Next-Generation Radio Interferometric Imaging for the SKA 2015

A Royal Society South Africa-UK Scientific Seminar

Last week saw the first workshop on Next-Generation Radio Interferometric Imaging for the SKA 2015, with the aim of promoting scientific collaboration between South Africa and the UK, focusing on next-gen radio interferometric imaging techniques for the Square Kilometre Array (SKA) and pathfinder telescopes.

The SKA promises exquisite radio observations of unprecedented resolution and sensitivity, which will lead to many scientific advances. However, the imaging pipelines of current radio interferometric telescopes have been identified as a critical bottleneck in the “big-data” regime of the SKA. A lot of progress has been made recently to develop new radio interferometric imaging techniques, for example those based on the revolutionary new theory of compressive sensing.

VLA dish

VLA dish

The workshop brought together experts in radio interferometry, with experts in image processing and compressive sensing, to bring emerging radio imaging techniques to bear on real interferometric data.  A significant portion of the meeting was devoted to hack sessions to work together on codes and data.

We started with a brainstorming session collectively editing a Google Doc, which soon took on a life of its own!  The plan was to come back together after a coffee break to finalise projects and people to focus on them — but that wasn’t necessary.  By that time everyone had self-organised and started working together on many exciting projects!

It was great fun to get our hands dirty with code and data, while experts from a broad range of different areas were on hand to provide support.  Lot’s of progress was made during the week and we have a number of ongoing projects now that were initiated during the workshop.  I’m very much looking forward to seeing how these progress.  We’ll keep you updated!

Sundowners during the workshop  (Courtesy of Rahim Lakhoo)

Sundowners during the workshop (Courtesy of Rahim Lakhoo)

Many thanks once again to our sponsors:

rslogo_NRF_SouthAfrica

Biomedical and Astronomical Signal Processing (BASP) Frontiers 2015

Last week saw the third instalment of the BASP conference, which brings together the communities of astronomy, biomedical sciences, and signal processing. Although astronomical and biomedical sciences share common roots in the signal processing problems that are faced, the corresponding communities are almost completely disconnected. The goal of the BASP workshop series is to foster collaboration between the astronomical and biomedical physics communities, around common signal processing challenges.

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Discussions during one of the deluxe poster sessions at BASP

As an astrophysicist, I was amazed to see the progress made in High Intensity Focused Ultrasound. Test patients suffering from Parkinson’s disease showed huge progress immediately following treatment, demonstrating a huge impact on people’s lives. Many biomedical scientists I spoke to were similarly amazed by the progress being made in cosmology, where we have recovered a remarkably complete picture of the history and evolution of our Universe.  I also had some very interesting discussions on how some of the techniques we have been developing for astronomical imaging might be useful for studying the development of Glaucoma, which we’ll certainly be investigating further.

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The slopes to ourselves at BASP

The meeting was held in a delightful setting in the Swiss Alps and many interesting scientific discussions (and debates!) were had on the ski slopes.

Proceedings are available on the website. For further discussions surrounding the meeting check out the Twitter hashtag #BASP2015.

Looking forward to BASP 2017 already!

Pioneering work helps to join the dots across the known universe… and the human brain

Compressive sensing is a recent breakthrough in information theory that has the potential to revolutionise the acquisition and analysis of data in many fields. We recently secured grants from the UK research councils to develop compressive sensing techniques to address the challenge of extracting meaningful information from big-data.

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Artist’s impression of the Square Kilometre Array at night (Credit: SKA Organisation)

 

Reconstructed neuronal connections in the brain (Credt: Thomas Schultz)

Reconstructed neuronal connections in the brain

The techniques developed will find application in a broad range of academic fields and industries, from astronomy to medicine. They will allow high-fidelity astronomical images to be recovered from the overwhelming volumes of raw data that will be acquired by next-generation radio telescopes like the Square Kilometre Array (SKA). The new techniques will also be of direct use in neuro-imaging to accelerate the acquisition time of diffusion magnetic resonance imaging (MRI), potentially rendering its clinical use possible.

