André Ferrari

Total coronagraphic extinction of rectangular apertures using linear prolate apodizations

This paper presents a theoretical study of stellar coronagraphy with apodized entrance apertures. The study is restricted to a perfect telescope operating in space, and a monochromatic on-axis unresolved star. It is shown that linear prolate functions are the optimal apodizers for rectangular apertures in stellar coronagraphy. With the phase mask technique (Roddier & Roddier 1997), prolate functions can produce a total extinction of the star light. For Lyots coronagraphy, the extinction is not complete, but prolate apodizations lead to an optimal star residual intensity with surprising interesting properties: the residual star light and the planet enjoy the same apodized intensity pattern (but dierent dynamic) with the optimal light concentration. With this technique, very high rejection rates can be obtained for Lyots coronagraphy, with smaller mask sizes.

Speckle Noise and Dynamic Range in Coronagraphic Images

This paper is concerned with the theoretical properties of high-contrast coronagraphic images in the context of exoplanet searches. We derive and analyze the statistical properties of the residual starlight in coronagraphic images and describe the effect of a coronagraph on the speckle and photon noise. Current observations with coronagraphic instruments have shown that the main limitations to high-contrast imaging are due to residual quasi-static speckles. We tackle this problem in this paper and propose a generalization of our statistical model to include the description of static, quasi-static, and fast residual atmospheric speckles. The results provide insight into the effects on the dynamic range of wave front control, coronagraphy, active speckle reduction, and differential speckle calibration. The study is focused on ground-based imaging with extreme adaptive optics, but the approach is general enough to be applicable to space, with different parameters.

Bivariate Gamma Distributions for Image Registration and Change Detection

This paper evaluates the potential interest of using bivariate gamma distributions for image registration and change detection. The first part of this paper studies estimators for the parameters of bivariate gamma distributions based on the maximum likelihood principle and the method of moments. The performance of both methods are compared in terms of estimated mean square errors and theoretical asymptotic variances. The mutual information is a classical similarity measure which can be used for image registration or change detection. The second part of the paper studies some properties of the mutual information for bivariate gamma distributions. Image registration and change detection techniques based on bivariate gamma distributions are finally investigated. Simulation results conducted on synthetic and real data are very encouraging. Bivariate gamma distributions are good candidates allowing us to develop new image registration algorithms and new change detectors.

APODIZED PUPIL LYOT CORONAGRAPHS FOR ARBITRARY APERTURES. II. THEORETICAL PROPERTIES AND APPLICATION TO EXTREMELY LARGE TELESCOPES

We study the application of Lyot coronagraphy to future Extremely Large Telescopes (ELTs), showing that Apodized Pupil Lyot Coronagraphs enable high-contrast imaging for exoplanet detection and characterization with ELTs. We discuss the properties of the optimal pupil apodizers for this application (generalized prolate spheroidal functions). The case of a circular aperture telescope with a central obstruction is considered in detail, and we discuss the effects of primary mirror segmentation and secondary mirror support structures as a function of the occulting mask size. In most cases where inner working distance is critical, e.g., for exoplanet detection, these additional features do not alter the solutions derived with just the central obstruction, although certain applications such as quasar-host galaxy coronagraphic observations could benefit from designs that explicitly accomodate ELT spider geometries. We illustrate coronagraphic designs for several ELT geometries including ESO/OWL, the Thirty Mirror Telescope, the Giant Magellan Telescope, and describe numerical methods for generating these designs.

Interferometric apodization of rectangular apertures - Application to stellar coronagraphy

We describe the principle of an apodization technique for rectangular apertures that can be implemented using a Michelson or a Mach-Zender interferometer. Using several interferometers, any integer power of cosine functions can be obtained. The technique is considered for application to the Apodized Square Aperture (ASA) concept recently proposed by Nisenson & Papaliolios (2001). Simple analytic expressions for the Point Spread Functions of such apodized apertures are given. For a cosine to the power N apodization, the resulting focal plane amplitude is simply the sum of N + 1 weighted and shifted sine cardinal functions. The interest of such apodized apertures for coronagraphy is investigated. It appears that these apodization functions are very ecient provided that only a central part of the cosine-arch is used. Analytic expressions are derived for the residual amplitude left in an image of the aperture after the coronagraphic experiment. Best results are obtained with a cosine squared apodization.

