Fourier Interpolation and Reconstruction Via Shannon-type Techniques

Lannes, A.; Anterrieu, Éric; Bouyoucef, Karim

doi:10.1080/09500349414552411

Cited by 35 publications

(24 citation statements)

References 8 publications

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“…Sect. 4.3 of Lannes et al 1994). Let us finally note that H o is a subspace of L 2 R (R 2 ); its inner product can be explicitly expressed in the form (cf.…”

Section: Formulation Of the Problems Of Fourier Synthesis In Astronomymentioning

confidence: 99%

“…The problem is then stated in terms of Fourier interpolation (Lannes et al 1987a and1994). This is why q is of the form q e +αq r with α = 1.…”

Section: How Wipe Regularizes Cleanmentioning

confidence: 99%

“…WIPE is a Fourier synthesis method recently developed in radio imaging and optical interferometry (Lannes et al 1994(Lannes et al , 1996. The name of Wipe is associated with that of CLEAN, a deconvolution method intensively used in astronomy (Högbom 1974;Schwarz 1978).…”

Section: Introductionmentioning

confidence: 99%

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CLEAN and WIPE

Lannes

Anterrieu

Maréchal

1997

Astron. Astrophys. Suppl. Ser.

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Abstract. Clean is a matching pursuit process which has two weak points: in situations of astrophysical interest, the "clean map" is not stable in the corresponding object representation space, and the "atoms" of this representation (translated versions of the "clean beam") are not well suited for reconstructing the boundaries of the structuring entities of the object at the related resolution level. As a result, Clean must be interrupted before the best possible fit is reached. How does Wipe wipe Clean clean? First, by introducing a global regularization principle based on the concept of resolution; and second, by conducting the matching pursuit process at the level of the high-resolution basis functions of the object space.

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“…Sect. 4.3 of Lannes et al 1994). Let us finally note that H o is a subspace of L 2 R (R 2 ); its inner product can be explicitly expressed in the form (cf.…”

Section: Formulation Of the Problems Of Fourier Synthesis In Astronomymentioning

confidence: 99%

“…The problem is then stated in terms of Fourier interpolation (Lannes et al 1987a and1994). This is why q is of the form q e +αq r with α = 1.…”

Section: How Wipe Regularizes Cleanmentioning

confidence: 99%

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CLEAN and WIPE

Lannes

Anterrieu

Maréchal

1997

Astron. Astrophys. Suppl. Ser.

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“…Note that extrapolation is considered as forbidden by some theoretical approaches. For example in the deterministic approach of Lannes et al (1994), a condition for the stability of the solution is that the data outside the sampled uv-region be set to zero.…”

Section: Parameterization Of the Imaging Processmentioning

confidence: 99%

Interferometric array design: Distributions of Fourier samples for imaging

Boone

2002

A&A

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Abstract. This paper is complementary to (Boone 2001) in which an optimization method was introduced. An analysis is developed in order to define the distributions of uv-plane samples that should be used as targets in the optimization of an array. The aim is to determine how should be distributed the uv-plane samples of a given interferometer array in order to allow imaging with the maximum of sensitivity at a given resolution and with a given level of side-lobes. A general analysis is developed taking into account the levels of interpolation and extrapolation that can be achieved in the uv-plane and the loss of sensitivity implied by an imperfect distribution. For a given number of antennas and a given antenna diameter two characteristic instrument sizes are introduced. They correspond to the largest size allowing single configuration observations and to the largest size allowing imaging with the full sensitivity of the instrument. The shape of the distribution of uv-plane samples minimizing the loss of sensitivity is derived for intermediate sizes and when a Gaussian beam is wanted. In conclusion it is shown that the shape of the distribution of samples and therefore of the array itself is entirely determined by a set of five parameters specifying the work (interpolation and extrapolation) that can be demanded to the imaging process, the level of side-lobes and the resolution at a given wavelength. It is also shown that new generation interferometers such as ALMA and ATA will be able to make clean images without deconvolution algorithms and with the full sensitivity of the instrument provided that the short spacings problem is solved.

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“…In 1990s, Lannes et al pointed out that the regularization could be used for reconstructing the MMW images of SAIR from the non-uniform visibility functions accurately, and the satisfying recovery effects were achieved [13,14]. Because regularization reconstructions of the SAIR with sparse arrays are an underdetermined problem, the accuracy of operation matrix G is very important for the reconstruction process.…”

Section: Introductionmentioning

confidence: 99%

Regularization Imaging Algorithm With Accurate G Matrix for Near-Field MMW Synthetic Aperture Imaging Radiometer

Chen¹,

Li²,

Wang³

et al. 2014

PIER B

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Abstract-In order to improve the reconstruction accuracy of near-field SAIR, a novel regularization imaging algorithm based on an accurate G matrix is proposed in this paper. Due to the fact that the regularization reconstruction is usually an underdetermined problem, inaccurate operation matrix G will lead to great reconstruction error in the imaging results, or even the normal imaging cannot be obtained. In this paper, we establish an accurate G matrix based on the accurate imaging model of near-field SAIR. Compared with the traditional G matrix with some unnecessary approximations, the proposed G matrix without approximation can improve the reconstruction accuracy effectively. For improving the accuracy of matrix G further, the corresponding parameters are corrected according to the RMSE between the imaging results of the regularization method and modified FFT method which is not sensitive to the parameters' change. The effectiveness of this calibration method has been tested by 1D simulation experiments. Moreover, the 2D simulation experiments demonstrate that the proposed accurate G matrix can improve the imaging accuracy of regularization method effectively. Finally, the 1D imaging experiment is performed to test the effectiveness of the proposed method for the actual synthetic aperture imaging further.

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Fourier Interpolation and Reconstruction Via Shannon-type Techniques

Cited by 35 publications

References 8 publications

CLEAN and WIPE

CLEAN and WIPE

Interferometric array design: Distributions of Fourier samples for imaging

Regularization Imaging Algorithm With Accurate G Matrix for Near-Field MMW Synthetic Aperture Imaging Radiometer

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