3,664 research outputs found
Compressed sensing imaging techniques for radio interferometry
Radio interferometry probes astrophysical signals through incomplete and
noisy Fourier measurements. The theory of compressed sensing demonstrates that
such measurements may actually suffice for accurate reconstruction of sparse or
compressible signals. We propose new generic imaging techniques based on convex
optimization for global minimization problems defined in this context. The
versatility of the framework notably allows introduction of specific prior
information on the signals, which offers the possibility of significant
improvements of reconstruction relative to the standard local matching pursuit
algorithm CLEAN used in radio astronomy. We illustrate the potential of the
approach by studying reconstruction performances on simulations of two
different kinds of signals observed with very generic interferometric
configurations. The first kind is an intensity field of compact astrophysical
objects. The second kind is the imprint of cosmic strings in the temperature
field of the cosmic microwave background radiation, of particular interest for
cosmology.Comment: 10 pages, 1 figure. Version 2 matches version accepted for
publication in MNRAS. Changes includes: writing corrections, clarifications
of arguments, figure update, and a new subsection 4.1 commenting on the exact
compliance of radio interferometric measurements with compressed sensin
Sparse Signal Recovery Under Sensing and Physical Hardware Constraints
This dissertation focuses on information recovery under two general types of sensing constraints and hardware limitations that arise in practical data acquisition systems. We study the effects of these practical limitations in the context of signal recovery problems from interferometric measurements such as for optical mode analysis. The first constraint stems from the limited number of degrees of freedom of an information gathering system, which gives rise to highly constrained sensing structures. In contrast to prior work on compressive signal recovery which relies for the most part on introducing additional hardware components to emulate randomization, we establish performance guarantees for successful signal recovery from a reduced number of measurements even with the constrained interferometer structure obviating the need for non-native components. Also, we propose control policies to guide the collection of informative measurements given prior knowledge about the constrained sensing structure. In addition, we devise a sequential implementation with a stopping rule, shown to reduce the sample complexity for a target performance in reconstruction. The second limitation considered is due to physical hardware constraints, such as the finite spatial resolution of the used components and their finite aperture size. Such limitations introduce non-linearities in the underlying measurement model. We first develop a more accurate measurement model with structured noise representing a known non-linear function of the input signal, obtained by leveraging side information about the sampling structure. Then, we devise iterative denoising algorithms shown to enhance the quality of sparse recovery in the presence of physical constraints by iteratively estimating and eliminating the non-linear term from the measurements. We also develop a class of clipping-cognizant reconstruction algorithms for modal reconstruction from interferometric measurements that compensate for clipping effects due to the finite aperture size of the used components and show they yield significant gains over schemes oblivious to such effects
Interferometry-based modal analysis with finite aperture effects
We analyze the effects of aperture finiteness on interferograms recorded to
unveil the modal content of optical beams in arbitrary basis using generalized
interferometry. We develop a scheme for modal reconstruction from
interferometric measurements that accounts for the ensuing clipping effects.
Clipping-cognizant reconstruction is shown to yield significant performance
gains over traditional schemes that overlook such effects that do arise in
practice. Our work can inspire further research on reconstruction schemes and
algorithms that account for practical hardware limitations in a variety of
contexts
Compressive optical interferometry
Compressive sensing (CS) combines data acquisition with compression coding to
reduce the number of measurements required to reconstruct a sparse signal. In
optics, this usually takes the form of projecting the field onto sequences of
random spatial patterns that are selected from an appropriate random ensemble.
We show here that CS can be exploited in `native' optics hardware without
introducing added components. Specifically, we show that random sub-Nyquist
sampling of an interferogram helps reconstruct the field modal structure. The
distribution of reduced sensing matrices corresponding to random measurements
is provably incoherent and isotropic, which helps us carry out CS successfully
PURIFY: a new algorithmic framework for next-generation radio-interferometric imaging
In recent works, compressed sensing (CS) and convex opti- mization techniques have been applied to radio-interferometric imaging showing the potential to outperform state-of-the-art imaging algorithms in the field. We review our latest contributions [1, 2, 3], which leverage the versatility of convex optimization 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 in a new software PURIFY (beta version) relies on the simultaneous-direction method of multipliers (SDMM). The performance of various sparsity priors is evaluated through simulations in the continuous visibility setting, confirming the superiority of our recent average sparsity approach SARA
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
Robust sparse image reconstruction of radio interferometric observations with purify
Next-generation radio interferometers, such as the Square Kilometre Array
(SKA), will revolutionise our understanding of the universe through their
unprecedented sensitivity and resolution. However, to realise these goals
significant challenges in image and data processing need to be overcome. The
standard methods in radio interferometry for reconstructing images, such as
CLEAN, have served the community well over the last few decades and have
survived largely because they are pragmatic. However, they produce
reconstructed inter\-ferometric images that are limited in quality and
scalability for big data. In this work we apply and evaluate alternative
interferometric reconstruction methods that make use of state-of-the-art sparse
image reconstruction algorithms motivated by compressive sensing, which have
been implemented in the PURIFY software package. In particular, we implement
and apply the proximal alternating direction method of multipliers (P-ADMM)
algorithm presented in a recent article. First, we assess the impact of the
interpolation kernel used to perform gridding and degridding on sparse image
reconstruction. We find that the Kaiser-Bessel interpolation kernel performs as
well as prolate spheroidal wave functions, while providing a computational
saving and an analytic form. Second, we apply PURIFY to real interferometric
observations from the Very Large Array (VLA) and the Australia Telescope
Compact Array (ATCA) and find images recovered by PURIFY are higher quality
than those recovered by CLEAN. Third, we discuss how PURIFY reconstructions
exhibit additional advantages over those recovered by CLEAN. The latest version
of PURIFY, with developments presented in this work, is made publicly
available.Comment: 22 pages, 10 figures, PURIFY code available at
http://basp-group.github.io/purif
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