An accelerated splitting algorithm for radio-interferometric imaging: when natural and uniform weighting meet

Onose, Alexandru; Dabbech, Arwa; Wiaux, Yves

doi:10.1093/mnras/stx755

Cited by 33 publications

(52 citation statements)

References 42 publications

(83 reference statements)

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“…The pioneering work on sparse reconstruction techniques for radio interferometry is presented in Wiaux et al (2009a) and Wiaux et al (2009b). Numerous other papers 1 have been presented, mostly geared toward data from next-generation low-frequency interferometers (Wiaux et al 2010;Wenger et al 2010;Li et al 2011;McEwen & Wiaux 2011;Carrillo et al 2012Carrillo et al , 2014Garsden et al 2015;Dabbech et al 2015;Onose et al 2016Onose et al , 2017. Both our and other groups' work have shown that these state-of-the-art sparse reconstruction techniques outperform the conventional CLEAN technique and its variants.…”

Section: Introductionmentioning

confidence: 79%

Superresolution Interferometric Imaging with Sparse Modeling Using Total Squared Variation: Application to Imaging the Black Hole Shadow

Kuramochi

Akiyama

Ikeda

et al. 2018

ApJ

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We propose a new superresolution imaging technique for interferometry using sparse modeling, utilizing two regularization terms: the 1 -norm and a new function named Total Squared Variation (TSV) of the brightness distribution. TSV is an edge-smoothing variant of Total Variation (TV), leading to reducing the sum of squared gradients. First, we demonstrate that our technique may achieve super-resolution of ∼ 30% compared to the traditional CLEAN beam size using synthetic observations of two point sources. Second, we present simulated observations of three physically motivated static models of Sgr A* with the Event Horizon Telescope (EHT) to show the performance of proposed techniques in greater detail. We find that 1 +TSV regularization outperforms 1 +TV regularization with the popular isotropic TV term and the Cotton-Schwab CLEAN algorithm, demonstrating that TSV is well-matched to the expected physical properties of the astronomical images, which are often nebulous. Remarkably, in both the image and gradient domains, the optimal beam size minimizing root-mean-squared errors is 10 % of the traditional CLEAN beam size for 1 +TSV regularization, and non-convolved reconstructed images have smaller errors than beam-convolved reconstructed images. This indicates that the traditional post-processing technique of Gaussian convolution in interferometric imaging may not be required for the 1 +TSV regularization. We also propose a feature extraction method to detect circular features from the image of a black hole shadow with the circle Hough transform (CHT) and use it to evaluate the performance of the image reconstruction. With our imaging technique and the CHT, the EHT can constrain the radius of the black hole shadow with an accuracy of ∼ 10 − 20 % in present simulations for Sgr A*, suggesting that the EHT would be able to provide useful independent measurements of the mass of the supermassive black holes in Sgr A* and also another primary target, M87.

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Section: Introductionmentioning

confidence: 79%

Superresolution Interferometric Imaging with Sparse Modeling Using Total Squared Variation: Application to Imaging the Black Hole Shadow

Kuramochi

Akiyama

Ikeda

et al. 2018

ApJ

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“…Note that R (∈ C 2F N ×2 ) in (14) has no dependence on the variables at frequency f , i.e., J f and Y f . Substituting (12) to (6), we get…”

Section: Radio Interferometric Calibrationmentioning

confidence: 99%

“…The main goal of calibration is the correction for systematic errors in the data and the removal of contaminating foregrounds from this data to reveal such weak signals. Consensus optimization [3] has proved to be a computationally efficient solution for calibration [4]- [8] as well as for imaging [9]- [12] massive amounts of radio interferometric data. Calibration is always imperfect due to the errors in the input sky model as well as the consensus polynomials being used.…”

Section: Introductionmentioning

confidence: 99%

Performance Analysis of Distributed Radio Interferometric Calibration

Yatawatta

2018

2018 IEEE 10th Sensor Array and Multichannel Signal Processing Workshop (SAM)

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Distributed calibration based on consensus optimization is a computationally efficient method to calibrate large radio interferometers such as LOFAR and SKA. Calibrating along multiple directions in the sky and removing the bright foreground signal is a crucial step in many science cases in radio interferometry. The residual data contain weak signals of huge scientific interest and of particular concern is the effect of incomplete sky models used in calibration on the residual. In order to study this, we consider the mapping between the input uncalibrated data and the output residual data. We derive an analytical relationship between the input and output probability density functions which can be used to study the performance of calibration.

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“…Nevertheless, it is worth emphasizing that the forward-backward algorithm, and in general optimization algorithms (Combettes & Pesquet 2010;Komodakis & Pesquet 2015), can be used to introduce more sophisticated regularization terms. Moreover, it has been shown in the last years that using optimization and compressive sensing theories leads to very competitive results with respect to traditional radio interferometric methods such as CLEAN (Onose et al , 2017), yet comparisons have mostly been performed on smaller images, and the computational costs so far have not been competitive.…”

Section: Imaging Problemmentioning

confidence: 99%

“…by using an 1 regularization term. Note that this approach has subsequently been investigated in several works (Wiaux et al 2009b;Wenger et al 2010;Li et al 2011;McEwen & Wiaux 2011;Carrillo et al 2012;Dabbech et al 2015;Onose et al 2017). Furthermore, in the field of RI imaging, the resulting minimization problem involves large dimensional variables, especially for the big data problems encountered in the era of modern radio telescopes such as the Square Kilometer Array (SKA) 1 and LOw Frequency ARray (LOFAR) 2 .…”

Section: Introductionmentioning

confidence: 99%

Non-convex optimization for self-calibration of direction-dependent effects in radio interferometric imaging

Repetti

Birdi²,

Dabbech³

et al. 2017

Monthly Notices of the Royal Astronomical Society

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Radio interferometric imaging aims to estimate an unknown sky intensity image from degraded observations, acquired through an antenna array. In the theoretical case of a perfectly calibrated array, it has been shown that solving the corresponding imaging problem by iterative algorithms based on convex optimization and compressive sensing theory can be competitive with classical algorithms such as CLEAN. However, in practice, antenna-based gains are unknown and have to be calibrated. Future radio telescopes, such as the SKA, aim at improving imaging resolution and sensitivity by orders of magnitude. At this precision level, the direction-dependency of the gains must be accounted for, and radio interferometric imaging can be understood as a blind deconvolution problem. In this context, the underlying minimization problem is non-convex, and adapted techniques have to be designed. In this work, leveraging recent developments in non-convex optimization, we propose the first joint calibration and imaging method in radio interferometry, with proven convergence guarantees. Our approach, based on a block-coordinate forward-backward algorithm, jointly accounts for visibilities and suitable priors on both the image and the direction-dependent effects (DDEs). As demonstrated in recent works, sparsity remains the prior of choice for the image, while DDEs are modelled as smooth functions of the sky, i.e. spatially band-limited. Finally, we show through simulations the efficiency of our method, for the reconstruction of both images of point sources and complex extended sources. MATLAB code is available on GitHub.

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An accelerated splitting algorithm for radio-interferometric imaging: when natural and uniform weighting meet

Cited by 33 publications

References 42 publications

Superresolution Interferometric Imaging with Sparse Modeling Using Total Squared Variation: Application to Imaging the Black Hole Shadow

Superresolution Interferometric Imaging with Sparse Modeling Using Total Squared Variation: Application to Imaging the Black Hole Shadow

Performance Analysis of Distributed Radio Interferometric Calibration

Non-convex optimization for self-calibration of direction-dependent effects in radio interferometric imaging

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