Data driven model based least squares image reconstruction for radio astronomy

Wijnholds, Stefan J.; Veen, Alle-Jan van der

doi:10.1109/icassp.2011.5947043

Cited by 4 publications

(9 citation statements)

References 9 publications

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“…One would naturally want to estimate x 2 from the dirty image. This is supported by recent work showing that x can be bounded by the dirty image (Wijnholds & van der Veen 2011;Sardarabadi et al 2016). …”

Section: Further Reduction By Thresholdingsupporting

confidence: 60%

A Fourier dimensionality reduction model for big data interferometric imaging

Kartik

Carrillo

Thiran

et al. 2017

Monthly Notices of the Royal Astronomical Society

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Data dimensionality reduction in radio interferometry can provide savings of computational resources for image reconstruction through reduced memory footprints and lighter computations per iteration, which is important for the scalability of imaging methods to the big data setting of the next-generation telescopes. This article sheds new light on dimensionality reduction from the perspective of the compressed sensing theory and studies its interplay with imaging algorithms designed in the context of convex optimization. We propose a post-gridding linear data embedding to the space spanned by the left singular vectors of the measurement operator, providing a dimensionality reduction below image size. This embedding preserves the null space of the measurement operator and hence its sampling properties are also preserved in light of the compressed sensing theory. We show that this can be approximated by first computing the dirty image and then applying a weighted subsampled discrete Fourier transform to obtain the final reduced data vector. This Fourier dimensionality reduction model ensures a fast implementation of the full measurement operator, essential for any iterative image reconstruction method. The proposed reduction also preserves the i.i.d. Gaussian properties of the original measurement noise. For convex optimization-based imaging algorithms, this is key to justify the use of the standard 2 -norm as the data fidelity term. Our simulations confirm that this dimensionality reduction approach can be leveraged by convex optimization algorithms with no loss in imaging quality relative to reconstructing the image from the complete visibility data set. Reconstruction results in simulation settings with no direction dependent effects or calibration errors show promising performance of the proposed dimensionality reduction. Further tests on real data are planned as an extension of the current work. matlab code implementing the proposed reduction method is available on GitHub.

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Section: Further Reduction By Thresholdingsupporting

confidence: 60%

A Fourier dimensionality reduction model for big data interferometric imaging

Kartik

Carrillo

Thiran

et al. 2017

Monthly Notices of the Royal Astronomical Society

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“…However as the complexity of the telescopes is increasing, parametric methods and sparse reconstruction techniques are becoming more popular [2], [3]. As we will show here, with the correct formulation, finding the solution to a parametric method could lead to an active-set algorithm that is strongly related to sequential source removing techniques and hence benefit from both approaches.…”

Section: Introductionmentioning

confidence: 93%

“…It is then straightforward to find the Hessian which is equal to H as defined in (2). Now that the gradient and the Hessian are found we can use them to find the constrained solution for the LS cost function.…”

Section: A Ls and Cleanmentioning

confidence: 99%

Constrained imaging for radio astronomy

Sardarabadi

Veen

2013

2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)

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Abstract-We show that the imaging problem for radio astronomy is not only bounded below (the image is non-negative), but there is also an upper bound. We show that the tightest upper bound is the MVDR dirty image. We propose using active-set methods to solve the imaging problem and show that this algorithm is strongly related to sequential source removal techniques like the CLEAN. Also recent studies show the relation between non-negativity and sparsity which means that the proposed optimization also benefits from sparsity in an automatic way.

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“…To formulate the problem, we follow the notations as proposed in [2] and [5]. In these notations, p.q T ,p.q H , p.q˚,˝and b denote transpose, the Hermitian transpose, complex conjugate, Khatri-Rao product and the Kronecker product, respectively.…”

Section: Data Modelmentioning

confidence: 99%

“…In practice, we use the modified weighting method described in [8,5] to remove the effect of the noise source from the data.…”

Section: Problem Statementmentioning

confidence: 99%

Radioastronomical image reconstruction with regularized least squares

Naghibzadeh

Sardarabadi

Veen

2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Image formation using the data from an array of sensors is a familiar problem in many fields such as radio astronomy, biomedical and geodetic imaging. The problem can be formulated as a least squares (LS) estimation problem and becomes ill-posed at high resolutions, i.e. large number of image pixels. In this paper we propose two regularization methods, one based on weighted truncation of the eigenvalue decomposition of the image deconvolution matrix and the other based on the prior knowledge of the "dirty image" using the available data. The methods are evaluated by simulations as well as actual data from a phased-array radio telescope in the Netherlands, the Low Frequency Array Radio Telescope (LOFAR).

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Data driven model based least squares image reconstruction for radio astronomy

Cited by 4 publications

References 9 publications

A Fourier dimensionality reduction model for big data interferometric imaging

A Fourier dimensionality reduction model for big data interferometric imaging

Constrained imaging for radio astronomy

Radioastronomical image reconstruction with regularized least squares

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