521 research outputs found
Gauge freedom for Gravitational Wave problems in tensor-scalar theories of gravity
A specific choice of gauge is shown to imply a decoupling between the tensor
and scalar components of Gravitational Radiation in the context of Brans-Dicke
type theories of gravitation. The comparison of the predictions of these
theories with those of General Relativity is thereby made straightforward.Comment: 11 pages, no figur
Compressed sensing for wide-field radio interferometric imaging
For the next generation of radio interferometric telescopes it is of
paramount importance to incorporate wide field-of-view (WFOV) considerations in
interferometric imaging, otherwise the fidelity of reconstructed images will
suffer greatly. We extend compressed sensing techniques for interferometric
imaging to a WFOV and recover images in the spherical coordinate space in which
they naturally live, eliminating any distorting projection. The effectiveness
of the spread spectrum phenomenon, highlighted recently by one of the authors,
is enhanced when going to a WFOV, while sparsity is promoted by recovering
images directly on the sphere. Both of these properties act to improve the
quality of reconstructed interferometric images. We quantify the performance of
compressed sensing reconstruction techniques through simulations, highlighting
the superior reconstruction quality achieved by recovering interferometric
images directly on the sphere rather than the plane.Comment: 15 pages, 8 figures, replaced to match version accepted by MNRA
Compressed sensing for radio interferometric imaging: review and future direction
Radio interferometry is a powerful technique for astronomical imaging. The
theory of Compressed Sensing (CS) has been applied recently to the ill-posed
inverse problem of recovering images from the measurements taken by radio
interferometric telescopes. We review novel CS radio interferometric imaging
techniques, both at the level of acquisition and reconstruction, and discuss
their superior performance relative to traditional approaches. In order to
remain as close to the theory of CS as possible, these techniques necessarily
consider idealised interferometric configurations. To realise the enhancement
in quality provided by these novel techniques on real radio interferometric
observations, their extension to realistic interferometric configurations is
now of considerable importance. We also chart the future direction of research
required to achieve this goal.Comment: 4 pages, 4 figures, Proceedings of IEEE International Conference on
Image Processing (ICIP) 201
Polca SARA - Full polarization, direction-dependent calibration and sparse imaging for radio interferometry
New generation of radio interferometers are envisaged to produce high
quality, high dynamic range Stokes images of the observed sky from the
corresponding under-sampled Fourier domain measurements. In practice, these
measurements are contaminated by the instrumental and atmospheric effects that
are well represented by Jones matrices, and are most often varying with
observation direction and time. These effects, usually unknown, act as a
limiting factor in achieving the required imaging performance and thus, their
calibration is crucial. To address this issue, we develop a global algorithm,
named Polca SARA, aiming to perform full polarization, direction-dependent
calibration and sparse imaging by employing a non-convex optimization
technique. In contrast with the existing approaches, the proposed method offers
global convergence guarantees and flexibility to incorporate sophisticated
priors to regularize the imaging as well as the calibration problem. Thus, we
adapt a polarimetric imaging specific method, enforcing the physical
polarization constraint along with a sparsity prior for the sought images. We
perform extensive simulation studies of the proposed algorithm. While
indicating the superior performance of polarization constraint based imaging,
the obtained results also highlight the importance of calibrating for
direction-dependent effects as well as for off-diagonal terms (denoting
polarization leakage) in the associated Jones matrices, without inclusion of
which the imaging quality deteriorates
Wideband Super-resolution Imaging in Radio Interferometry via Low Rankness and Joint Average Sparsity Models (HyperSARA)
We propose a new approach within the versatile framework of convex
optimization to solve the radio-interferometric wideband imaging problem. Our
approach, dubbed HyperSARA, solves a sequence of weighted nuclear norm and l21
minimization problems promoting low rankness and joint average sparsity of the
wideband model cube. On the one hand, enforcing low rankness enhances the
overall resolution of the reconstructed model cube by exploiting the
correlation between the different channels. On the other hand, promoting joint
average sparsity improves the overall sensitivity by rejecting artefacts
present on the different channels. An adaptive Preconditioned Primal-Dual
algorithm is adopted to solve the minimization problem. The algorithmic
structure is highly scalable to large data sets and allows for imaging in the
presence of unknown noise levels and calibration errors. We showcase the
superior performance of the proposed approach, reflected in high-resolution
images on simulations and real VLA observations with respect to single channel
imaging and the CLEAN-based wideband imaging algorithm in the WSCLEAN software.
