Stabilized Reconstruction in Signal and Image Processing

Lannes, A.; Roques, S.; Casanove, Marie‐José

doi:10.1080/09500348714550241

Cited by 52 publications

(28 citation statements)

References 38 publications

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“…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%

“…1.1. (The reader who is not familiar with the related basic notions is invited to consult Appendices 1 to 4 of Lannes et al 1987a). As Clean was first used as a Fourier synthesis technique, it was natural to compare the principles of Clean and WIPE in this context.…”

Section: Introductionmentioning

confidence: 99%

“…(WIPE can also be used as a deconvolution technique.) As a matter of fact, WIPE was devised, quite independently, on the grounds of well known properties in harmonic analysis and band-limited interpolation (Lannes et al 1987a). There also exists a probabilistic interpretation of this method (Maréchal & Lannes 1997).…”

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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“…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%

Section: Introductionmentioning

confidence: 99%

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CLEAN and WIPE

Lannes

Anterrieu

Maréchal

1997

Astron. Astrophys. Suppl. Ser.

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“…As was shown in [4] and [1], the convolution equation cannot be directly solved in the case of an ill-posed problem, since in this case the solution cannot exist. Even if the solution exists, it can be non-unique or unstable.…”

Section: Approximation Of the Visibility Function On The (U V)-planementioning

confidence: 97%

“…In 1983, the regularization methods developed by A. N. Tikhonov were first used for image retrieval in VLBI [3]. In 1987, the paper [4] devoted to mathematical justification of the problem of correct image synthesis of cosmic radio sources in VLBI was published. The approach to the image synthesis based on the regularization methods in radio interferometry was also considered in [5].…”

Section: Introductionmentioning

confidence: 99%

Regularization methods in radio interferometry

Лихачев

2007

Radiophys Quantum Electron

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UDC 52-17The problem of image retrieval in radio interferometry is a classical example of an ill-posed problem. In this paper, we consider a new approach to the radio-interferometric imaging based on regularization, which is computationally more flexible. A new type of a weighting function suitable for managing the interferometer antenna pattern is obtained. The regularization procedure was implemented in the VLBI-image processing software developed at the Astrospace Center of the Lebedev Physical Institute (ASC LPI). It is shown that the joint use of the developed regularization methods with traditional deconvolution algorithms such as CLEAN and self-calibration improve the quality of images of cosmic radio-emission sources.

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