For more details see: http://www.ucl.ac.uk/mathematical-physical-sciences/maps-news-publication/maps1431

Spatial-spectral concentration on the ball

Post by Jason McEwen

In cosmology, observations are made over the celestial sphere, giving rise to observations defined on the two-dimensional sphere, i.e. a spherical surface.  If depth information is also available (i.e. redshift), then observations are defined on the three-dimensional ball, i.e. on a spherical volume.  For example, observations of the cosmic microwave background (CMB) are made on the sphere, while observations of the galaxy distribution that traces the large-scale structure (LSS) are made on the ball.

Often, however, observations cannot be made over the full sky.  For example, we must look through our galaxy, which contaminates observations. Foreground contamination can sometimes be modelled and reduced, however regions of significant contamination must be removed altogether. In addition, telescopes often simply cannot see the entire sky.

Dealing with partial-sky coverage can be difficult.  Wavelets are a powerful method to do this due to their dual spatial and spectral localisation properties.  Alternatively, one can build a basis concentrated in the observed region.  This is a well-studied problem in signal processing and is known as the Slepian spatial-spectral concentration problem.  Although this problem has been solved in the Euclidean setting, and also on the sphere, it has not been solved on the ball.  We recently submitted a paper solving the Slepian spatial-spectral concentration problem on the ball.

The abstract of our submission is reproduced below and you can find the full paper on the arXiv.

“We formulate and solve the Slepian spatial-spectral concentration problem on the three-dimensional ball. Both the standard Fourier-Bessel and also the Fourier-Laguerre spectral domains are considered since the latter exhibits a number of practical advantages (spectral decoupling and exact computation). The Slepian spatial and spectral concentration problems are formulated as eigenvalue problems, the eigenfunctions of which form an orthogonal family of concentrated functions. Equivalence between the spatial and spectral problems is shown. The spherical Shannon number on the ball is derived, which acts as the analog of the space-bandwidth product in the Euclidean setting, giving an estimate of the number of concentrated eigenfunctions and thus the dimension of the space of functions that can be concentrated in both the spatial and spectral domains simultaneously. Various symmetries of the spatial region are considered that reduce considerably the computational burden of recovering eigenfunctions, either by decoupling the problem into smaller subproblems or by affording analytic calculations. The family of concentrated eigenfunctions forms a Slepian basis that can be used be represent concentrated signals efficiently. We illustrate our results with numerical examples and show that the Slepian basis indeeds permits a sparse representation of concentrated signals.”

In additional to considering the standard Fourier-Bessel basis on the ball, we also consider the Fourier-Laguerre basis, which exhibits a number of practical advantages.  The first few Slepian functions concentrated within an example region are shown in the following plots for each basis on the ball.

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Fourier-Bessel spatially concentrated Slepian functions

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Fourier-Laguerre spatially concentrated Slepian functions

 

Cosmological image processing

Post by Jason McEwen

Modern science is becoming increasingly interdisciplinary, and cosmology is no exception. The analysis of observational data in order to constrain cosmological theories is drawing more and more heavily on methods from other fields, such as statistics and applied mathematics. These interdisciplinary approaches often go far beyond the level of straightforward application of techniques from other fields, often uncovering fundamental connections or new results in disparate fields. In fact, such interdisciplinary research has given rise to new terminologies: astrostatistics and astroinformatics.

I recently had the pleasure of attending IVCNZ 2013, an Image and Vision Computing conference in New Zeland, where I spoke about cosmological image processing.  While the general focus of the meeting covered image processing and computer vision and graphics, a diverse range of applications of these techniques were discussed, from vehicle classification, to crystallography, to medial and biological imaging, to cosmology… and many others.  I particularly enjoyed many interesting discussions over coffee, often contemplating the application of methods from one field to another.

