Astronomical Data Analysis and Sparsity: from Wavelets to Compressed Sensing

Wavelets have been used extensively for several years now in astronomy for many purposes, ranging from data filtering and deconvolution, to star and galaxy detection or cosmic ray removal. More recent sparse representations such ridgelets or curvelets have also been proposed for the detection of anisotropic features such cosmic strings in the cosmic microwave background. We review in this paper a range of methods based on sparsity that have been proposed for astronomical data analysis. We also discuss what is the impact of Compressed Sensing, the new sampling theory, in astronomy for collecting the data, transferring them to the earth or reconstructing an image from incomplete measurements.Comment: Submitted. Full paper will figures available at http://jstarck.free.fr/IEEE09_SparseAstro.pd

Sparsity and adaptivity for the blind separation of partially correlated sources

Blind source separation (BSS) is a very popular technique to analyze multichannel data. In this context, the data are modeled as the linear combination of sources to be retrieved. For that purpose, standard BSS methods all rely on some discrimination principle, whether it is statistical independence or morphological diversity, to distinguish between the sources. However, dealing with real-world data reveals that such assumptions are rarely valid in practice: the signals of interest are more likely partially correlated, which generally hampers the performances of standard BSS methods. In this article, we introduce a novel sparsity-enforcing BSS method coined Adaptive Morphological Component Analysis (AMCA), which is designed to retrieve sparse and partially correlated sources. More precisely, it makes profit of an adaptive re-weighting scheme to favor/penalize samples based on their level of correlation. Extensive numerical experiments have been carried out which show that the proposed method is robust to the partial correlation of sources while standard BSS techniques fail. The AMCA algorithm is evaluated in the field of astrophysics for the separation of physical components from microwave data.Comment: submitted to IEEE Transactions on signal processin

Unsupervised feature-learning for galaxy SEDs with denoising autoencoders

With the increasing number of deep multi-wavelength galaxy surveys, the spectral energy distribution (SED) of galaxies has become an invaluable tool for studying the formation of their structures and their evolution. In this context, standard analysis relies on simple spectro-photometric selection criteria based on a few SED colors. If this fully supervised classification already yielded clear achievements, it is not optimal to extract relevant information from the data. In this article, we propose to employ very recent advances in machine learning, and more precisely in feature learning, to derive a data-driven diagram. We show that the proposed approach based on denoising autoencoders recovers the bi-modality in the galaxy population in an unsupervised manner, without using any prior knowledge on galaxy SED classification. This technique has been compared to principal component analysis (PCA) and to standard color/color representations. In addition, preliminary results illustrate that this enables the capturing of extra physically meaningful information, such as redshift dependence, galaxy mass evolution and variation over the specific star formation rate. PCA also results in an unsupervised representation with physical properties, such as mass and sSFR, although this representation separates out. less other characteristics (bimodality, redshift evolution) than denoising autoencoders.Comment: 11 pages and 15 figures. To be published in A&

NESTA: A Fast and Accurate First-order Method for Sparse Recovery

Accurate signal recovery or image reconstruction from indirect and possibly undersampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by recent breakthroughs in the development of novel first-order methods in convex optimization, most notably Nesterov's smoothing technique, this paper introduces a fast and accurate algorithm for solving common recovery problems in signal processing. In the spirit of Nesterov's work, one of the key ideas of this algorithm is a subtle averaging of sequences of iterates, which has been shown to improve the convergence properties of standard gradient-descent algorithms. This paper demonstrates that this approach is ideally suited for solving large-scale compressed sensing reconstruction problems as 1) it is computationally efficient, 2) it is accurate and returns solutions with several correct digits, 3) it is flexible and amenable to many kinds of reconstruction problems, and 4) it is robust in the sense that its excellent performance across a wide range of problems does not depend on the fine tuning of several parameters. Comprehensive numerical experiments on realistic signals exhibiting a large dynamic range show that this algorithm compares favorably with recently proposed state-of-the-art methods. We also apply the algorithm to solve other problems for which there are fewer alternatives, such as total-variation minimization, and convex programs seeking to minimize the l1 norm of Wx under constraints, in which W is not diagonal

Blind Source Separation with Outliers in Transformed Domains

International audienceBlind Source Separation (BSS) methods are well suited for the analysis of multichannel data. In many applications, the observations are corrupted by an additional structured noise, which hinders most of the standard BSS techniques. In this article, we propose a novel BSS method able to jointly unmix the sources and separate the source contribution from the structured noise or outliers. This separation builds upon the difference of morphology between the components of interest, often encountered in imaging problems, by exploiting a sparse modeling of the components in two different domains. Numerical experiments highlight the robustness and precision of the proposed method in a wide variety of settings, including the full-rank regime

Non-linear interpolation learning for example-based inverse problem regularization

A large number of signal recovery problems are not well-posed-if not ill-posed-that require extra regularization to be tackled. In this context, the ability to inject physical knowledge is of utmost importance to design effective regularization schemes. However, most physically relevant models are generally nonlinear: signals generally lie on an unknown low-dimensional manifolds structure, which needs to be learnt. This is however quite challenging when available training samples are scarce. To that end, we investigate a novel approach that builds upon learning a non-linear interpolatory scheme from examples. We show how the proposed approach resonates with transportbased methods, but with a learnt metric. This eventually allows to build efficient non-linear regularizations for linear inverse problems. Extensive numerical experiments have been carried out to evaluate the performances of the proposed approach. We further illustrate its application to a blind regression problem in the field of γ-ray spectroscopy

Sparse estimation of model-based diffuse thermal dust emission

International audienceComponent separation for the Planck High Frequency Instrument (HFI) data is primarily concerned with the estimation of thermal dust emission, which requires the separation of thermal dust from the cosmic infrared background (CIB). For that purpose, current estimation methods rely on filtering techniques to decouple thermal dust emission from CIB anisotropies, which tend to yield a smooth, low-resolution, estimation of the dust emission. In this paper, we present a new parameter estimation method, premise: Parameter Recovery Exploiting Model Informed Sparse Estimates. This method exploits the sparse nature of thermal dust emission to calculate all-sky maps of thermal dust temperature, spectral index, and optical depth at 353 GHz. premise is evaluated and validated on full-sky simulated data. We find the percentage difference between the premise results and the true values to be 2.8, 5.7, and 7.2 per cent at the 1σ level across the full sky for thermal dust temperature, spectral index, and optical depth at 353 GHz, respectively. A comparison between premise and a GNILC-like method over selected regions of our sky simulation reveals that both methods perform comparably within high signal-to-noise regions. However, outside of the Galactic plane, premise is seen to outperform the GNILC-like method with increasing success as the signal-to-noise ratio worsens