A low-rank and joint-sparsity model for hyper-spectral radio-interferometric imaging

Abdulaziz, Abdullah; Dabbech, Arwa; Onose, Alexandru; Wiaux, Yves

doi:10.1109/eusipco.2016.7760276

Cited by 7 publications

(11 citation statements)

References 8 publications

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“…The work herein fits within the last class of methods and extends our recent works in Abdulaziz et al (2016Abdulaziz et al ( , 2017. Our proposed approach, dubbed HyperSARA, solves a sequence of weighted nuclear norm and 2,1 minimization problems, aiming to approximate low rankness and joint average sparsity in 0 sense.…”

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confidence: 53%

“…In the context of wideband RI image reconstruction, we adopt the linear mixture model originally proposed by (Golbabaee & Vandergheynst 2012). It assumes that the wideband sky is made of few sources, each having a distinct spectral signature (Abdulaziz et al 2016(Abdulaziz et al , 2017. The wideband model cube reads:…”

Section: Low Rankness and Joint Sparsity Sky Modelmentioning

confidence: 99%

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

Abdulaziz

Dabbech

Wiaux

2019

Monthly Notices of the Royal Astronomical Society

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We propose a new approach within the versatile framework of convex optimization to solve the radio-interferometric wideband imaging problem. Our approach, dubbed HyperSARA, solves a sequence of weighted nuclear norm and 2,1 minimization problems promoting low rankness and joint average sparsity of the wideband model cube. On the one hand, enforcing low rankness enhances the overall resolution of the reconstructed model cube by exploiting the correlation between the different channels. On the other hand, promoting joint average sparsity improves the overall sensitivity by rejecting artefacts present on the different channels. An adaptive Preconditioned Primal-Dual algorithm is adopted to solve the minimization problem. The algorithmic structure is highly scalable to large data sets and allows for imaging in the presence of unknown noise levels and calibration errors. We showcase the superior performance of the proposed approach, reflected in high-resolution images on simulations and real VLA observations with respect to single channel imaging and the clean-based wideband imaging algorithm in the wsclean software. Our matlab code is available online on github.

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confidence: 53%

Section: Low Rankness and Joint Sparsity Sky Modelmentioning

confidence: 99%

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

Abdulaziz

Dabbech

Wiaux

2019

Monthly Notices of the Royal Astronomical Society

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“…More precisely, each wavelength is associated to a compute node where the time consuming steps are computed in parallel which drastically reduces the execution time. This is in contrast with the work of [14] where the most expensive step requiring a singular value decomposition is not parallelized.…”

Section: Problem Descriptionmentioning

confidence: 99%

“…However, CLEAN and most of the algorithms that belong to the CLEAN family are not tailored for large-scale data. For this reason, a lot of effort has gone into designing scalable methods based on convex optimization [8]- [14]. These algorithms, which unrestrictedly operate in the image or visibility plane, adopt sparse models in an adequate domain, and This work was partly supported by the Agence Nationale pour la Recherche, France, (MAGELLAN project, ANR-14-CE23-0004-01).…”

Section: Introductionmentioning

confidence: 99%

Multi-frequency image reconstruction for radio-interferometry with self-tuned regularization parameters

Ammanouil¹,

Ferrari²,

Flamary³

et al. 2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-As the world's largest radio telescope, the Square Kilometer Array (SKA) will provide radio interferometric data with unprecedented detail. Image reconstruction algorithms for radio interferometry are challenged to scale well with TeraByte image sizes never seen before. In this work, we investigate one such 3D image reconstruction algorithm known as MUFFIN (MUlti-Frequency image reconstruction For radio INterferometry). In particular, we focus on the challenging task of automatically finding the optimal regularization parameter values. In practice, finding the regularization parameters using classical grid search is computationally intensive and nontrivial due to the lack of groundtruth. We adopt a greedy strategy where, at each iteration, the optimal parameters are found by minimizing the predicted Stein unbiased risk estimate (PSURE). The proposed self-tuned version of MUFFIN involves parallel and computationally efficient steps, and scales well with largescale data. Finally, numerical results on a 3D image are presented to showcase the performance of the proposed approach.

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“…In the monochromatic case, we have considered promoting sparsity prior with a, possibly weighted, ℓ 1 regularization term (Section 3.4). In the context of hyperspectral imaging, joint sparsity gives an additional degree of possible regularization, in the spectral dimension, that should be leveraged to improve the overall image reconstruction quality compared to reconstructing each channel separately (Soulez et al 2011;Thiébaut et al 2013;Abdulaziz et al 2016). Mathematically, joint sparsity is defined for a set of sparse signals such that the non-zero entries of each signal are located at the same spatial position.…”

Section: Realistic U − V Coveragementioning

confidence: 99%

A regularized tri-linear approach for optical interferometric imaging

Birdi¹,

Repetti²,

Wiaux³

2017

Monthly Notices of the Royal Astronomical Society

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In the context of optical interferometry, only undersampled power spectrum and bispectrum data are accessible. It poses an ill-posed inverse problem for image recovery. Recently, a trilinear model was proposed for monochromatic imaging, leading to an alternated minimization problem. In that work, only a positivity constraint was considered, and the problem was solved by an approximated Gauss-Seidel method. In this paper, we propose to improve the approach on three fundamental aspects. First, we define the estimated image as a solution of a regularized minimization problem, promoting sparsity in a fixed dictionary using either an ℓ 1 or a (re)weighted-ℓ 1 regularization term. Secondly, we solve the resultant non-convex minimization problem using a block-coordinate forward-backward algorithm. This algorithm is able to deal both with smooth and non-smooth functions, and benefits from convergence guarantees even in a non-convex context. Finally, we generalize our model and algorithm to the hyperspectral case, promoting a joint sparsity prior through an ℓ 2,1 regularization term. We present simulation results, both for monochromatic and hyperspectral cases, to validate the proposed approach.

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A low-rank and joint-sparsity model for hyper-spectral radio-interferometric imaging

Cited by 7 publications

References 8 publications

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

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

Multi-frequency image reconstruction for radio-interferometry with self-tuned regularization parameters

A regularized tri-linear approach for optical interferometric imaging

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