One of the highlights was certainly the opportunity to test-drive Google Glass (kindly provided by Mark Billinghurst)!

Mark Billinghurst test-driving Google Glass.

Mark Billinghurst test-driving Google Glass.

Wavelets for studying the large-scale structure (LSS) of the Universe

Post by Jason McEwen

Why wavelets?

It can be insightful to analyse data, or “signals”, in different domains. For example, the frequency spectrum of music is often studied, where contributions to the base and treble are more clearly visible.

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Music in time (lower panel) and frequency (upper panel).  These representations can be computed on your iPhone.

In the Fourier domain, we can probe the frequency content of signals but lose information about the time localisation of signal structure. In the time domain, the reverse is true: we can probe the time content of signals but lose information about the frequency localisation of signal structure.  Wavelets overcome this problem by looking at signal content in time and frequency (scale) simultaneously.  

Often, we may be interested in signals that are defined on domains other than time.  For example, a standard image is a two-dimensional signal defined on a spatial domain.  Nevertheless, for such signals it can also be insightful to view the signal content in the frequency domain, rather than the spatial domain, or in the wavelet domain.

Many physical processes are manifest on particular physical scales, while also spatially localised.  Wavelets are therefore a powerful analysis tool for extracting the fingerprint of a physical process of interest when it is embedded in some background signal.

Wavelet analysis of the CMB

Wavelets have now become a standard analysis technique for studying the anisotropies of the cosmic microwave background (CMB).

In this setting, the signal of interest (the CMB) is defined on the celestial sphere.  We therefore need wavelet transforms defined on the sphere.

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Temperature anisotropies of the CMB defined on the celestial sphere. [Credit: WMAP]

A number of wavelet transforms have been defined on the sphere.  The construction of many of these analysis methods has been motivated directly by the desire to study the CMB but these techniques are of general use for studying signals on the sphere, such as observations made in geophysics and computer graphics.  

Wavelets defined on the sphere are now a prevalent analysis technique for studying the CMB.  In fact, many of the cosmological studies performed in the 2013 analysis and release of Planck data used wavelet methods .

Exact wavelet on the ball for studying LSS

The large-scale structure (LSS) of the Universe, as traced by the distribution of galaxies, is another powerful cosmological probe.  Observations tracing the LSS are made in three-dimensions, with the radial dimension measuring redshift.  These observations therefore also live in spherical space and are made on the ball, i.e. on the sphere augmented with depth information.

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Observations tracing the LSS defined on the ball. [Credit: SDSS]

Recently, we have developed wavelet methods defined on the ball for the purpose of extracting cosmological information from observations tracing the LSS.   More technical details on wavelets on the ball will appear in a future post.

We hope that these types of methods can prove as useful for studying the LSS as they have for studying the CMB.

We’re now busy applying them for various cosmological analyses and will keep you posted!

Related reading

B. Leistedt, J. D. McEwen, Exact Wavelets on the Ball

J. D. McEwen, B. Leistedt, Fourier-Laguerre transform, convolution and wavelets on the ball

F. Lanusse, A. Rassat, J.-L. Starck, Spherical 3D isotropic wavelets

B. Leistedt, H. V. Peiris, J. D. McEwen, Flaglets for studying the large-scale structure of the Universe

Y. Wiaux, J. D. McEwen, P. Vandergheynst, O. Blanc, Exact reconstruction with directional wavelets on the sphere

B. Leistedt, J. D. McEwen, P. Vandergheynst, Y. Wiaux, S2LET: A code to perform fast wavelet analysis on the sphere,

D. Marinucci, D. Pietrobon, A. Balbi, P. Baldi, P. Cabella, G. Kerkyacharian, P. Natoli, D. Picard, N. Vittorio, Spherical needlets for CMB data analysis

J.-L. Starck, Y. Moudden, P. Abrial, M. Nguyen, Wavelets, ridgelets and curvelets on the sphere