in practice, reduces the odds of being trapped in a bad local minimum. These features make our algorithm suitable for being embedded into a simple procedure to automatically tune the remaining hyper-parameter(s) and obtain a fully unsupervised method. We also propose a homogeneous version of an edge-preserving regularization to be used by our algorithm. Using Stein's Unbiased Risk Estimator (SURE) as a criterion to automatically tune the hyper-parameter(s), we assess the advantages of our algorithm for empirical astronomical images compared to other methods.
The FRiM fractal operator belongs to a family of operators, called ASAP, defined by an ordered selection of nearest neighbors. This generalization provides means to improve upon the good properties of FRiM. We propose a fast algorithm to build an ASAP operator mimicking the fractal structure of FRiM for pupils of any size and geometry and to learn the sparse coefficients from empirical data. We empirically show the good approximation by ASAP of correlated statistics and the benefits of ASAP for solving phase restoration problems.
To better understand the phenomena which take place during the formation and evolution of substellar objects, it is necessary to have access to their spectra. For that purpose, the SPHERE-IRDIS long-slit spectroscopy mode, allied with extreme adaptive optics and coronagraphy, has been designed to spectrally characterize substellar objects in the near-infrared (J, H and K bands). Residual aberrations are however responsible for stellar leaks in the form of dispersed speckles that are much brighter than the spectrum of the faint companion. Post-processing methods are thus required to extract the companion spectrum. Most existing methods consist in first subtracting the stellar contribution from the data and then measuring the companion spectrum in the residuals. We are developing a novel approach, named EXOSPEC and based on the inverse problems framework, which jointly estimates the two contributions; that of the star and that of the companion. Exospec exploits the differences of behavior of their spatio-spectral distributions in the data in order to disentangle them. The parameters of the instrumental model, which is a critical part of the approach, are refined by means of self-calibration directly from the science data. Other parameters of the problem are automatically tuned, leading to a fully unsupervised method. Compared to current methods, EXOSPEC is able to extract companion spectra with less contamination by the stellar leaks and succeeds in harder cases (e.g., closer to the mask). The benefits of our approach is demonstrated on real datasets.
We recently proposed REXPACO, an algorithm for imaging circumstellar environments from high-contrast angular differential imaging (ADI) data. In the context of high-contrast imaging where the signal of interest is largely dominated by a nuisance term due to the stellar light leakages and the noise, our algorithm amounts to jointly estimating the object of interest and the statistics (mean and covariance matrix) of the nuisance component. In this contribution, we first extend the REXPACO algorithm by refining the statistical model of the nuisance component it embeds. Capitalizing on the improved robustness of this new method named robust REXPACO, we then show how it can be modified to deal with angular plus spectral differential imaging (ASDI) datasets. We apply our methods on several ADI and ASDI datasets from the IRDIS and IFS imagers of the VLT/SPHERE instrument and we show that the proposed algorithms significantly reduce the typical artifacts produced by state-of-the-art algorithms. By also taking into account the instrumental point spread function (PSF), our algorithms yield a deblurred estimate of the object of interest without the artifacts observed with other methods.
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