Our MATLAB code is available online on GITHUB
On the computation of directional scale-discretized wavelet transforms on the sphere
We review scale-discretized wavelets on the sphere, which are directional and
allow one to probe oriented structure in data defined on the sphere.
Furthermore, scale-discretized wavelets allow in practice the exact synthesis
of a signal from its wavelet coefficients. We present exact and efficient
algorithms to compute the scale-discretized wavelet transform of band-limited
signals on the sphere. These algorithms are implemented in the publicly
available S2DW code. We release a new version of S2DW that is parallelized and
contains additional code optimizations. Note that scale-discretized wavelets
can be viewed as a directional generalization of needlets. Finally, we outline
future improvements to the algorithms presented, which can be achieved by
exploiting a new sampling theorem on the sphere developed recently by some of
the authors.Comment: 13 pages, 3 figures, Proceedings of Wavelets and Sparsity XV, SPIE
Optics and Photonics 2013, Code is publicly available at http://www.s2dw.org
Complex data processing: fast wavelet analysis on the sphere
In the general context of complex data processing, this paper reviews a
recent practical approach to the continuous wavelet formalism on the sphere.
This formalism notably yields a correspondence principle which relates wavelets
on the plane and on the sphere. Two fast algorithms are also presented for the
analysis of signals on the sphere with steerable wavelets.Comment: 20 pages, 5 figures, JFAA style, paper invited to J. Fourier Anal.
and Appli
Localisation of directional scale-discretised wavelets on the sphere
Scale-discretised wavelets yield a directional wavelet framework on the
sphere where a signal can be probed not only in scale and position but also in
orientation. Furthermore, a signal can be synthesised from its wavelet
coefficients exactly, in theory and practice (to machine precision).
Scale-discretised wavelets are closely related to spherical needlets (both were
developed independently at about the same time) but relax the axisymmetric
property of needlets so that directional signal content can be probed. Needlets
have been shown to satisfy important quasi-exponential localisation and
asymptotic uncorrelation properties. We show that these properties also hold
for directional scale-discretised wavelets on the sphere and derive similar
localisation and uncorrelation bounds in both the scalar and spin settings.
Scale-discretised wavelets can thus be considered as directional needlets.Comment: 28 pages, 8 figures, minor changes to match version accepted for
publication by ACH
PURIFY: a new approach to radio-interferometric imaging
In a recent article series, the authors have promoted convex optimization algorithms for radio-interferometric imaging in the framework of compressed sensing, which leverages sparsity regularization priors for the associated inverse problem and defines a minimization problem for image reconstruction. This approach was shown, in theory and through simulations in a simple discrete visibility setting, to have the potential to outperform significantly CLEAN and its evolutions. In this work, we leverage the versatility of convex optimization in solving minimization problems to both handle realistic continuous visibilities and offer a highly parallelizable structure paving the way to significant acceleration of the reconstruction and high-dimensional data scalability. The new algorithmic structure promoted relies on the simultaneous-direction method of multipliers (SDMM), and contrasts with the current major-minor cycle structure of CLEAN and its evolutions, which in particular cannot handle the state-of-the-art minimization problems under consideration where neither the regularization term nor the data term are differentiable functions. We release a beta version of an SDMM-based imaging software written in C and dubbed PURIFY (http://basp-group.github.io/purify/) that handles various sparsity priors, including our recent average sparsity approach SARA. We evaluate the performance of different priors through simulations in the continuous visibility setting, confirming the superiority of SARA
On sparsity averaging
Recent developments in Carrillo et al. (2012) and Carrillo et al. (2013)
introduced a novel regularization method for compressive imaging in the context
of compressed sensing with coherent redundant dictionaries. The approach relies
on the observation that natural images exhibit strong average sparsity over
multiple coherent frames. The associated reconstruction algorithm, based on an
analysis prior and a reweighted scheme, is dubbed Sparsity Averaging
Reweighted Analysis (SARA). We review these advances and extend associated
simulations establishing the superiority of SARA to regularization methods
based on sparsity in a single frame, for a generic spread spectrum acquisition
and for a Fourier acquisition of particular interest in radio astronomy.Comment: 4 pages, 3 figures, Proceedings of 10th International Conference on
Sampling Theory and Applications (SampTA), Code available at
https://github.com/basp-group/sopt, Full journal letter available at
http://arxiv.org/abs/arXiv:1208.233
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