arXiv subjects

André Ferrari

Publications and source records attributed to André Ferrari.

30 records · Page 2Linked to original sources

arXiv2016

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 non-differentiable 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 $\ell_1$-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.

eess.SY↗

arXiv2016

Distributed multi-frequency image reconstruction for radio-interferometry

The advent of enhanced technologies in radio interferometry and the perspective of the SKA telescope bring new challenges in image reconstruction. One of these challenges is the spatio-spectral reconstruction of large (Terabytes) data cubes with high fidelity. This contribution proposes an alternative implementation of one such 3D prototype algorithm, MUFFIN (MUlti-Frequency image reconstruction For radio INterferometry), which combines spatial and spectral analysis priors. Using a recently proposed primal dual algorithm, this new version of MUFFIN allows a parallel implementation where computationally intensive steps are split by spectral channels. This parallelization allows to implement computationally demanding translation invariant wavelet transforms (IUWT), as opposed to the union of bases used previously. This alternative implementation is important as it opens the possibility of comparing these efficient dictionaries, and others, in spatio-spectral reconstruction. Numerical results show that the IUWT-based version can be successfully implemented at large scale with performances comparable to union of bases.

astro-ph.IM↗

arXiv2016

Multi-frequency image reconstruction for radio interferometry. A regularized inverse problem approach

We describe a "spatio-spectral" deconvolution algorithm for wide-band imaging in radio interferometry. In contrast with the existing multi-frequency reconstruction algorithms, the proposed method does not rely on a model of the sky-brightness spectral distribution. This non-parametric approach can be of particular interest for the new generation of low frequency radiotelescopes. The proposed solution formalizes the reconstruction problem as a convex optimization problem with spatial and spectral regularizations. The efficiency of this approach has been already proven for narrow-band image reconstruction and the present contribution can be considered as its extension to the multi-frequency case. Because the number of frequency bands multiplies the size of the inverse problem, particular attention is devoted to the derivation of an iterative large scale optimization algorithm. It is shown that the main computational bottleneck of the approach, which lies in the resolution of a linear system, can be efficiently overcome by a fully parallel implementation w.r.t. the frequencies, where each processor reconstructs a narrow-band image. All the other optimization steps are extremely fast. A parallel implementation of the algorithm in Julia is publicly available at https://github.com/andferrari. Preliminary simulations illustrate the performances of the method and its ability to reconstruct complex spatio-spectral structures.

astro-ph.IM↗

arXiv2015

Distributed image reconstruction for very large arrays in radio astronomy

Current and future radio interferometric arrays such as LOFAR and SKA are characterized by a paradox. Their large number of receptors (up to millions) allow theoretically unprecedented high imaging resolution. In the same time, the ultra massive amounts of samples makes the data transfer and computational loads (correlation and calibration) order of magnitudes too high to allow any currently existing image reconstruction algorithm to achieve, or even approach, the theoretical resolution. We investigate here decentralized and distributed image reconstruction strategies which select, transfer and process only a fraction of the total data. The loss in MSE incurred by the proposed approach is evaluated theoretically and numerically on simple test cases.

astro-ph.IM↗

arXiv2015

Large Scale 3D Image Reconstruction in Optical Interferometry

Astronomical optical interferometers (OI) sample the Fourier transform of the intensity distribution of a source at the observation wavelength. Because of rapid atmospheric perturbations, the phases of the complex Fourier samples (visibilities) cannot be directly exploited , and instead linear relationships between the phases are used (phase closures and differential phases). Consequently, specific image reconstruction methods have been devised in the last few decades. Modern polychromatic OI instruments are now paving the way to multiwavelength imaging. This paper presents the derivation of a spatio-spectral ("3D") image reconstruction algorithm called PAINTER (Polychromatic opticAl INTErferometric Reconstruction software). The algorithm is able to solve large scale problems. It relies on an iterative process, which alternates estimation of polychromatic images and of complex visibilities. The complex visibilities are not only estimated from squared moduli and closure phases, but also from differential phases, which help to better constrain the polychromatic reconstruction. Simulations on synthetic data illustrate the efficiency of the algorithm.

