Wideband super-resolution imaging in Radio Interferometry via low rankness and joint average sparsity models (HyperSARA)

Abdulaziz, Abdullah; Dabbech, Arwa; Wiaux, Yves

doi:10.1093/mnras/stz2117

Cited by 18 publications

(44 citation statements)

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“…Another approach to deconvolution has leveraged convex optimization theory, and in particular, the relatively new field of compressive sensing (Candès et al 2006). Originally formulated as the SARA (sparsity averaging) reconstruction algorithm (Carrillo et al 2012), this has produced approaches such as PU-RIFY (Carrillo et al 2014) and HyperSARA (Abdulaziz et al 2019). These methods have demonstrated good performance on extended emission, and in particular, on the data we use for this study (Dabbech et al 2018).…”

Section: Introductionmentioning

confidence: 99%

Comparison of classical and Bayesian imaging in radio interferometry

Arras

Bester

Perley

et al. 2021

A&A

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CLEAN, the commonly employed imaging algorithm in radio interferometry, suffers from a number of shortcomings: In its basic version, it does not have the concept of diffuse flux, and the common practice of convolving the CLEAN components with the CLEAN beam erases the potential for super-resolution; it does not output uncertainty information; it produces images with unphysical negative flux regions; and its results are highly dependent on the so-called weighting scheme as well as on any human choice of CLEAN masks for guiding the imaging. Here, we present the Bayesian imaging algorithm resolve , which solves the above problems and naturally leads to super-resolution. We take a VLA observation of Cygnus A at four different frequencies and image it with single-scale CLEAN, multi-scale CLEAN, and resolve. Alongside the sky brightness distribution, resolve estimates a baseline-dependent correction function for the noise budget, the Bayesian equivalent of a weighting scheme. We report noise correction factors between 0.4 and 429. The enhancements achieved by resolve come at the cost of higher computational effort.

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Section: Introductionmentioning

confidence: 99%

Comparison of classical and Bayesian imaging in radio interferometry

Arras

Bester

Perley

et al. 2021

A&A

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“…RML methods have had recent success in the radio interferometry community in their use for reconstructing the first image of a black hole, M87* (Event Horizon Telescope Collaboration, et al 2019). Since RML methods do not rely on the CLEAN assumption that the sky is composed of point-sources, they can achieve super-resolution (Abdulaziz et al 2019). However, they are very computationally expensive since they are iterative and model every measurement in the visibility domain.…”

Section: Prior Interferometric Imaging Techniquesmentioning

confidence: 99%

Deep Radio Interferometric Imaging with POLISH: DSA-2000 and weak lensing

Connor,

Bouman,

Ravi

et al. 2021

Preprint

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Radio interferometry allows astronomers to probe small spatial scales that are often inaccessible with single-dish instruments. However, recovering the radio sky from an interferometer is an ill-posed deconvolution problem that astronomers have worked on for half a century. More challenging still is achieving resolution below the array's diffraction limit, known as super-resolution imaging. To this end, we have developed a new learning-based approach for radio interferometric imaging, leveraging recent advances in the computer vision problems deconvolution and single-image super-resolution (SISR). We have developed and trained a high dynamic range residual neural network to learn the mapping between the dirty image and the true radio sky. We call this procedure POLISH, in contrast to the traditional CLEAN algorithm. The feed forward nature of learning-based approaches like POLISH is critical for analyzing data from the upcoming Deep Synoptic Array (DSA-2000). We show that POLISH achieves super-resolution, and we demonstrate its ability to deconvolve real observations from the Very Large Array (VLA). Super-resolution on DSA-2000 will allow us to measure the shapes and orientations of several hundred million star forming radio galaxies (SFGs), making it a powerful cosmological weak lensing survey and probe of dark energy. We forecast its ability to constrain the lensing power spectrum, finding that it will be complementary to next-generation optical surveys such as Euclid.

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“…Definition 2.13. A set L E of functions from a set E to R is said to be a lattice if, for every (h (1) , h (2) ) ∈ L 2 E , min{h (1) , h (2) } and max{h (1) , h (2)…”

Section: Stationary Maximally Monotone Operatorsmentioning

confidence: 99%

“…First note that N F (V, R) is a lattice. Indeed, if h (1) : V → R and h (2) : V → R are 1-Lipschitzian, then min{h (1) , h (2) } and max{h (1) , h (2) } are 1-Lipschitzian. In addition, if h (1) and h (2) are elements in N F (V, R), then by applying sorting operations on the two outputs of these two networks, min{h (1) , h (2) } and max{h (1) , h (2) } are generated.…”

Section: Stationary Maximally Monotone Operatorsmentioning

confidence: 99%

“…For example, it can model some upper bound on some functional of the discrete gradient of the sought signal, this bound playing then a role equivalent to a regularization parameter [19]. Using an indicator function can also model standard constraints in some image restoration problems, where the image values are bounded [1,10]. By denoting by Γ 0 (H) the class of lower-semicontinuous convex functions from H to ]−∞, +∞] with a nonempty domain, let us now assume that both f and g belong to Γ 0 (H).…”

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Learning Maximally Monotone Operators for Image Recovery

Pesquet¹,

Repetti²,

Terris³

et al. 2020

Preprint

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We introduce a new paradigm for solving regularized variational problems. These are typically formulated to address ill-posed inverse problems encountered in signal and image processing. The objective function is traditionally defined by adding a regularization function to a data fit term, which is subsequently minimized by using iterative optimization algorithms. Recently, several works have proposed to replace the operator related to the regularization by a more sophisticated denoiser. These approaches, known as plug-and-play (PnP) methods, have shown excellent performance. Although it has been noticed that, under nonexpansiveness assumptions on the denoisers, the convergence of the resulting algorithm is guaranteed, little is known about characterizing the asymptotically delivered solution. In the current article, we propose to address this limitation. More specifically, instead of employing a functional regularization, we perform an operator regularization, where a maximally monotone operator (MMO) is learned in a supervised manner. This formulation is flexible as it allows the solution to be characterized through a broad range of variational inequalities, and it includes convex regularizations as special cases. From an algorithmic standpoint, the proposed approach consists in replacing the resolvent of the MMO by a neural network (NN). We provide a universal approximation theorem proving that nonexpansive NNs provide suitable models for the resolvent of a wide class of MMOs. The proposed approach thus provides a sound theoretical framework for analyzing the asymptotic behavior of first-order PnP algorithms. In addition, we propose a numerical strategy to train NNs corresponding to resolvents of MMOs. We apply our approach to image restoration problems and demonstrate its validity in terms of both convergence and quality.

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Wideband super-resolution imaging in Radio Interferometry via low rankness and joint average sparsity models (HyperSARA)

Cited by 18 publications

References 45 publications

Comparison of classical and Bayesian imaging in radio interferometry

Comparison of classical and Bayesian imaging in radio interferometry

Deep Radio Interferometric Imaging with POLISH: DSA-2000 and weak lensing

Learning Maximally Monotone Operators for Image Recovery

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