Multitask Diffusion Adaptation Over Asynchronous Networks

The multitask diffusion LMS is an efficient strategy to simultaneously infer, in a collaborative manner, multiple parameter vectors. Existing works on multitask problems assume that all agents respond to data synchronously. In several applications, agents may not be able to act synchronously because networks can be subject to several sources of uncertainties such as changing topology, random link failures, or agents turning on and off for energy conservation. In this paper, we describe a model for the solution of multitask problems over asynchronous networks and carry out a detailed mean and mean-square error analysis. Results show that sufficiently small step-sizes can still ensure both stability and performance. Simulations and illustrative examples are provided to verify the theoretical findings.

Blind and Fully Constrained Unmixing of Hyperspectral Images

This paper addresses the problem of blind and fully constrained unmixing of hyperspectral images. Unmixing is performed without the use of any dictionary, and assumes that the number of constituent materials in the scene and their spectral signatures are unknown. The estimated abundances satisfy the desired sum-to-one and nonnegativity constraints. Two models with increasing complexity are developed to achieve this challenging task, depending on how noise interacts with hyperspectral data. The first one leads to a convex optimization problem and is solved with the alternating direction method of multipliers. The second one accounts for signal-dependent noise and is addressed with a reweighted least squares algorithm. Experiments on synthetic and real data demonstrate the effectiveness of our approach.

Proximal Multitask Learning Over Networks With Sparsity-Inducing Coregularization

In this work, we consider multitask learning problems where clusters of nodes are interested in estimating their own parameter vector. Cooperation among clusters is beneficial when the optimal models of adjacent clusters have a good number of similar entries. We propose a fully distributed algorithm for solving this problem. The approach relies on minimizing a global mean-square error criterion regularized by nondifferentiable terms to promote cooperation among neighboring clusters. A general diffusion forward-backward splitting strategy is introduced. Then, it is specialized to the case of sparsity promoting regularizers. A closed-form expression for the proximal operator of a weighted sum of ℓ1-norms is derived to achieve higher efficiency. We also provide conditions on the step-sizes that ensure convergence of the algorithm in the mean and mean-square error sense. Simulations are conducted to illustrate the effectiveness of the strategy.

Detection Tests Using Sparse Models, With Application to Hyperspectral Data

The problem of finding efficient methods for the detection of unknown sparse signals buried in noise is addressed. We present two detection tests adapted to sparse signals, based on the maximum a posteriori (MAP) estimate of the sparse vector of parameters. The first is the posterior density ratio test, which computes the ratio of the a posteriori distribution under each hypothesis of the data model. The second is a likelihood ratio test in which the MAP replaces the maximum likelihood (ML) estimate. The behaviors and the relative differences between these tests are investigated through a detailed study of their structural characteristics. The proposed approaches are compared to the generalized likelihood ratio test (GLR), showing successful results in the case of a simple model first and then for a model in which sparsity is promoted through the use of a highly redundant dictionary.

Statistical hypothesis testing with time-frequency surrogates to check signal stationarity

An operational framework is developed for testing stationarity relatively to an observation scale. The proposed method makes use of a family of stationary surrogates for defining the null hypothesis of stationarity. As a further contribution to the field, we demonstrate the strict-sense stationarity of surrogate signals and we exploit this property to derive the asymptotic distributions of their spectrogram and power spectral density. A statistical hypothesis testing framework is then proposed to check signal stationarity. Finally, some results are shown on a typical model of signals that can be thought of as stationary or nonstationary, depending on the observation scale used.