Spread spectrum for imaging techniques in radio interferometry

Wiaux, Yves; Puy, Gilles; Boursier, Yannick; Vandergheynst, Pierre

doi:10.1111/j.1365-2966.2009.15519.x

Cited by 61 publications

(117 citation statements)

References 24 publications

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“…For example, chirp sequences were applied to radio interferometry in [31], where the sensing matrix was constructed in a different way, namely, it was the product of a rectangular binary matrix M, Fourier matrix F, diagonal matrix C implementing chirp modulation and diagonal matrix D implementing the primary beam. The coherence was analyzed when Ψ is formed by Gaussian waveforms.…”

Section: Connections With Existing Workmentioning

confidence: 99%

Convolutional Compressed Sensing Using Deterministic Sequences

Liu

Ling

2013

IEEE Trans. Signal Process.

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Abstract-In this paper, a new class of circulant matrices built from deterministic sequences is proposed for convolutionbased compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the discrete Fourier transform of a deterministic sequence with good autocorrelation. Both uniform recovery and non-uniform recovery of sparse signals are investigated, based on the coherence parameter of the proposed sensing matrices. Many examples of the sequences are investigated, particularly the Frank-ZadoffChu (FZC) sequence, the m-sequence and the Golay sequence. A salient feature of the proposed sensing matrices is that they can not only handle sparse signals in the time domain, but also those in the frequency and/or or discrete-cosine transform (DCT) domain.

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Section: Connections With Existing Workmentioning

confidence: 99%

Convolutional Compressed Sensing Using Deterministic Sequences

Liu

Ling

2013

IEEE Trans. Signal Process.

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“…This is a convex relaxation of Equation (1) and can be transformed into the Lagrange form: (Honma et al 2014;Akiyama et al 2016;Ikeda et al 2016) and found that LASSO can potentially reconstruct structure on scales ∼4 times finer than D max l (Honma et al 2014). Techniques of compressed sensing are beginning to be used in other fields of radio interferometry 15 after pioneering work by Wiaux et al (2009a) and Wiaux et al (2009b) (see Garsden et al 2015, and references therein).…”

Section: Introductionmentioning

confidence: 99%

Superresolution Full-polarimetric Imaging for Radio Interferometry with Sparse Modeling

Akiyama

Ikeda

Pleau

et al. 2017

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We propose a new technique for radio interferometry to obtain superresolution full-polarization images in all four Stokes parameters using sparse modeling. The proposed technique reconstructs the image in each Stokes parameter from the corresponding full-complex Stokes visibilities by utilizing two regularization functions: the ℓ 1 norm and the total variation (TV) of the brightness distribution. As an application of this technique, we present simulated linear polarization observations of two physically motivated models of M87 with the Event Horizon Telescope. We confirm that ℓ 1 +TV regularization can achieve an optimal resolution of ∼25%-30% of the diffraction limit D max l , which is the nominal spatial resolution of a radio interferometer for both the total intensity (i.e., Stokes I) and linear polarizations (i.e., Stokes Q and U). This optimal resolution is better than that obtained from the widely used Cotton-Schwab CLEAN algorithm or from using ℓ 1 or TV regularizations alone. Furthermore, we find that ℓ 1 +TV regularization can achieve much better image fidelity in linear polarization than other techniques over a wide range of spatial scales, not only in the superresolution regime, but also on scales larger than the diffraction limit. Our results clearly demonstrate that sparse reconstruction is a useful choice for high-fidelity full-polarimetric interferometric imaging.

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“…In their paper, they did not consider a sparse representation that is appropriate for extended sources in the sky. In a subsequent paper, Wiaux and other authors propose a new spread spectrum technique for radio interferometry (Wiaux et al 2009b) by using the non-negligible and constant component of the antenna separation in the pointing direction. Moreover, in their second paper, they assumed that any kind of astrophysical structure consist of Gaussian waveforms of equal size and similar standard deviation.…”

Section: Introductionmentioning

confidence: 99%

The application of compressive sampling to radio astronomy

Cornwell

Hoog

2011

A&A

103

114

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Compressive sampling is a new paradigm for sampling, based on sparseness of signals or signal representations. It is much less restrictive than Nyquist-Shannon sampling theory and thus explains and systematises the widespread experience that methods such as the Högbom CLEAN can violate the Nyquist-Shannon sampling requirements. In this paper, a CS-based deconvolution method for extended sources is introduced. This method can reconstruct both point sources and extended sources (using the isotropic undecimated wavelet transform as a basis function for the reconstruction step). We compare this CS-based deconvolution method with two CLEANbased deconvolution methods: the Högbom CLEAN and the multiscale CLEAN. This new method shows the best performance in deconvolving extended sources for both uniform and natural weighting of the sampled visibilities. Both visual and numerical results of the comparison are provided.

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Spread spectrum for imaging techniques in radio interferometry

Cited by 61 publications

References 24 publications

Convolutional Compressed Sensing Using Deterministic Sequences

Convolutional Compressed Sensing Using Deterministic Sequences

Superresolution Full-polarimetric Imaging for Radio Interferometry with Sparse Modeling

The application of compressive sampling to radio astronomy

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