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The design of starshades, i.e. external occulters for stellar coronography, relies on the fast and precise computation of their associated diffraction patterns of incoming plane waves in the telescope aperture plane. We present here a method based on a polygonal approximation of the occulter's shape, that allows fast computation of their diffraction patterns in the Fresnel approximation, without aliasing artefacts. It is competitive with respect to methods based on direct 2D Fourier transforms, or Boundary Diffraction Wave algorithms., Comment: 8 pages, 4 figures

Solar and stellar externally occulted coronagraphs share similar concepts, but are actually very different because of geometric characteristics. Solar occulters were first developed with a simple geometric model of diffraction perpendicular to the occulter edges. We apply this mere approach to starshades, and introduce a simple shifted circular integral of the occulter which allows to illustrate the influence of the number of petals on the extent of the deep central dark zone. We illustrate the reasons for the presence of an internal coronagraph in the solar case and its absence in the exoplanet case., Comment: 8 pages, 10 figures

The automatic detection of changes or anomalies between multispectral and hyperspectral images collected at different time instants is an active and challenging research topic. To effectively perform change-point detection in multitemporal images, it is important to devise techniques that are computationally efficient for processing large datasets, and that do not require knowledge about the nature of the changes. In this paper, we introduce a novel online framework for detecting changes in multitemporal remote sensing images. Acting on neighboring spectra as adjacent vertices in a graph, this algorithm focuses on anomalies concurrently activating groups of vertices corresponding to compact, well-connected and spectrally homogeneous image regions. It fully benefits from recent advances in graph signal processing to exploit the characteristics of the data that lie on irregular supports. Moreover, the graph is estimated directly from the images using superpixel decomposition algorithms. The learning algorithm is scalable in the sense that it is efficient and spatially distributed. Experiments illustrate the detection and localization performance of the method.

Change-points in time series data are usually defined as the time instants at which changes in their properties occur. Detecting change-points is critical in a number of applications as diverse as detecting credit card and insurance frauds, or intrusions into networks. Recently the authors introduced an online kernel-based change-point detection method built upon direct estimation of the density ratio on consecutive time intervals. This paper further investigates this algorithm, making improvements and analyzing its behavior in the mean and mean square sense, in the absence and presence of a change point. These theoretical analyses are validated with Monte Carlo simulations. The detection performance of the algorithm is illustrated through experiments on real-world data and compared to state of the art methodologies.

Detecting abrupt changes in streaming graph signals is relevant in a variety of applications ranging from energy and water supplies, to environmental monitoring. In this paper, we address this problem when anomalies activate localized groups of nodes in a network. We introduce an online change-point detection algorithm, which is fully distributed across nodes to monitor large-scale dynamic networks. We analyze the detection statistics for controlling the probability of a global type 1 error. Finally we illustrate the detection and localization performance with simulated data.

This article investigates the quality of the estimator of the linear Monge mapping between distributions. We provide the first concentration result on the linear mapping operator and prove a sample complexity of $n^{-1/2}$ when using empirical estimates of first and second order moments. This result is then used to derive a generalization bound for domain adaptation with optimal transport. As a consequence, this method approaches the performance of theoretical Bayes predictor under mild conditions on the covariance structure of the problem. We also discuss the computational complexity of the linear mapping estimation and show that when the source and target are stationary the mapping is a convolution that can be estimated very efficiently using fast Fourier transforms. Numerical experiments reproduce the behavior of the proven bounds on simulated and real data for mapping estimation and domain adaptation on images.

