Fourier interpolation and reconstruction via shannon-type techniques II. Technical developments and applications

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

doi:10.1080/09500349608232728

Cited by 24 publications

(26 citation statements)

References 1 publication

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“…As explicitly shown in Sect. 2 of Lannes et al (1996), the computation of the corresponding coefficients does not raise any particular difficulty.…”

Section: Formulation Of the Problems Of Fourier Synthesis In Astronomymentioning

confidence: 99%

“…, r n−1 form an orthogonal basis for E n (see Appendix 4 of Lannes et al 1987b). As established in Appendix 2 of Lannes et al (1996), the matrix of B n expressed in this basis is tridiagonal (this matrix is of course symmetric). Its diagonal and upper-diagonal elements are respectively given by the relationships…”

Section: Effective Object Representation Spacementioning

confidence: 99%

“…In most cases, the termination test of the basic algorithm is then satisfied (see Fig. 3 of Lannes et al 1996).…”

Section: Effective Object Representation Spacementioning

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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“…As explicitly shown in Sect. 2 of Lannes et al (1996), the computation of the corresponding coefficients does not raise any particular difficulty.…”

Section: Formulation Of the Problems Of Fourier Synthesis In Astronomymentioning

confidence: 99%

Section: Effective Object Representation Spacementioning

confidence: 99%

“…In most cases, the termination test of the basic algorithm is then satisfied (see Fig. 3 of Lannes et al 1996).…”

Section: Effective Object Representation Spacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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CLEAN and WIPE

Lannes

Anterrieu

Maréchal

1997

Astron. Astrophys. Suppl. Ser.

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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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Image Reconstruction

Lannes¹

1997

High Angular Resolution in Astrophysics

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Fourier interpolation and reconstruction via shannon-type techniques II. Technical developments and applications

Cited by 24 publications

References 1 publication

CLEAN and WIPE

CLEAN and WIPE

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

Image Reconstruction

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