7,383 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
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
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
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
- …