In the era of big data, radio astronomical image reconstruction algorithms are challenged to estimate clean images given limited computing resources and time. This article is driven by the need for large scale image reconstruction for the future Square Kilometre Array (SKA), which will become in the next decades the largest low and intermediate frequency radio telescope in the world. This work proposes a scalable wideband deconvolution algorithm called MUFFIN, which stands for "MUlti Frequency image reconstruction For radio INterferometry". MUFFIN estimates the sky images in various frequency bands given the corresponding dirty images and point spread functions. The reconstruction is achieved by minimizing a data fidelity term and joint spatial and spectral sparse analysis regularization terms. It is consequently non-parametric w.r.t. the spectral behaviour of radio sources. MUFFIN algorithm is endowed with a parallel implementation and an automatic tuning of the regularization parameters, making it scalable and well suited for big data applications such as SKA. Comparisons between MUFFIN and the state-of-the-art wideband reconstruction algorithm are provided.

In radio astronomy, accurate calibration is of crucial importance for the new generation of radio interferometers. More specifically, because of the potential presence of outliers which affect the measured data, robustness needs to be ensured. On the other hand, calibration is improved by taking advantage of these new instruments and exploiting the known structure of parameters of interest across frequency. Therefore, we propose in this paper an iterative robust multi-frequency calibration algorithm based on a distributed and consensus optimization scheme which aims to estimate the complex gains of the receivers and the directional perturbations caused by the ionosphere. Numerical simulations reveal that the proposed distributed calibration technique outperforms the conventional non-robust algorithm and per-channel calibration.

In this paper, we aim to design robust estimation techniques based on the compound-Gaussian (CG) process and adapted for calibration of radio interferometers. The motivation beyond this is due to the presence of outliers leading to an unrealistic traditional Gaussian noise assumption. Consequently, to achieve robustness, we adopt a maximum a posteriori (MAP) approach which exploits Bayesian statistics and follows a sequential updating procedure here. The proposed algorithm is applied in a multi-frequency scenario in order to enhance the estimation and correction of perturbation effects. Numerical simulations assess the performance of the proposed algorithm for different noise models, Student's t, K, Laplace, Cauchy and inverse-Gaussian compound-Gaussian distributions w.r.t. the classical non-robust Gaussian noise assumption.

This paper investigates calibration of sensor arrays in the radio astronomy context. Current and future radio telescopes require computationally efficient algorithms to overcome the new technical challenges as large collecting area, wide field of view and huge data volume. Specifically, we study the calibration of radio interferometry stations with significant direction dependent distortions. We propose an iterative robust calibration algorithm based on a relaxed maximum likelihood estimator for a specific context: i) observations are affected by the presence of outliers and ii) parameters of interest have a specific structure depending on frequency. Variation of parameters across frequency is addressed through a distributed procedure, which is consistent with the new radio synthesis arrays where the full observing bandwidth is divided into multiple frequency channels. Numerical simulations reveal that the proposed robust distributed calibration estimator outperforms the conventional non-robust algorithm and/or the mono-frequency case.

We present a new formulation of a family of proximity operators that generalize the projector step for phase retrieval. These proximity operators for noisy intensity measurements can replace the classical "noise free" projection in any projection-based algorithm. They are derived from a maximum likelihood formulation and admit closed form solutions for both the Gaussian and the Poisson cases. In addition, we extend these proximity operators to undersampled intensity measurements. To assess their performance, these operators are exploited in a classical Gerchberg Saxton algorithm. We present numerical experiments showing that the reconstructed complex amplitudes with these proximity operators perform always better than using the classical intensity projector while their computational overhead is moderate.

Image deblurring is an economic way to reduce certain degradations (blur and noise) in acquired images. Thus, it has become essential tool in high resolution imaging in many applications, e.g., astronomy, microscopy or computational photography. In applications such as astronomy and satellite imaging, the size of acquired images can be extremely large (up to gigapixels) covering wide field-of-view suffering from shift-variant blur. Most of the existing image deblurring techniques are designed and implemented to work efficiently on centralized computing system having multiple processors and a shared memory. Thus, the largest image that can be handle is limited by the size of the physical memory available on the system. In this paper, we propose a distributed nonblind image deblurring algorithm in which several connected processing nodes (with reasonable computational resources) process simultaneously different portions of a large image while maintaining certain coherency among them to finally obtain a single crisp image. Unlike the existing centralized techniques, image deblurring in distributed fashion raises several issues. To tackle these issues, we consider certain approximations that trade-offs between the quality of deblurred image and the computational resources required to achieve it. The experimental results show that our algorithm produces the similar quality of images as the existing centralized techniques while allowing distribution, and thus being cost effective for extremely large images., Comment: 16 pages, 10 figures, submitted to IEEE Trans. on Image Processing