astro-ph.IM↗

arXiv2014

A graph Laplacian regularization for hyperspectral data unmixing

This paper introduces a graph Laplacian regularization in the hyperspectral unmixing formulation. The proposed regularization relies upon the construction of a graph representation of the hyperspectral image. Each node in the graph represents a pixel's spectrum, and edges connect spectrally and spatially similar pixels. The proposed graph framework promotes smoothness in the estimated abundance maps and collaborative estimation between homogeneous areas of the image. The resulting convex optimization problem is solved using the Alternating Direction Method of Multipliers (ADMM). A special attention is given to the computational complexity of the algorithm, and Graph-cut methods are proposed in order to reduce the computational burden. Finally, simulations conducted on synthetic data illustrate the effectiveness of the graph Laplacian regularization with respect to other classical regularizations for hyperspectral unmixing.

cs.CV↗

arXiv2014

PAINTER: a spatio-spectral image reconstruction algorithm for optical interferometry

Astronomical optical interferometers sample the Fourier transform of the intensity distribution of a source at the observation wavelength. Because of rapid perturbations caused by atmospheric turbulence, the phases of the complex Fourier samples (visibilities) cannot be directly exploited. Consequently, specific image reconstruction methods have been devised in the last few decades. Modern polychromatic optical interferometric instruments are now paving the way to multiwavelength imaging. This paper is devoted to the derivation of a spatio-spectral (3D) image reconstruction algorithm, coined PAINTER (Polychromatic opticAl INTErferometric Reconstruction software). The algorithm relies on an iterative process, which alternates estimation of polychromatic images and of complex visibilities. The complex visibilities are not only estimated from squared moduli and closure phases, but also differential phases, which helps to better constrain the polychromatic reconstruction. Simulations on synthetic data illustrate the efficiency of the algorithm and in particular the relevance of injecting a differential phases model in the reconstruction.

astro-ph.IM↗

arXiv2014

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.

stat.AP↗

arXiv2013

A normalized scaled gradient method to solve non-negativity and equality constrained linear inverse problem - Application to spectral mixture analysis

This paper addresses the problem of minimizing a convex cost function under non-negativity and equality constraints, with the aim of solving the linear unmixing problem encountered in hyperspectral imagery. This problem can be formulated as a linear regression problem whose regression coefficients (abundances) satisfy sum-to-one and positivity constraints. A normalized scaled gradient iterative method (NSGM) is proposed for estimating the abundances of the linear mixing model. The positivity constraint is ensured by the Karush Kuhn Tucker conditions whereas the sum-to-one constraint is fulfilled by introducing normalized variables in the algorithm. The convergence is ensured by a one-dimensional search of the step size. Note that NSGM can be applied to any convex cost function with non negativity and flux constraints. In order to compare the NSGM with the well-known fully constraint least squares (FCLS) algorithm, this latter is reformulated in term of a penalized function, which reveals its suboptimality. Simulations on synthetic data illustrate the performances of the proposed algorithm in comparison with other unmixing algorithms and, more particulary, demonstrate its efficiency when compared to the popular FCLS. Finally, results on real data are given.

math.OC↗

arXiv2007

The Strehl Ratio in Adaptive Optics Images: Statistics and Estimation

Statistical properties of the intensity in adaptive optics images are usually modeled with a Rician distribution. We study the central point of the image, where this model is inappropriate for high to very high correction levels. The central point is an important problem because it gives the Strehl ratio distribution. We show that the central point distribution can be modeled using a non-central Gamma distribution.

astro-ph↗

arXiv2007

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 wavefront 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.

astro-ph↗

arXiv2006

Analytical analysis of Lyot coronographs

We derive an analytical solution to the computation of the output of a Lyot coronagraph for a given complex amplitude on the pupil plane. This solution, which does not require any simplifying assumption, relies on an expansion of the entrance complex amplitude on a Zernike base. According to this framework, the main contribution of the paper is the expression of the response of the coronagraph to a single base function. This result is illustrated by a computer simulation which describes the classical effect of propagation of a tip-tilt error in a coronagraph.

astro-ph↗