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Compressed sensing imaging techniques for radio interferometry

English title Compressed sensing imaging techniques for radio interferometry
Applicant Wiaux Yves
Number 130359
Funding scheme Project funding (Div. I-III)
Research institution Laboratoire de traitement des signaux 5 EPFL - STI - IEL - LTS5
Institution of higher education EPF Lausanne - EPFL
Main discipline Information Technology
Start/End 01.06.2010 - 31.07.2012
Approved amount 204'850.00
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All Disciplines (2)

Discipline
Information Technology
Astronomy, Astrophysics and Space Sciences

Keywords (13)

Signal processing: Complex data analysis; Signal processing: Inverse problems; Signal processing: Compressed sensing; Signal processing: Wavelets; Astrophysics: Radio astronomy; signal processing; imaging; compressed sensing; radio interferometry; wavelets; inverse problems; astrophysics; radio astronomy

Lay Summary (English)

Lead
Lay summary
Aperture synthesis in radio interferometry is a powerful technique for probing astrophysical signals. It also lies at the core of new international projects such as LOFAR and SKA. In this context, signals are probed through incomplete and noisy Fourier measurements, hence defining an ill-posed inverse problem in the perspective of signal reconstruction. Already powerful imaging techniques have been developed in the field. However, these methods do not explicitly take advantage of the fact that a large variety of natural signals are sparse or compressible in some basis, such as wavelet dictionaries. The recent theory of compressed sensing demonstrates that, for sparse or compressible signals, a small number of random measurements, in a sensing basis incoherent with the sparsity basis, will suffice for an accurate and stable reconstruction. Random Fourier measurements of a signal sparse in real space are a particular example of a good sensing procedure in this context. As a matter of fact, if compressed sensing had been developed before the advent of radio interferometry, one would probably not have thought of a better acquisition procedure in an imaging perspective. In the last years, Dr Y. Wiaux has undertaken research on compressed sensing imaging techniques for radio interferometry, on the grounds of both signal acquisition and associated reconstruction algorithms. The two-year postdoctoral project funded by the Swiss National science Foundation (SNSF) aims at extending previous results of the applicant, both in the perspective of realistic Fourier coverage and noise conditions, and of signals on the sphere as expected for interferometers that will map the sky on wide fields of view. This project is one of the first, at the international level, to lie at the intersection between the two monuments of signal processing and astronomy that are compressed sensing and aperture synthesis in radio interferometry.
Direct link to Lay Summary Last update: 21.02.2013

Responsible applicant and co-applicants

Employees

Publications

Publication
A novel sampling theorem on the sphere
McEwen Jason, Wiaux Yves (2011), A novel sampling theorem on the sphere, in {IEEE} Transactions on Signal Processing, 59, 5876-5876.
Compressed sensing for radio interferometric imaging: review and future
McEwen Jason, Wiaux Yves (2011), Compressed sensing for radio interferometric imaging: review and future, in Proc. 18th International Conference on Image Processing (ICIP), Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa.
Compressed sensing for wide-field radio interferometric imaging
McEwen Jason, Wiaux Yves (2011), Compressed sensing for wide-field radio interferometric imaging, in Monthly Notices- Royal Astronomical Society, 413(2), 1318-1332.
Implications for compressed sensing of a new sampling theorem on the sphere
McEwen Jason, Puy Gilles, Thiran Jean-Philippe, Vandergheynst Pierre, Van De Ville Dimitri, Wiaux Yves (2011), Implications for compressed sensing of a new sampling theorem on the sphere, in Proc. 4th Workshop on Signal Processing with Adaptive Sparse Structured Representations.
Intrinsic advantages of the w component and spherical imaging for wide-field radio interferometry
McEwen Jason, Wiaux Yves (2011), Intrinsic advantages of the w component and spherical imaging for wide-field radio interferometry, in Proc. XXXth General Assembly and Scientific Symposium of the International Union of Radio Science.
Sampling theorems and compressive sensing on the sphere
McEwen Jason, Puy Gilles, Thiran Jean-Philippe, Vandergheynst Pierre, Van De Ville Dimitri, Wiaux Yves (2011), Sampling theorems and compressive sensing on the sphere, in Proc. Wavelets and Sparsity XIV, 8138 81381F-1, Spie-Int Soc Optical Engineering, Po Box 10, Bellingham, Wa 98227-0010 Usa, 8138 81381F-1.
The application of Compressed Sensing Techniques in Radio Astronomy
Scaife A., Wiaux Y. (2011), The application of Compressed Sensing Techniques in Radio Astronomy, in Proc. XXXth General Assembly and Scientific Symposium of the International Union of Radio Science, IEEE.
Sparsity Averaging Reweighted Analysis (SARA): a novel algorithm for radio-interferometric imaging
Carrillo Rafael, McEwen Jason, Wiaux Yves, Sparsity Averaging Reweighted Analysis (SARA): a novel algorithm for radio-interferometric imaging, in Monthly Notices- Royal Astronomical Society.