As the world's largest radio telescope, the Square Kilometer Array (SKA) will provide radio interferometric data with unprecedented detail. Image reconstruction algorithms for radio interferometry are challenged to scale well with TeraByte image sizes never seen before. In this work, we investigate one such 3D image reconstruction algorithm known as MUFFIN (MUlti-Frequency image reconstruction For radio INterferometry). In particular, we focus on the challenging task of automatically finding the optimal regularization parameter values. In practice, finding the regularization parameters using classical grid search is computationally intensive and nontrivial due to the lack of ground- truth. We adopt a greedy strategy where, at each iteration, the optimal parameters are found by minimizing the predicted Stein unbiased risk estimate (PSURE). The proposed self-tuned version of MUFFIN involves parallel and computationally efficient steps, and scales well with large- scale data. Finally, numerical results on a 3D image are presented to showcase the performance of the proposed approach.

We consider distributed multitask learning problems over a network of agents where each agent is interested in estimating its own parameter vector, also called task, and where the tasks at neighboring agents are related according to a set of linear equality constraints. Each agent possesses its own convex cost function of its parameter vector and a set of linear equality constraints involving its own parameter vector and the parameter vectors of its neighboring agents. We propose an adaptive stochastic algorithm based on the projection gradient method and diffusion strategies in order to allow the network to optimize the individual costs subject to all constraints. Although the derivation is carried out for linear equality constraints, the technique can be applied to other forms of convex constraints. We conduct a detailed mean-square-error analysis of the proposed algorithm and derive closed-form expressions to predict its learning behavior. We provide simulations to illustrate the theoretical findings. Finally, the algorithm is employed for solving two problems in a distributed manner: a minimum-cost flow problem over a network and a space-time varying field reconstruction problem.

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.

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.

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., Comment: Sensor Array and Multichannel Signal Processing Workshop (SAM), 2014 IEEE 8th, Jun 2014, Coruna, Spain. 2014

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., Comment: 16 pages, 8 figures, SPARCS 2015

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., Comment: EUSIPCO, Aug 2015, NICE, France

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 work, 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. The framework is applied to a particular application involving spectral sensing.

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.

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., Comment: 12 pages, 10 figures, http://www.opticsinfobase.org/submit/review/copyright_permissions.cfm

In optical interferometry, the visibility squared modulus are generally assumed to follow a Gaussian distribution and to be independent of each other. A quantitative analysis of the relevance of such assumptions is important to help improving the exploitation of existing and upcoming multi-wavelength interferometric instruments. Analyze the statistical behaviour of both the absolute and the colour-differential squared visibilities: distribution laws, correlations and cross-correlations between different baselines. We use observations of stellar calibrators obtained with AMBER instrument on VLTI in different instrumental and observing configurations, from which we extract the frame-by-frame transfer function. Statistical hypotheses tests and diagnostics are then systematically applied. For both absolute and differential squared visibilities and under all instrumental and observing conditions, we find a better fit for the Student distribution than for the Gaussian, log-normal and Cauchy distributions. We find and analyze clear correlation effects caused by atmospheric perturbations. The differential squared visibilities allow to keep a larger fraction of data with respect to selected absolute squared visibilities and thus benefit from reduced temporal dispersion, while their distribution is more clearly characterized. The frame selection based on the criterion of a fixed SNR value might result in either a biased sample of frames or in a too severe selection., Comment: A&A, 13 pages and 9 figures

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.

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.

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., Comment: 31 pages, 18 figures

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., Comment: 8 pages, 5 figures

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.