Optimal arrays for compressed sensing in snapshot-mode radio interferometry

Fannjiang, Clara

doi:10.1051/0004-6361/201321079

Cited by 6 publications

(4 citation statements)

References 27 publications

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“…On the other hand, the disadvantages of these sequences include (i) the absence of known CS recovery guarantees and (ii) a logistically challenging implementation of these schemes in the field due to off-grid locations of sources (or receivers). Furthermore, the numerical studies on CS reconstruction with the Hammersley points demonstrate discouraging results [38] and, finally, low-discrepancy sequences may require additional transformation to reduce aliasing [39].…”

Section: Overview Of Sampling Methodsmentioning

confidence: 99%

Achieving Robust Compressive Sensing Seismic Acquisition with a Two-Step Sampling Approach

Titova,

Wakin,

Tura

2023

Sensors

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The compressive sensing (CS) framework offers a cost-effective alternative to dense alias-free sampling. Designing seismic layouts based on the CS technique imposes the use of specific sampling patterns in addition to the logistical and geophysical requirements. We propose a two-step design process for generating CS-based schemes suitable for seismic applications. During the first step, uniform random sampling is used to generate a random scheme, which is supported theoretically by the restricted isometry property. Following that, designated samples are added to the random scheme to control the maximum distance between adjacent sources (or receivers). The null space property theoretically justifies the additional samples of the second step. Our sampling method generates sampling patterns with a CS theoretical background, controlled distance between adjacent samples, and a flexible number of active and omitted samples. The robustness of two-step sampling schemes for reallocated samples is investigated and CS reconstruction tests are performed. In addition, using this approach, a CS-based 3D seismic survey is designed, and the distributions of traces in fold maps and rose diagrams are analyzed. It is shown that the two-step scheme is suitable for CS-based seismic surveys and field applications.

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Section: Overview Of Sampling Methodsmentioning

confidence: 99%

Achieving Robust Compressive Sensing Seismic Acquisition with a Two-Step Sampling Approach

Titova,

Wakin,

Tura

2023

Sensors

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“…Indeed, there is a close relationship between CS principles and the aperture-synthesis image reconstruction problem, which was first addressed in Wiaux et al (2009a), Wenger et al (2010), Li et al (2011b) and Carrillo et al (2012). Wide-field observations were subsequently studied in McEwen & Wiaux (2011), and different antenna configurations (Fannjiang 2013) and non-coplanar effects (Wiaux et al 2009a,b;Wolz et al 2013) were analysed in a compressedsensing framework. Aperture synthesis presents the three main ingredients that are fundamental in CS: From the CS perspective, the best way to reconstruct an image X from its visibilities is to use sparse recovery by solving the following optimization problem:…”

Section: Compressed Sensing and Sparse Recoverymentioning

confidence: 99%

“…Several minimization methods have been used for aperture synthesis, the FISTA method (fast iterative shrinkagethresholding algorithm in Beck & Teboulle (2009) Wenger et al (2010), Hardy (2013) and Wenger et al (2013), the OMP (orthogonal matching pursuit) (G. Davis et al 1997) in Fannjiang (2013), Douglas-Rachford splitting in Wiaux et al (2009b), Wiaux (2011) andCarrillo et al (2012) or the SDMM (simultaneous-direction method of multipliers in Combettes &Pesquet (2011) andCarrillo et al (2014). In our experiments, we investigated mainly two algorithms, FISTA, and a recent algorithm proposed by Vũ (2013), which works in the analysis framework.…”

Section: Algorithmmentioning

confidence: 99%

LOFAR sparse image reconstruction

Garsden¹,

Girard²,

Starck³

et al. 2015

A&A

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Context. The LOFAR (LOw Frequency ARray) radio telescope is a giant digital phased array interferometer with multiple antennas distributed in Europe. It provides discrete sets of Fourier components of the sky brightness. Recovering the original brightness distribution with aperture synthesis forms an inverse problem that can be solved by various deconvolution and minimization methods. Aims. Recent papers have established a clear link between the discrete nature of radio interferometry measurement and the "compressed sensing" (CS) theory, which supports sparse reconstruction methods to form an image from the measured visibilities. Empowered by proximal theory, CS offers a sound framework for efficient global minimization and sparse data representation using fast algorithms. Combined with instrumental direction-dependent effects (DDE) in the scope of a real instrument, we developed and validated a new method based on this framework. Methods. We implemented a sparse reconstruction method in the standard LOFAR imaging tool and compared the photometric and resolution performance of this new imager with that of CLEAN-based methods (CLEAN and MS-CLEAN) with simulated and real LOFAR data. Results. We show that i) sparse reconstruction performs as well as CLEAN in recovering the flux of point sources, ii) performs much better on extended objects (the root mean square error is reduced by a factor of up to 10), and iii) provides a solution with an effective angular resolution 2-3 times better than the CLEAN images. Conclusions. Sparse recovery gives a correct photometry on high dynamic and wide-field images and improved realistic structures of extended sources (of simulated and real LOFAR datasets). This sparse reconstruction method is compatible with modern interferometric imagers that handle DDE corrections (A-and W-projections) required for current and future instruments such as LOFAR and SKA.

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“…This sparsity can be used on purpose in the design of an array (e.g. [58]). Instruments such as the SKA will provide a tremendous amount of redundant data that are difficult to calibrate.…”

Section: Conclusion and Future Developmentsmentioning

confidence: 99%

Sparse representations and convex optimization as tools for LOFAR radio interferometric imaging

et al. 2015

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Compressed sensing theory is slowly making its way to solve more and more astronomical inverse problems. We address here the application of sparse representations, convex optimization and proximal theory to radio interferometric imaging. First, we expose the theory behind interferometric imaging, sparse representations and convex optimization, and second, we illustrate their application with numerical tests with SASIR, an implementation of the FISTA, a ForwardBackward splitting algorithm hosted in a LOFAR imager. Various tests have been conducted in Garsden et al., 2015. The main results are: i) an improved angular resolution (super resolution of a factor ≈ 2) with point sources as compared to CLEAN on the same data, ii) correct photometry measurements on a field of point sources at high dynamic range and iii) the imaging of extended sources with improved fidelity. SASIR provides better reconstructions (five time less residuals) of the extended emission as compared to CLEAN. With the advent of large radiotelescopes, there is scope for improving classical imaging methods with convex optimization methods combined with sparse representations.

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Optimal arrays for compressed sensing in snapshot-mode radio interferometry

Cited by 6 publications

References 27 publications

Achieving Robust Compressive Sensing Seismic Acquisition with a Two-Step Sampling Approach

Achieving Robust Compressive Sensing Seismic Acquisition with a Two-Step Sampling Approach

LOFAR sparse image reconstruction

Sparse representations and convex optimization as tools for LOFAR radio interferometric imaging

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