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
BASP Frontiers 2011 04.09.2011 Villars-sur-Ollon, Switzerland
Wavelets and Sparsity XIV 21.08.2011 San Diego, USA
5th SKA Workshop on Calibration and Imaging (CALIM 2010) 22.08.2010 Dwingeloo, The Netherlands


Self-organised

Title Date Place
BASP Frontiers 2011 04.09.2011 Villars-sur-Ollon, Switzerland

Associated projects

Number Title Start Funding scheme
146594 Next-generation calibration and imaging in radio interferometry 01.08.2013 Project funding (Div. I-III)
138311 Advanced signal processing on the sphere for high angular resolution diffusion magnetic resonance imaging 01.04.2012 Project funding (Div. I-III)
140861 Advanced signal processing for calibration and imaging in radio interferometry 01.08.2012 Project funding (Div. I-III)

Abstract

Aperture synthesis in radio interferometry is a powerful technique that dates back to more than sixty years ago. It allows observations of the sky with otherwise inaccessible angular resolutions and sensitivities. With new international projects under construction and design (LOFAR, SKA, etc.), it also represents a significant part of the future of radio astronomy. Technically, for small fields of view the astrophysical signals under scrutiny are considered to be planar. In the context of aperture synthesis these signals are probed through incomplete and noisy Fourier measurements, which define an ill-posed inverse problem in the perspective of signal reconstruction. Already powerful imaging techniques have been developed in the field. However, these methods do not explicitly take advantage of the fact that a large variety of natural signals are sparse or compressible in some basis, such as wavelet dictionaries.The very new theory of compressed sensing generically aims at merging the two steps of signal acquisition and compression, precisely relying on this idea of sparsity. It represents a significant evolution in sampling theory, beyond the well-known Nyquist-Shannon theorem. The theory demonstrates that, for sparse or compressible signals, a small number of random measurements, in a sensing basis incoherent with the sparsity basis, will indeed suffice for an accurate and stable reconstruction. It also provides the required reconstruction algorithms. Random Fourier measurements of a signal sparse in real space are a particular example of a good sensing procedure in this context.As a matter of fact, if compressed sensing had been developed before the advent of radio interferometry, one would probably not have thought of a better acquisition procedure in an imaging perspective. This fact urges for large efforts to be undertaken to study the practical interest of compressed sensing for radio interferometry.The applicant has very recently undertaken research on compressed sensing imaging techniques for radio interferometry. On one side new reconstruction algorithms relying on the versatility of compressed sensing to introduce specific prior information for signal reconstruction were developed. On the other side a spread spectrum technique was defined that could allow a drastic enhancement of signal reconstruction by a careful design of the acquisition process of the radio-interferometric data. This research clearly illustrates the high potential of compressed sensing in improving imaging techniques for radio interferometry. But a huge amount of work is required along these lines.The present two-year postdoctoral project proposed for funding to the Swiss National science Foundation (SNSF) aims at extending previous results, both in the perspective of realistic Fourier coverage and noise conditions, and of signals on the sphere as expected for interferometers that will map the sky on wide fields of view. This proposal represents the first project, at the international level, to lie at the intersection between the two monuments of signal processing and astronomy that are compressed sensing and aperture synthesis in radio interferometry. As such, and as suggested by the promising preliminary results recently obtained by the applicant, it will with no doubt contribute to the definition of imaging techniques beyond the current state-of-the-art.These techniques will enhance the quality of scientific interpretation of the data in all fields of application of the interferometer projects concerned, from radio astronomy to agriculture. Moreover, the probe of two-dimensional planar signals through incomplete and noisy Fourier coverages represents an acquisition strategy shared by various sensing techniques in science and technology beyond radio interferometry. The interest of the project results consequently directly extends in fields well beyond radio astronomy, notably in biomedical imaging.
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