14 research outputs found
Radio astronomical imaging in the presence of strong radio interference
Radio-astronomical observations are increasingly contaminated by
interference, and suppression techniques become essential. A powerful candidate
for interference mitigation is adaptive spatial filtering. We study the effect
of spatial filtering techniques on radio astronomical imaging. Current
deconvolution procedures such as CLEAN are shown to be unsuitable to spatially
filtered data, and the necessary corrections are derived. To that end, we
reformulate the imaging (deconvolution/calibration) process as a sequential
estimation of the locations of astronomical sources. This not only leads to an
extended CLEAN algorithm, the formulation also allows to insert other array
signal processing techniques for direction finding, and gives estimates of the
expected image quality and the amount of interference suppression that can be
achieved. Finally, a maximum likelihood procedure for the imaging is derived,
and an approximate ML image formation technique is proposed to overcome the
computational burden involved. Some of the effects of the new algorithms are
shown in simulated images. Keywords: Radio astronomy, synthesis imaging,
parametric imaging, interference mitigation, spatial filtering, maximum
likelihood, minimum variance, CLEAN.Comment: 27 pages, 7 figures. Paper with higher resolution color figures at
http://cobalt.et.tudelft.nl/~leshem/postscripts/leshem/imaging.ps.g
Calibration Challenges for Future Radio Telescopes
Instruments for radio astronomical observations have come a long way. While
the first telescopes were based on very large dishes and 2-antenna
interferometers, current instruments consist of dozens of steerable dishes,
whereas future instruments will be even larger distributed sensor arrays with a
hierarchy of phased array elements. For such arrays to provide meaningful
output (images), accurate calibration is of critical importance. Calibration
must solve for the unknown antenna gains and phases, as well as the unknown
atmospheric and ionospheric disturbances. Future telescopes will have a large
number of elements and a large field of view. In this case the parameters are
strongly direction dependent, resulting in a large number of unknown parameters
even if appropriately constrained physical or phenomenological descriptions are
used. This makes calibration a daunting parameter estimation task, that is
reviewed from a signal processing perspective in this article.Comment: 12 pages, 7 figures, 20 subfigures The title quoted in the meta-data
is the title after release / final editing
Fundamental Imaging Limits of Radio Telescope Arrays
The fidelity of radio astronomical images is generally assessed by practical
experience, i.e. using rules of thumb, although some aspects and cases have
been treated rigorously. In this paper we present a mathematical framework
capable of describing the fundamental limits of radio astronomical imaging
problems. Although the data model assumes a single snapshot observation, i.e.
variations in time and frequency are not considered, this framework is
sufficiently general to allow extension to synthesis observations. Using tools
from statistical signal processing and linear algebra, we discuss the
tractability of the imaging and deconvolution problem, the redistribution of
noise in the map by the imaging and deconvolution process, the covariance of
the image values due to propagation of calibration errors and thermal noise and
the upper limit on the number of sources tractable by self calibration. The
combination of covariance of the image values and the number of tractable
sources determines the effective noise floor achievable in the imaging process.
The effective noise provides a better figure of merit than dynamic range since
it includes the spatial variations of the noise. Our results provide handles
for improving the imaging performance by design of the array.Comment: 12 pages, 8 figure
Image formation in synthetic aperture radio telescopes
Next generation radio telescopes will be much larger, more sensitive, have
much larger observation bandwidth and will be capable of pointing multiple
beams simultaneously. Obtaining the sensitivity, resolution and dynamic range
supported by the receivers requires the development of new signal processing
techniques for array and atmospheric calibration as well as new imaging
techniques that are both more accurate and computationally efficient since data
volumes will be much larger. This paper provides a tutorial overview of
existing image formation techniques and outlines some of the future directions
needed for information extraction from future radio telescopes. We describe the
imaging process from measurement equation until deconvolution, both as a
Fourier inversion problem and as an array processing estimation problem. The
latter formulation enables the development of more advanced techniques based on
state of the art array processing. We demonstrate the techniques on simulated
and measured radio telescope data.Comment: 12 page
Parametric high resolution techniques for radio astronomical imaging
The increased sensitivity of future radio telescopes will result in
requirements for higher dynamic range within the image as well as better
resolution and immunity to interference. In this paper we propose a new matrix
formulation of the imaging equation in the cases of non co-planar arrays and
polarimetric measurements. Then we improve our parametric imaging techniques in
terms of resolution and estimation accuracy. This is done by enhancing both the
MVDR parametric imaging, introducing alternative dirty images and by
introducing better power estimates based on least squares, with positive
semi-definite constraints. We also discuss the use of robust Capon beamforming
and semi-definite programming for solving the self-calibration problem.
Additionally we provide statistical analysis of the bias of the MVDR beamformer
for the case of moving array, which serves as a first step in analyzing
iterative approaches such as CLEAN and the techniques proposed in this paper.
Finally we demonstrate a full deconvolution process based on the parametric
imaging techniques and show its improved resolution and sensitivity compared to
the CLEAN method.Comment: To appear in IEEE Journal of Selected Topics in Signal Processing,
Special issue on Signal Processing for Astronomy and space research. 30 page
Radio Astronomical Image Formation using Constrained Least Squares and Krylov Subspaces
Image formation for radio astronomy can be defined as estimating the spatial
power distribution of celestial sources over the sky, given an array of
antennas. One of the challenges with image formation is that the problem
becomes ill-posed as the number of pixels becomes large. The introduction of
constraints that incorporate a-priori knowledge is crucial. In this paper we
show that in addition to non-negativity, the magnitude of each pixel in an
image is also bounded from above. Indeed, the classical "dirty image" is an
upper bound, but a much tighter upper bound can be formed from the data using
array processing techniques. This formulates image formation as a least squares
optimization problem with inequality constraints. We propose to solve this
constrained least squares problem using active set techniques, and the steps
needed to implement it are described. It is shown that the least squares part
of the problem can be efficiently implemented with Krylov subspace based
techniques, where the structure of the problem allows massive parallelism and
reduced storage needs. The performance of the algorithm is evaluated using
simulations