My thesis is approaching its final destination after 3 years of work! I am pleased to announce you that my defense will be held at 2 pm on November 10th in Galilée room. You are welcomed to my defense!
Multichannel Compressed Sensing and its Applications in Radioastronomy
The new generation of radio interferometer instruments, such as LOFAR and SKA, will allow us to build radio images with very high angular resolution and sensitivity. One of the major problems in interferometry imaging is that it involves an ill-posed inverse problem because only a few Fourier components (visibility points) can be acquired by a radio interferometer. Compressed Sensing (CS) theory is a paradigm to solve many underdetermined inverse problems and has shown its strength in radio astronomy.
This thesis focuses on the methodology of Multichannel Compressed Sensing data reconstruction and its application in radio astronomy. For instance, radio transients are an active research field in radio astronomy but their detection is a challenging problem because of low angular resolution and low signal-to-noise observations. To address this issue, we investigated the sparsity of temporal information of radio transients and proposed a spatial-temporal sparse reconstruction method to efficiently detect radio sources. Experiments have shown the strength of this sparse recovery method compared to the state-of-the-art methods.
A second application is concerned with multi-wavelength radio interferometry imaging in which the data are degraded differently in terms of wavelength due to the wavelength-dependent varying instrumental beam. Based on a source mixture model, a novel Deconvolution Blind Source Separation (DBSS) model is proposed. The DBSS problem is not only non-convex but also ill-conditioned due to convolution kernels. Our proposed DecGMCA method, which benefits from a sparsity prior and leverages an alternating projected least squares, is an efficient algorithm to tackle simultaneously the deconvolution and BSS problems. Experiments have shown that taking into account joint deconvolution and BSS gives much better results than applying sequential deconvolution and BSS.
Description F-CUR3D is a software, based on the MATLAB package, which contains routines for the Fast 3D Curvelet transform and reconstruction. The F-CUR3D documentation is available in PDF format.
- A. Woiselle, J.L. Starck and M.J. Fadili, "3D curvelet transforms and astronomical data restoration", Applied and Computational Harmonic Analysis, Vol. 28, No. 2, pp. 171-188, 2010.
- A. Woiselle, J.L. Starck, M.J. Fadili, "3D Data Denoising and Inpainting with the Fast Curvelet transform", J. of Mathematical Imaging and Vision (JMIV), 39, 2, pp 121-139, 2011.
BAOlab is related to the study of Baryon Acoustic Oscillations (BAO) using the 2-point correlation function. It enables to perform different tasks, namely BAO detection and BAO parameter constraints. The main novelty of this approach is that it enables to obtain a model-dependent covariance matrix which can change the results both for BAO detection and for parameter constraints.
Software: BAOlab Version 1.0
- BAOlab contains IDL and C++ routines.
- Source code and more information are available here.
Papers related to the software:
- A. Labatie, J.L. Starck, M. Lachieze-Rey, P. Arnalte-Mur, "Uncertainty in 2-point correlation function estimators and baryon acoustic oscillation detection in galaxy surveys", Statistical Methodology, 9, 85-100, 2012.
- A. Labatie, J.L. Starck, M. Lachieze-Rey, "Detecting Baryon Acoustic Oscillations", The Astrophysical Journal, 746, 172, 2012.
- A. Labatie, J.L. Starck, M. Lachieze-Rey, "Effect of model-dependent covariance matrix for studying Baryon Acoustic Oscillation", The Astrophysical Journal, 760, 97, 2012.
Blind Source Separation (BSS) is a challenging matrix factorization problem that plays a central role in multichannel imaging science. In a large number of applications, such as astrophysics, current unmixing methods are limited since real-world mixtures are generally affected by extra instrumental effects like blurring. Therefore, BSS has to be solved jointly with a deconvolution problem, which requires tackling a new inverse problem: deconvolution BSS (DBSS). In this article, we introduce an innovative DBSS approach, called DecGMCA, based on sparse signal modeling and an efficient alternative projected least square algorithm. Numerical results demonstrate that the DecGMCA algorithm performs very well on simulations. It further highlights the importance of jointly solving BSS and deconvolution instead of considering these two problems independently. Furthermore, the performance of the proposed DecGMCA algorithm is demonstrated on simulated radio-interferometric data.
Our beautiful radio-interferometry reconstructed image, using a method based on Compressed Sensing Theory, has been highlighted by the Square Kilometre Array (SKA) project:.
Soutenance de thèse du Service d’Astrophysique, Mardi 18 Octobre – 14h00
FRED NGOLE MBOULA
METHODES ET ALGORITHMES AVANCES POUR L'IMAGERIE ASTRONOMIQUE DE HAUTE PRECISION