Exploiting spatial sparsity for multi-wavelength imaging in optical interferometry

Optical interferometers provide multiple wavelength measurements. In order to fully exploit the spectral and spatial resolution of these instruments, new algorithms for image reconstruction have to be developed. Early attempts to deal with multi-chromatic interferometric data have consisted in recovering a gray image of the object or independent monochromatic images in some spectral bandwidths. The main challenge is now to recover the full 3-D (spatio-spectral) brightness distribution of the astronomical target given all the available data. We describe a new approach to implement multi-wavelength image reconstruction in the case where the observed scene is a collection of point-like sources. We show the gain in image quality (both spatially and spectrally) achieved by globally taking into account all the data instead of dealing with independent spectral slices. This is achieved thanks to a regularization which favors spatial sparsity and spectral grouping of the sources. Since the objective function is not differentiable, we had to develop a specialized optimization algorithm which also accounts for non-negativity of the brightness distribution.Comment: This version has been accepted for publication in J. Opt. Soc. Am.

PeX 1. Multi-spectral expansion of residual speckles for planet detection

The detection of exoplanets in coronographic images is severely limited by residual starlight speckles. Dedicated post-processing can drastically reduce this "stellar leakage" and thereby increase the faintness of detectable exoplanets. Based on a multi-spectral series expansion of the diffraction pattern, we derive a multi-mode model of the residuals which can be exploited to estimate and thus remove the residual speckles in multi-spectral coronographic images. Compared to other multi-spectral processing methods, our model is physically grounded and is suitable for use in an (optimal) inverse approach. We demonstrate the ability of our model to correctly estimate the speckles in simulated data and demonstrate that very high contrasts can be achieved. We further apply our method to removing speckles from a real data cube obtained with the SPHERE IFS instrument.Comment: accepted for publication in MNRAS on 25th of August 2017, 17 pages, 15 figure

Image Reconstruction in Optical Interferometry

This tutorial paper describes the problem of image reconstruction from interferometric data with a particular focus on the specific problems encountered at optical (visible/IR) wavelengths. The challenging issues in image reconstruction from interferometric data are introduced in the general framework of inverse problem approach. This framework is then used to describe existing image reconstruction algorithms in radio interferometry and the new methods specifically developed for optical interferometry.Comment: accepted for publication in IEEE Signal Processing Magazin

Mixed models for longitudinal left-censored repeated measures

Longitudinal studies could be complicated by left-censored repeated measures. For example, in Human Immunodeficiency Virus infection, there is a detection limit of the assay used to quantify the plasma viral load. Simple imputation of the limit of the detection or of half of this limit for left-censored measures biases estimations and their standard errors. In this paper, we review two likelihood-based methods proposed to handle left-censoring of the outcome in linear mixed model. We show how to fit these models using SAS Proc NLMIXED and we compare this tool with other programs. Indications and limitations of the programs are discussed and an example in the field of HIV infection is shown

Holomorphic Approximation via Dolbeault Cohomology

The purpose of this paper is to study holomorphic approximation and approximation of $\bar\partial$-closed forms in complex manifolds of complex dimension $n\geq 1$. We consider extensions of the classical Runge theorem and the Mergelyan property to domains in complex manifolds for the smooth and the $L^2$ topology. We characterize the Runge or Mergelyan property in terms of certain Dolbeault cohomology groups and some geometric sufficient conditions are given

High dynamic range imaging with a single-mode pupil remapping system : a self-calibration algorithm for redundant interferometric arrays

The correction of the influence of phase corrugation in the pupil plane is a fundamental issue in achieving high dynamic range imaging. In this paper, we investigate an instrumental setup which consists in applying interferometric techniques on a single telescope, by filtering and dividing the pupil with an array of single-mode fibers. We developed a new algorithm, which makes use of the fact that we have a redundant interferometric array, to completely disentangle the astronomical object from the atmospheric perturbations (phase and scintillation). This self-calibrating algorithm can also be applied to any - diluted or not - redundant interferometric setup. On an 8 meter telescope observing at a wavelength of 630 nm, our simulations show that a single mode pupil remapping system could achieve, at a few resolution elements from the central star, a raw dynamic range up to 10^6; depending on the brightness of the source. The self calibration algorithm proved to be very efficient, allowing image reconstruction of faint sources (mag = 15) even though the signal-to-noise ratio of individual spatial frequencies are of the order of 0.1. We finally note that the instrument could be more sensitive by combining this setup with an adaptive optics system. The dynamic range would however be limited by the noise of the small, high frequency, displacements of the deformable mirror.Comment: 11 pages, 7 figures. Accepted for publication in MNRA