3,755 research outputs found
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
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
S2LET: A code to perform fast wavelet analysis on the sphere
We describe S2LET, a fast and robust implementation of the scale-discretised
wavelet transform on the sphere. Wavelets are constructed through a tiling of
the harmonic line and can be used to probe spatially localised, scale-depended
features of signals on the sphere. The scale-discretised wavelet transform was
developed previously and reduces to the needlet transform in the axisymmetric
case. The reconstruction of a signal from its wavelets coefficients is made
exact here through the use of a sampling theorem on the sphere. Moreover, a
multiresolution algorithm is presented to capture all information of each
wavelet scale in the minimal number of samples on the sphere. In addition S2LET
supports the HEALPix pixelisation scheme, in which case the transform is not
exact but nevertheless achieves good numerical accuracy. The core routines of
S2LET are written in C and have interfaces in Matlab, IDL and Java. Real
signals can be written to and read from FITS files and plotted as Mollweide
projections. The S2LET code is made publicly available, is extensively
documented, and ships with several examples in the four languages supported. At
present the code is restricted to axisymmetric wavelets but will be extended to
directional, steerable wavelets in a future release.Comment: 8 pages, 6 figures, version accepted for publication in A&A. Code is
publicly available from http://www.s2let.or
Higher-Order Spectra of Weak Lensing Convergence Maps in Parameterized Theories of Modified Gravity
We compute the low- limit of the family of higher-order spectra for
projected (2D) weak lensing convergence maps. In this limit, these spectra are
computed to an arbitrary order using {\em tree-level} perturbative
calculations. We use the flat-sky approximation and Eulerian perturbative
results based on a generating function approach. We test these results for the
lower-order members of this family, i.e. the skew- and kurt-spectra against
state-of-the-art simulated all-sky weak lensing convergence maps and find our
results to be in very good agreement. We also show how these spectra can be
computed in the presence of a realistic sky-mask and Gaussian noise. We
generalize these results to three-dimensions (3D) and compute the {\em
equal-time} higher-order spectra. These results will be valuable in analyzing
higher-order statistics from future all-sky weak lensing surveys such as the
{\em Euclid} survey at low- modes. As illustrative examples, we compute
these statistics in the context of the {\em Horndeski} and {\em Beyond
Horndeski} theories of modified gravity. They will be especially useful in
constraining theories such as the Gleyzes-Langlois-Piazza-Vernizzi (GLPV)
theories and Degenerate Higher-Order Scalar-Tensor (DHOST) theories as well as
the commonly used normal-branch of Dvali-Gabadadze-Porrati (nDGP) model,
clustering quintessence models, and scenarios with massive neutrinos.Comment: 22 pages, 5 figure
Strength in diversity: enhancing learning in vocationally-orientated, master's level courses
Postgraduate education in geography, especially at the Master’s level, is undergoing significant changes in the developed world. There is an expansion of vocationally-oriented degree programmes, increasing recruitment of international students, integration of work place skills, and the engagement of non-traditional postgraduate students as departments respond to policies for a more ‘inclusive’ higher education. This paper sets the context by outlining some programmatic changes in selected countries (Australia, the UK, and the USA). We briefly reflect on how postgraduate ‘bars’ or ‘levels’ are defined and explore in detail what ‘diversity’ or ‘heterogeneity’ means in these new postgraduate settings. The paper then explores some examples of practice drawn from our own experiences, whilst recognising that relevance will vary in other contexts. Finally we consider how diversity can be harnessed as a strength that has potential to enhance taught elements of contemporary postgraduate education in and beyond the discipline
A novel sampling theorem on the rotation group
We develop a novel sampling theorem for functions defined on the
three-dimensional rotation group SO(3) by connecting the rotation group to the
three-torus through a periodic extension. Our sampling theorem requires
samples to capture all of the information content of a signal band-limited at
, reducing the number of required samples by a factor of two compared to
other equiangular sampling theorems. We present fast algorithms to compute the
associated Fourier transform on the rotation group, the so-called Wigner
transform, which scale as , compared to the naive scaling of .
For the common case of a low directional band-limit , complexity is reduced
to . Our fast algorithms will be of direct use in speeding up the
computation of directional wavelet transforms on the sphere. We make our SO3
code implementing these algorithms publicly available.Comment: 5 pages, 2 figures, minor changes to match version accepted for
publication. Code available at http://www.sothree.or
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
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